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Performance Evaluation and Troubleshooting of

1. 44 Fig II 13 Evolution versus time of the test signal sess 45 Fig II 14 Instantaneous frequency trajectory gained when optimal values of STFT parameters are used Measured solid line and nominal dotted line trajectories Ea E opi eeut pta de tesa tu de bdede decet 47 Fig II 15 Instantaneous power trajectory gained when optimal values of STFT parameters are used Measured solid line and nominal dotted line trae ctories are COMM ARC da oett ien es oe ces 47 Fig II 16 Evolution versus time of the signal acquired from the bug transmitter 48 Fig II 17 Instantaneous frequency trajectory obtained through the use of CT of the signal at the output of the bug transmitter eeeeessssseeeeeeeeeel 49 Fig II 18 Instantaneous power trajectory obtained through the use of CT of the signal at the output or the DUG 49 Fig II 19 Evolution versus time of the signal acquired from the walkie talkie 50 Ere IET Signaler e e PE breton etia teda 54 Fig III 2 I Q diagram for 16 QAM 5 54 List of Figures Tas IIS DO impatient rHodel eoo nS Moat QU iU I mn educat duae 55 Fig III 4 Ideal 64
2. 20 11 23 Proposed HUE DOO asc Dad Debes bed utbs dalaa eA eq 23 1 2 5 85565 2 1 27 1 2 EC Oe USO soene a e aa e ie inane a E 32 Thee CDEP Curve mea a 22 TEST odit ue pube dieto edi 32 IL3 2 Proposed Approac NC a eee 34 I3 3 Pee ets pen d Rondo eae 36 IA Transmitter transient measuremelll o eoo te peer portenta e aat ae eta uota otras uon 40 MATa IntroducbloDse scie conor Eb cont outs tb a Ouid 40 IL2 2 edo tee eSI oO Md oda da skates 4 ILAS Performance assess Mie busted pese nen pe paces Eee eene Do Peau 43 114 4 5T este leone S duo 45 50 CHAPTER III I Q Impairments Detection and Evaluation eeeeesssssssss 53 LBS Loin OCC BLU EL E 53 IIL 2 A measurement method based on 53 ON obo 53 III 2 2 Impairments affecting I Q
3. 55 II s Proposed 56 111 2 4 Performance a5 SOS SITIGTIE 55d eoru a DER RU eee 59 USE eode i A TS 62 11 3 A measurement method based on error vector 63 1H 5 1 s IntroqueoTis uoce ooa eins tee matita eee ua iiec tien in mos bxnl ecu se eei naui eue 63 15 2 11531 36 51 1151 2 64 MELo a 66 1II 3 4 Perrormance assessment erede bon be verbere a un 71 IL 5 5 cC OM CIS OU 75 1 4 I Q impairment detection and evaluation on OFDM transmitters 76 TEN TOC UCU OM RR o 76 Contents Id 2 s Ptobleti State VS I sco So reesei 77 on ERE Ite idm uS 80 HAA Performalce assessment scout si Sones ce n 83 WAS COMO US OM icc UU UT 85 CHAPTER IV COUCUSIODTSS 87 IS de E gt ERR TTE 89 IBS UM ated UU Tm 977
4. 73 Fig III 14 Symbol by symbol estimation of gain 1 4 84 66 75 Fig III 15 Basic OFDM modulation scheme sss T 1 0 diagram or am OR DIM Sina sais secto en eme Reda Rebate tete np ronde dedi sinus 78 Fig IIL 17 I Q diagram of an OFDM sub carrier QPSK cccccesessssssssessssesesessessseeeeeens 79 Fig III 18 I Q diagram of an OFDM sub carrier 16 QAM sss 80 Fig III 19 Measurement results for QPSK sub carrier modulation in the presence of gain imbalance and quadrature error a difference from imposed and measured amounts and b experimental standard deviation concerning gain imbalance measurements c difference from imposed and measured amounts and d experimental standard deviation concerning quadrature error measurements All differences and experimental standard deviations are expressed in percentaee relative Te FINS titel eae 86 99 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 100 List of Tables LIST OF TABLES Table II 1 Comparison of measurement results obtained in the experiments on uplink WCDMA SS oil Sic cham 29 Table II 2 Comparison of measurement results obtained in the experiments on downlink VC PE UII I tan S 30 Table II 3 Comparison of channel
5. 10 Pio L4 DO SECtiOm ACO ital ians oi 13 Fig I 5 Effect of the presence of gain imbalance for a 64 QAM signal constellation with unitary maximum component value eoe aida RE 13 Fig I 6 Effect of the presence of quadrature error for a 64 QAM signal constellation with unitary maximum I Q component value esee 14 Fig I 7 Effect of the presence of positive offsets on the in phase and quadrature components for a 64 QAM signal constellation with unitary maximum I Q G0 401 610 ree PE Ce 14 Fig I 8 Incorrect symbol rate and evolution versus 0 15 Fig I 9 Evolution versus time of EVM in the presence of wrong filter coefficients and or ICOPIECCUSVIDOONWITIB aie tcc tetd Siete hnenc tdt tma em det rata 16 Fig I 10 Magnitude spectrum of EV in the presence of an interfering tone inside signal AACN EP PDIROETNEERR 17 Fig II 1 Flow chart diagram of the PSD 5 1 6 26 FIL Measurement SUA UO a eol du ed nace sede ate dando 28 97 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Fig II 3 PSD of a WCDMA signal estimated through the proposed approach 30 Fig II 4 PSD of Rai International 4 s
6. LEM DEP asd 101 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Introduction INTRODUCTION Digital communications have been experiencing a significant development since the last decade of last century both in terms of users and provided services The increasing demand for ubiquitous wireless communication and the willingness to enhance the video and audio broadcasting offer are probably the main reasons for such a rapid and extended growth A milestone in this process 15 represented by GSM Global System for Mobile communications 1 whose ex ante standardization has been one of the key factors for its worldwide great and unprecedented success Following the example of GSM several new continental and world standards for wireless digital communication systems have been developed in the last years They range from mobile communication UMTS 2 CDMA2000 PHS etc to both local and wide area connectivity Bluetooth 3 802 11 A4 5 6 7 and WiMax 8 respectively up to digital video and audio broadcasting DAB 9 DVB 10 11 12 A direct consequence of such a sustained development is that R amp D Research and Development engineers and manufactures have been and still are involved in designing and developing components and systems characterized by higher and higher performance in terms of achievable transmission rate and spectral effectiveness Moreover to encourage customers
7. 428MSis E 0 000196 pz eias 0 00001 paid f l1 7TM5S s PS ins f 0 01 4MMSh E 0 001 p 2u NC aide 214MSis 1 e QE 1 i5 10 107MSis yl Fig II 9 Comparison between the CCDF provided by the VSA and those provided by a the time domain approach and 5 the time frequency approach when different values of the sampling frequency f and therefore of the ratio p are taken into account Details of low and high power levels are given in a1 a2 b1 b2 39 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters frequency equal to 214 MS s p 10 111 the solid line refers to a sampling frequency equal to 107 MS s p 5 and finally iv the bold line is the CCDF curve provided by the VSA The results show that the correspondence between the CCDF curve gained through the application of the proposed approaches and that provided by the VSA is greater than that assured by analogous attempts recently made 60 In particular as the magnified subfigures prove the point to point difference is particularly small for power levels in proximity to the mean value and is substantially independent from p With regard to higher power values lower values of p p 5 in Fig II 9 seem to provide better results It is worth noting that the y axis 15 logarithmically scaled and therefore the point to point difference that
8. 61 In particular the standard defines transmitter attack time in terms of power and frequency transients establishes its maximum duration and proposes a related measurement setup The standard measurement setup is sketched in Fig II 10 It requires the employment of several instruments such as an RF detector or a spectrum analyzer an FM Frequency Modulation 40 Chapter II Performance Evaluation apectrum analyzer FM modulation meter Fig II 10 Standard measurement setup Transmitter Power under test attenuator modulation meter and a DSO Some major manufacturers have recently proposed the use of VSA equipped with demodulation capability to measure transmitter transients with a single instrument and simultaneously display amplitude and frequency versus time 62 63 Such instruments however demodulate output signal to measure transmitter transient and therefore need some information on the transmitted signal such as carrier frequency and modulation type In the following a digital signal processing method based on TFRs 23 and optimal sampling strategies 58 15 proposed for measuring transmitter attack time The method which simultaneously measures both power and frequency transients requires no signal demodulation thus overcoming VSA limitation Moreover it simply processes a few thousand signal samples acquired by means of a common data acquisition system rather than involving the use of sev
9. 75 76 77 78 S Mann S Haykin The chirplet transform Physical considerations JEEE Trans On Signal Processing vol 41 pp 2745 2761 Nov 1993 L Angrisani M D Arco A Measurement Method Based on a Modified Version of the Chirplet Transform for Instantaneous Frequency Estimation IEEE Trans on Instr and Meas vol 51 No 4 pp 704 712 August 2002 A D Poularikas The transforms and applications handbook CRC Press 2000 L Angrisani R Colella Detection and Evaluation of I Q Impairments in RF Digital Transmitters IEE Proceedings Science Measurement and Technology Vol 151 No 1 January 2004 pp 39 45 J Hartigan Clustering Algorithms Wiley New York 1975 V Faber Clustering and the Continuous k Means Algorithm Los Alamos Science N 22 1994 pp 138 144 Digital cellular telecommunications system Phase 2 amp Phase 2 Base Station System BSS equipment specification Radio aspects ETSI EN 301 087 Ver 8 2 1 2000 Designing and testing WCDMA User Equipment Application Note 1356 Agilent Technologies Literature No 5980 1238E 2003 99 EDGE Wireless Networks Challenges 1 Maintainance and Testing Tektronix Literature No 2EW 17611 O 2004 W CDMA UMTS Wireless Networks Challenges in Maintainance and Testing 24 edition Tektronix Literature No 2EW 12789 O 2004 A Mashhour A Borjak A Method for Computing Error Vector Magnitude in GSM EDGE Systems Si
10. III 3 where the distance between the points i and j i lt j is the element dij Y i 1 N i 2 j i The sorted vector is passed to an algorithm named single linkage algorithm that merges the N points into M clusters N has to be large enough to grant that each symbol in the constellation occurs at least once In detail at the first step the N points are considered as clusters made up of a single point At the i th step the single linkage procedure finds the two nearest clusters and merges them so that N i clusters are left The algorithm stops at the N M th step when the N points are collected into M clusters C Choice of the representative points Representative points are chosen so as to minimize the average distance from all the points in the cluster It can be easily shown that this criterion leads to the choice of the points characterized by the coordinates 3 y r J j Y k 1 2 M III 5 Nm 57 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters where and are the coordinates of the N points belonging to the k th cluster D Impairment evaluation Each representative point Q is matched to its own ideal position y in the I Q diagram In particular representative and ideal points are both numbered following a top down left to right order and matched accordingly It is worth noting that the required matching cannot be
11. The scheme in Fig III 3 is generally adopted to model the presence of I Q impairments in a digital transmitter In particular it accounts for gain imbalance 5 which is defined as E max G G min G 00 B e where G and Gg are the gain respectively of the I and Q branch quadrature error which reveals an angle between the two quadrature carriers different from 772 voltage offsets on the two branches c and co Ynn 1 t IF Local Oscillator 7 2 q rad Fig III 3 I Q impairment model 55 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters A general expression for the IF signal y r t at the output of an I Q modulator affected by such impairments 15 given by yp f G c T Ypa t cos 2z firt Go co T Yobo sin Zz firt 11 2 where impairments are assumed not to vary in the observation interval The contributions of the considered impairments are evident from the analysis of Fig III 4 which refers to the constellation diagram of a 64 QAM signal In particular crosses represent the actual positions of symbols as the outcome of a modulator affected by impairments whereas dots are their ideal ones Fig III 4 shows that some symbols cross the boundaries of their own decision regions as a consequence of impairments 1 2 5 Proposed method A Signal demodulation To recognize the actual I Q constellation diagra
12. Amplitude V 0 2 0 0 001 0 002 0 003 0 004 0 005 0 006 0 007 0 008 0 009 0 01 Time 5 Fig II 19 Evolution versus time of the signal acquired from the walkie talkie Table II 7 Measurement results related to the walkie talkie 1 4 5 Conclusion A digital signal processing method based on linear TFRs has been proposed to measure wireless transmitter attack time The method simultaneously measures both power and 50 Chapter II Performance Evaluation frequency transients and requires neither signal demodulation nor costly special purpose instrumentation Moreover thanks to the use of band pass sampling strategies just a few thousand samples acquired by means of a common laboratory DSO are needed for the scope To single out the optimal values of TFR parameters proper signals have been digitally synthesized whose instantaneous power and frequency trajectories evolve in accordance to those reported in 61 Optimal parameter values have then been selected as those granting the minimum rmse with regard to nominal trajectories Experimental results have assessed the reliability and efficacy of the method in measuring instantaneous power and frequency trajectories Experienced values of rmse for optimized STFT and CT are equal respectively to 0 032 and 0 021 Moreover transmitter attack time measurements carried out on real wireless transmitters utilizing either one of the linear TFRs considered provide
13. Correction of 7 8 whereas BBC Prime signal 1s characterized by a central frequency equal to 11 131 GHz a symbol rate equal to 5 632 Msymbol s and a FEC of 3 4 The choice of such signals 1s imposed by the maximum resolution bandwidth of the spectrum analyzer Anritsu MS2687B After being received through the 1 790 m diameter parabolic antenna satellite signals are routed to the low noise downconverter which performs a low noise amplification and a downconversion from Ku band 10 7 12 75 GHz to L band 950 2150 MHz The L band signal is then given in input to the spectrum analyzer Anritsu MS2687B which operates in zero span mode to downconvert it to 66 MHz intermediate frequency The downconverted signal is digitized by the DSO at 200 MS s and a record of 32 768 acquired samples is retrieved Measurement algorithms are then applied to the acquired samples in order to evaluate channel power D Results Table and Table II 2 depict the results of measurements performed on respectively uplink and downlink WCDMA signals a typical PSD provided by the proposed method 1s shown in Fig II 3 Table II 3 gives the results of channel power measurements performed on RAI International 4 and BBC Prime DVB S signals All results are expressed in terms of average value u and experimental standard deviation o over 50 consecutive measurements Table II 1 Comparison of measurement results obtained in the experiments on uplink WCDMA sig
14. I I I I I I I I th x x Fig III 4 Ideal 64 QAM constellation with amplitude imbalance 20 1 quadrature error 27 64 and voltage offsets c 0 05 cg 0 075 Red crosses and blue dots represent nominal and actual symbol positions respectively I and Q components are normalized to their maximum value 56 Chapter III Impairments Detection and Evaluation symbols much greater than the constellation cardinality M 15 required The N symbols are then grouped into M clusters by means of a clustering procedure 68 69 and for each cluster a single representative point is chosen in order to prevent symbol spread from affecting impairment evaluation b Clustering procedure A clustering procedure involves dividing a set of points into separated groups or clusters where points in a cluster are more similar to one another than to points in other clusters The expression more similar in this case means closer by some measure of proximity As the outcome of a clustering procedure every point 1s assigned to some cluster and every cluster can be characterized by a single representative point The clustering procedure utilized 1s based on an agglomerative approach It calculates the pair wise distance between all the N points d i and stores them in a vector Y named similarity vector The N N 1 2 elements in the vector Y are then sorted according to Y d 1 2 4 1 3 d 1 N 4 2 3 d N 1 N
15. I O Impairments Detection and Evaluation The proposed method provides good results in terms of difference between imposed and measured impairment amounts A is in fact mostly inferior to 6 except for some rare cases enlisted in the table in which the simultaneous presence of all impairments can result in a slightly higher value The method performs well also with respect to repeatability the experienced values of o are in fact mostly inferior to 6 7 Measurement of voltage offset on the Q branch cg is characterized by the lowest values of 4 and o This 1s probably due to the fact that the other impairments do not appear in relation III 57 utilized to estimate cg and therefore do not have any influence on its estimation The performance of the method seems to be independent of sub carrier modulation pattern Maximum values of 4 and o experienced for the three considered patterns concur Fig III 19 allows a more detailed analysis of the performance of the method It refers to experiments conducted in the presence of gain imbalance and quadrature error for QPSK sub carrier modulation pattern In particular Fig IlII 19a and Fig IIL19b show the values respectively of A and o experienced with regard to gain imbalance measurements for several impairment amount combinations Similarly Fig III 19c and Fig III 19d refer to quadrature error measurements and account for respectively A and o achieved with the same c
16. Transmitter Testing and 5 Ne Die a eee dor cre 5 ee s ide ho OH ne eT eee Z 1 2 Te Insbandanedsuremebls 22565 ee a e a ida EH FU UE 8 I 2 2 Out of band measurements nnn 11 1 5 5 Transmitter troublesSbOOLUfig so e tetti RS veo tte 1 ease 12 1 5 2 DO dit palttide 12 2 N 15 I 3 4 Wrong filter coefficients and incorrect windowing eeeeeseeeeeeeee 15 I 5 5 5 JE Ber MOM ICCA TCS oU tots Luo US Die 16 Eo6aboscillator INSTA DINIOY cesar tarte aan nte e 16 7 5 Interte tito Ole etas D 16 1 378 DAC a 17 1 53 95 Burst shapin Impar ments neers 17 CHAPTER Periormance E va at On uen o Pro eet HERD EROS Ee Ee RE 19 VII Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters IIT e TRUEOGQUCLTOT S eio bete oasis dos etu rase ete Duo rao 19 11 2 POW ni eo na nds een Buen u sd uae ee 19 IL2 T S ne te eet eae oot dota 19 2 2 Theory underlying the proposed
17. measurement personalities 4 a spectrum analyzer Anritsu MS2687B 51 9 kHz 30 GHz input frequency range up to 20 MHz resolution bandwidth acting as downconverter at 66 MHz intermediate frequency 5 a vector signal analyzer Agilent Technologies E4406A 52 7 MHz 4 0 GHz input frequency range 6 a performance spectrum analyzer Agilent Technologies E4440A 53 3 Hz 26 5 GHz input frequency range 7 an RF power meter Agilent Technologies E4416A 54 100 kHz 6 0 GHz input frequency range 300 kHz 1 5 MHz and 5 MHz selectable bandwidth and 8 the signal source which is either a digital RF signal generator Agilent Technologies 44328 55 Zi Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Signal source H W CDMA EE SES bU eel HE signals AES 8 Signal generato l TE 3 Processing and gt 1 ownconverter Me i control unit LOW NOISE PAM S DOWNCONV 66 MHz IF signals d Ni Measurement section I E dz a Pee LE IEEE 488 INTERFACE BUS L pe Performance spectrum analyzer Spectrum analyzer Power meter Data acquisition system Vector signal analyzer AS Fig II 2 Measurement station 250 kHz 3 0 GHz output frequency range I Q analog inputs with arbitrary waveform generation AWG capability 14 bit vertical resolution 1 Megasample mem
18. provided by the VSA while Fig III 14 reports the symbol by symbol estimation of gain imbalance The measurement result is the mean value of the symbol by symbol estimations Table III 4 and Table III 5 summarize the entire set of results for respectively WCDMA and DVB signals They are presented in terms of difference from imposed values A and experimental standard deviation o both expressed in percentage relative terms In particular all measurement results fall within the lower and upper limits summarized in the tables From the analysis of the experimental results the following considerations can be drawn Values of 4 and o below 5 have been experienced in most cases The lower the amount of the imposed impairment the higher the related values of A 9o and o 96 A comparison with the results achieved on WCDMA signals through the application of the method proposed in 67 shows that the values of 4 and o respectively included in the ranges 0 53 10 and 0 9 9 0 concur with those experienced in 67 which are included in 0 50 10 and 0 51 9 0 Table III 4 Measurement results for WCDMA signals min max min Max e fas sme Table III 5 Measurement results for DVB signals min max min max s eee me 74 Chapter III Impairments Detection and Evaluation A comparison with the results achieved on DVB signals through the application of the method proposed
19. to be preliminarily applied A linear TFR should in particular be chosen in order to avoid cross terms peculiar to quadratic ones 23 Two linear TFRs have been considered and related results compared the STFT 23 and a modified version of the chirplet transform CT 64 65 The discrete short time Fourier transform of the digitized signal s k STFT is evaluated according to II 29 The modified version of CT is calculated in accordance to 65 as m N jag CT m n g k n ke 1 31 k 0 where g k is a modulated Gaussian window given by 11 32 in which a b and c are respectively the scaling bending and chirping factor whereas T is the sample period characterizing the acquired signal As with regard to STFT modified CT in 1 31 is computed via an FFT based algorithm and results are taken in modulus and squared in order to achieve the evolution versus time of the power spectral contents of the analyzed signal C Power and frequency transient measurement ETSI standard 61 defines transmitter attack time ta as the maximum between power and frequency transient durations defined respectively as a the time which elapses between the initiation of the transmitter on function and the moment when the transmitter output power has reached a level 1 dB below or 1 5 dB above the steady state power Pe and maintains a level within 1 5 dB 1 dB from P b the time which elapses between the initi
20. voltage values over one carrier period which represents the minimum averaging interval for gaining a non trivial instantaneous power value Thanks to the application of algorithm I presented in 58 the same number of samples p are acquired per each carrier period Then the N acquired samples are divided into groups of p and each point of the power trajectory P k 15 determined as the mean square value over p consecutive samples 1G nt k 1 p P k s 1 28 gt Time frequency approach The second approach is based on the application of a particular TFR the STFT Short Time Fourier Transform 23 The instantaneous power of the signal under analysis is in fact evaluated by applying the STFT which is defined for discrete time signals as STFT m n w k n s k e 2d 1 29 k 0 where w k is the window function and N is the number of samples on which STFT is performed k stands for the discrete time variable The signal s k is divided into a number of segments each of which weighted by the window function w k is treated separately in order to evaluate its spectral content Expression 1 29 is computed via an FFT based algorithm the results are then taken in modulus and squared in order to attain the so called spectrogram In the presence of discrete time signals the spectrogram 15 represented by means of a matrix row index is connected to frequency while column index repr
21. with other proposals and results provided by instrumentation available on the market have shown the effectiveness and accuracy of the methods Possible future developments concern new methods for power measurement in the presence of in channel interference based on advanced signal processing techniques such as cyclostationary analysis optimization and or extension of methods for I Q impairment measurement to new communication standards and the implementation of some of the proposed algorithms on suitable digital signal processors or as add on software modules on DSOs 87 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 88 References p 1 2 3 4 5 6 7 REFERENCES Digital cellular telecommunications system Phase 2 Radio transmission and reception ETSI Tech Spec 100 910 Ver 8 19 0 2005 3rd Generation Partnership Project Technical Specification Group Radio Access Networks Base Station BS conformance testing FDD Release 6 3GPP TS 25 141 V 6 11 0 Sept 2005 Specification of the Bluetooth System Bluetooth SIG Core Package v 1 2 2003 IEEE Standard 802 11 Information Technology Telecommunication and information exchange between systems Local and Metropolitan area networks Specific Requirements Part 11 Wireless LAN Medium Access Control MAC and Physical Layer PHY specifications Reaffirmed 2003 IEEE Stand
22. QAM constellation with amplitude imbalance 4 0 1 quadrature error 6 7 64 and voltage offsets cj7 0 05 cg 0 075 Red crosses and blue dots represent nominal and actual symbol positions respectively I and Q components are normalized to their maximum Value iu ntc eio este e bes Se dibus 56 Fio III Measurement ette PRO ede nan A DI i eie t m d NA IN iei ut 60 Fig III 6 Difference A in percentage relative terms between measured and imposed a amplitude imbalance Azf and b quadrature error experimental standard deviation 0 in percentage relative terms related to c amplitude imbalance and dr Pei tte ot umm Sante Rott an So ee ien 61 Fig III 7 Effect of joint gain imbalance and quadrature error on the constellation diagram of a QPSK signal g and respectively equal to 0 1710 and 732 rad 65 Fig III 8 EV components due to a gain imbalance 0 46 67 Fig III 9 EV components due to a quadrature error equal to 77 16 rad 67 Fig III 10 EV components due to a voltage offset on component I 6 equal to 0 15 68 Fro HL TE Measurement Stan Ons T2 Fig I 12 I Q polar diagram of a DVB signal in the presence of gain imbalance 73 Fig IIIL 13 I and Q waveforms related to the signal in 1 2
23. UNIVERSITA DEGLI STUDI DI NAPOLI FEDERICO II POLO DELLE SCIENZE E DELLE TECNOLOGIE FACOLTA DI INGEGNERIA DIPARTIMENTO DI INGEGNERIA ELETTRICA Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Michele Vadursi TES D DOTTORATO DI RICERCA IN INGEGNERIA ELETTRICA XVIII CICLO Coordinatore Prof Giovanni Miano TUTOR Co TUTOR PROF Massimo D APUZZO PROF LEOPOLDO ANGRISANI UNIVERSITA NAPOLI FEDERICO II DEL UNIVERSITA DI NAPOLI FEDERICO II DIS DIPARTIMENTO DI INGEGNERIA ELETTRICA VIA CLAUDIO 21 80125 NAPOLI ITALIA Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters II Abstract ABSTRACT The research activity accounted for in this Ph D thesis belongs to the general field of electrical and electronic measurements The attention 1s focused in particular on performance evaluation and troubleshooting of radiofrequency digital communication transmitters a fundamental 1ssue in applied research and industrial production of modern communication systems Several measurements included in testing and troubleshooting procedures utilized by major manufacturers or included in international standards are taken into consideration The original contribution consists in the development of original measurement methods based on digital signal processing which result more reliable and or repeatable and or efficient than the publicized one
24. a M Morikura A New Vector Error Measurement Scheme for Transmit Modulation Accuracy of OFDM Systems Proc of IEEE Veh Tech Conf 2000 pp 1240 1244 S Rapuano G Truglia An improved image processing based method for disturbance classification in telecommunication networks IEEE Transactions on Instrumentation and Measurement Vol 54 No 5 Oct 2005 pp 2068 2074 R Van Nee R Prasad OFDM for Wireless Multimedia Communications Artech House Publishers 2000 S B Weinstein and P M Ebert Data Transmission by Frequency Division Multiplexing Using the Discrete Fourier Transform IEEE Trans Commun Techn vol COM 19 no 5 pp 628 634 Oct 1971 A R S Bahai B R Saltzeberg Multi Carrier Digital Communications Theory and Applications of OFDM Kluwer Academic Plenum Publishers New York 1999 Broadband Radio Access Networks BRAN HIPERLAN Type 2 Physical layer ETSI Technical Specification TS 101 475 v 1 3 1 2001 J Tubbax B Come L Van der Perre L Deneire S Donnay M Engels Compensation of IQ imbalance in OFDM systems Proc of ICC 05 IEEE Intern Conf on Communications 2003 vol 5 pp 3403 3407 95 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 96 List of Figures LIST OF FIGURES Fig I 1 Block diagram of a radiofrequency digital transmitter 6 1512 CCDE curve ora 9 Fig 3
25. a known amplitude have been imposed on its I Q modulator The choice of the impairment amount to be introduced 15 in fact possible from the generator user panel The then downconverts the RF generated signal to IF and demodulates it thus extracting the baseband components I and Q To this end the VSA needs to be synchronized to the signal generator 71 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters IEEE 488 T pi 10MHz signal amp sort hisss j h t ow ef Bs fe fe TEn pis ls w ao ow ESG E4432B RF signal Fig III 11 Measurement station they both have the same 10 MHz reference clock The I and Q components made available by the VSA as 30 001 samples taken at a rate of 15 MS s are finally transferred via the IEEE 488 bus to the processing unit which calculates the components of the error vector and provides the final estimate of the detected impairments according to the proposed relations B Experimental results Table 11 2 and Table III 3 report imposed impairment amounts when respectively WCDMA and DVB signals are generated For each impairment sets of equally distributed values within reported ranges are taken into consideration It 1s worth noting that voltage offsets are expressed in normalized terms referenced to the maximum value of I and Q components The imposed impairment amo
26. a radiofrequency digital transmitter encoder also accounts for symbol clock which defines frequency and symbol timing I and Q baseband signals are then filtered to limit their spectrum and baseband filters are chosen according to specific optimization strategies which can involve the receiver as well The correct filters must be chosen so as to minimize ISI Inter Symbol Interference Nyquist filters are a relevant example 19 20 21 22 Filtered baseband components are then fed into the I Q modulator where they modulate two orthogonal carriers usually at intermediate frequency IF The signal at the output of the I Q modulator is a combination of the two modulated orthogonal carriers The signal is eventually IF filtered upconverted to radiofrequency RF and finally amplified for radio transmission The location of the DAC Digital to Analog Converter is not a trivial question Where does the digital section end Symbol encoder and baseband filters are usually implemented digitally Current trend is to implement digitally also the modulation section and place the DAC before the IF filter instead of utilizing two DACs on the I and Q branches before the IF modulator input The simplified block diagram depicted in Fig I 1 is quite general although several variations are possible in practice depending on the particular design choices related to multiplexing and modulation scheme Chapter I Transmitter Testing and Troubleshootin
27. a typical V shape as shown in Fig I 8 K 2 K 1 K k 1 k 2 Actual symbol period EVM PEINE Ideal symbol period k 2 k 1 k 1 k 2 Fig I 8 Incorrect symbol rate and evolution versus time of EVM 1 5 4 Wrong filter coefficients and incorrect windowing If baseband filtering is implemented incorrectly amplitude overshoot in the signal or interference in the adjacent frequency channel may occur In systems using Nyquist filters possible problems are caused by an incorrect choice of roll off factor Furthermore the approximation of the ideally IIR Infinite Impulse Response filter by means of a FIR Finite Impulse Response one can cause problems in case the truncation is too abrupt An incorrect value of as well as incorrect windowing cause incorrect transitions between successive symbols while the symbol points remain at their original location The analysis of evolution versus time of EVM can therefore be of great help for detecting such problems since a diagram similar to that depicted in Fig I 9 is experienced 15 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters y Fig I 9 Evolution versus time of EVM in the presence of wrong filter coefficients and or incorrect windowing 1 53 5 IF filter non idealities The IF filter is deputed to eliminate out of channel interference after the I Q modulation Its amplitude should ideally be flat in the band of in
28. als with performance evaluation and specifically presents some original proposals for power measurement CCDF curves evaluation and Introduction transient measurements the results of the wide experimental activity intended to assess the performance of the proposed measurement methods also with respect to pre existing solutions are also given In Chapter III troubleshooting issues are addressed with special regard to detection and evaluation of I Q impairments affecting the modulator which is the core of a digital transmitter in particular three different methods are proposed which are suitable for different operating conditions and modulation systems Although characterized by different pros and cons the three methods exhibit very good performance in terms of reliability and repeatability each of them representing a valid and useful choice for a specific case On the whole they cover all practical cases of generic I Q modulators including OFDM Orthogonal Frequency Division Multiplexing systems Along with details of the proposed methods the chapter accounts for the results achieved in the great number of experiments Finally conclusions are drawn in Chapter IV Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Chapter I Transmitter Testing and Troubleshooting CHAPTER I TRANSMITTER TESTING AND TROUBLESHOOTING I 1 Digital transmitters The simplified block diagram of a radiofrequency
29. amount of I Q impairments which is supposed to be constant over the observation interval each successive occurrence of the symbol can assume a different position depending on the particular symbol simultaneously conveyed by the mirror sub carrier With respect to a generic M QAM diagram possible symbol locations at the output of the FFT block turn out to be As a further example Fig III 18 shows the case of a 16 QAM diagram where symbols can occupy 256 different locations in particular bold dots represent symbol original positions whereas stars are all possible symbol positions under the effect of gain imbalance p 0 3 Q component 1 5 1 0 5 0 0 5 1 1 5 component Fig III 17 I Q diagram of an OFDM sub carrier QPSK 79 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters LJ component 15 1 0 5 0 5 l 1 5 I component Fig III 18 I Q diagram of an OFDM sub carrier 16 QAM The aforementioned effects induced by I Q impairments on a multicarrier modulation scheme make methods already proposed in 67 in Section II 2 and in Section II 3 as well as those suggested by major manufacturers unreliable with regard to OFDM transmitters 1II 4 5 Proposed method The measurement procedure is described in detail according to its fundamental stages The presentation order reflects a typical execution order A RF signal demodulation The RF output signal of the d
30. and Evaluation 1 B cos Q O O k L2 M In order to solve the system of 2M equations composed by 111 10 and 11 11 an estimate of the angle gis determined by evaluating the average value of the incremental ratios of the points 7 Q along the Q coordinate For the sake of clarity let us consider two generic representative points 7 Q and 1 Q which are adjacent on the Q axis Their 2 b ideal coordinates satisfy Jj 1 and Oi VM A and their incremental ratio defined as POE is consequently equal to tan 9 The estimated value for is substituted into relations III 10 and III 11 which are then solved by imposing the minimum average squared error on the estimate of f Voltage offsets c and co are finally evaluated from III 8 and 11 9 according to c O Og tang III 12 and EOM III 13 1 B cos 1 2 4 Performance assessment The performance of the proposed method has been assessed through a number of experiments on RF signals characterized by different baseband modulations In particular QPSK 16 QAM and 64 QAM signals have been taken into consideration A Measurement station A suitable automatic measurement station has been set up which 15 depicted in Fig III 5 It consists of an AWG a DSO and a control and processing unit PC which are all interconnected by means of an IEEE 488 standard interface bus The following operative steps
31. and therefore support the success of the new systems satisfying or at least acceptable quality of service QoS degrees must be pursued At the same time requirements imposed by both national and international standards and regulations have to be met The need for reliable and Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters repeatable testing solutions consequently arises Moreover in order to reduce time to market which is a fundamental issue in a more and more competitive commercial scenario R amp D engineers and manufacturers also need to test their designs and troubleshoot their products in a very short time Not only must testing and troubleshooting procedures be reliable and repeatable enough to conveniently verify QoS and regulations requirements but they should also be efficient enough to help reduce the time to market and speed up production installation and maintenance stages The research activity accounted for in this Ph D thesis has focused on performance evaluation and troubleshooting of radiofrequency digital transmitters a fundamental issue in applied research and industrial production of modern communication systems Several measurements included in testing and troubleshooting procedures utilized by major manufacturers or included in international standards have been taken into consideration The goal has been the development of original measurement methods based on digital signal processin
32. aracterized by different carrier frequencies and average power levels In particular the performance of the two approaches has been evaluated as a function of the number of samples per carrier period p To this aim CCDF measures gained through TIME INTERVALS OF INTEREST E AN NER Time ts Fig II 7 Evaluation of the CCDF from the instantaneous power trajectory the bold line is the mean power level while the thin dotted line is 1 dB above The value of CCDF x with x 1 dB is computed as the ratio between the duration of all the time intervals indicated by the arrows and the overall duration of the signal 36 Chapter II Performance Evaluation the application of the proposed approaches have been compared to those provided by a VSA A Measurement station The measurement station adopted for the experimental tests is shown in Fig II 8 It consists of 1 a processing and control unit namely a personal computer 11 a digital RF signal generator Agilent Technologies E4432B 55 250 kHz 3 0 GHz output frequency equipped with 3G standard compliant signal generation capability 11 a DSO LeCroy LC 584AL 49 8 bit resolution 1 GHz bandwidth 8 GS s maximum sample rate and 1v a synthesized arbitrary waveform generator 0 26 1030 MHz output frequency They are all interconnected by means of an IEEE 488 standard interface bus The RF signal provided by the digital signal generator and complying with the 3G sp
33. ard 802 1 1a Information Technology Telecommunication and information exchange between systems Local and Metropolitan area networks Specific Requirements Part 11 Wireless LAN Medium Access Control MAC and Physical Layer PHY specifications Amendment 1 High speed Physical Layer in the 5 GHz band Reaffirmed 2003 TEEE Standard 802 11b Information Technology Telecommunication and information exchange between systems Local and Metropolitan area networks Specific Requirements Part 11 Wireless LAN Medium Access Control MAC and Physical Layer PHY specifications Higher Speed Physical Layer Extension in the 2 4 GHz band Reaffirmed 2003 TEEE Standard 802 11g Information Technology Telecommunication and information exchange between systems Local and Metropolitan area networks Specific Requirements Part 11 Wireless LAN Medium Access Control MAC and Physical 89 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 8 9 10 11 12 15 14 15 16 17 18 19 20 21 22 25 Layer PHY specifications Amendment 4 Further Higher Data Rate Extension in the 2 4 GHz band Reaffirmed 2003 802 16 IEEE Standard for Local and Metropolitan Area Networks Part 16 Air Interface for Fixed Broadband Wireless Access Systems 2004 Radio Broadcasting Systems Digital Audio Broadcasting DAB to mobile portable and f
34. as been assessed by means of a number of experiments carried out on both laboratory and real wideband telecommunication signals through a suitable measurement station Experimental results have shown that repeatability problems experienced with specialized instrumentation are mitigated by the method Moreover a comparison of the achieved performance to that granted by the previous method has highlighted comparable experimental standard deviations along with reduced measurement time II 3 CCDF curve measurement II 3 1 Introduction CCDF curves provide a statistical description of power levels of an RF signal A CCDF curve is in fact a plot of relative power level expressed in dB versus probability Specifically CCDF x represents the probability that the signal envelope power 15 at least x dB above the average power the envelope power is defined as P t 2 I t Q t 11 27 where and Q are the baseband in phase and quadrature components of the RF signal As it 15 suggested by the definition a CCDF curve is a strictly decreasing function and its value in the origin of the x axis represents the percentage of time the signal spends above its average power level CCDF curves are very important for designing testing and troubleshooting telecommunication components and apparatuses 33 57 With regard to design they give a valid help in preventing signal compression due to the non linearity of some components such as power ampli
35. asurements on digitally modulated signals Product Note Agilent 8560E 8590E Spectrum Analyzers Agilent Technologies Literature no 5968 2602E 2000 4 steps for making better power measurements Applicat Note 64 4C Agilent Technologies Literature no 5965 8167E 2000 Real time spectrum analysis tools aid transition to third generation wireless technology Tektronix Literature No 2EW 13 227 0 1999 WCDMA measurement guide Agilent Technologies E4406A series transmitter tester Agilent Technologies Literature no E4406 90132 2000 Wolf and B Buxton Measure adjacent channel power with a spectrum analyzer Microwaves RF pp 55 63 Jan 1997 ACP measurements on amplifiers designed for digital cellular and PCS systems Tektronix Literature no 2DA 12 149 0 1998 Agilent EPM P series single and dual channel power meters Agilent E9320 family of peak and average power sensors Product Overview Agilent Technologies Literature 1471E 2000 L Angrisani M D Apuzzo M D Arco A New Method for Power Measurements in Digital Wireless Communication Systems JEEE Trans on Instrum and Measur vol 52 No 4 August 2003 pp 1097 1106 D Percival A Walden Spectral Analysis for Physical Applications Multitaper and Conventional Multivariate Techniques Cambridge University Press 1998 T W Anderson Comments on the performance of maximum entropy algorithms Proc IEEE vol 66 pp 1581 1582 A Papou
36. at power levels distanced of 0 01 dB one to another the value of the peak to average power ratio PAR measured by the proposed approach and that furnished by the VSA have sometimes been not equal In such cases P and Q the number of points constituting respectively the measured CCDF curve and the nominal one were different consequently the rmse has been evaluated as 30 where y i i 1 2 P are the values of the CCDF measured through the proposed approach y i i 1 2 Q are the values of the CCDF given by the VSA and M min P Q Table II 4 shows the average rmse values achieved for the considered window type and size aS resulting from measurements carried out on several 3G signals characterized by different carrier frequencies and average power levels Note that window size 1s expressed in terms of the carrier period The experimental results show that shorter windows have provided lower values of rmse This is not unexpected because the better time resolution granted by shorter windows at the expenses of frequency resolution 15 preferable for our purpose of gaining the instantaneous power trajectory In particular the 2 7 long Hanning window which grants the lowest rmse turns out to be the most suitable windowing function C Results A second set of experimental tests have then been carried out on 3G signals in order to assess the performance of the two proposed approaches Each generated signal has bee
37. ation of a parametric spectral estimator characterized by reduced convergence time is investigated in this section Specifically a new method for power measurement is proposed which first digitizes the RF signal under test then estimates its true PSD according to Burg s parametric solution and finally applies straightforward measurement algorithms to the PSD in order to evaluate the quantities of interest Advantages of the new method are proved through a number of experimental tests carried out on both laboratory WCDMA Wideband Code Domain Multiple Access signals peculiar to UMTS Universal Mobile Telecommunication System 2 synthesized by means of an arbitrary waveform generator and real DVB S Digital Video Broadcasting Satellite 10 signals received through a professional satellite station 1 2 2 Theory underlying the proposed method some theoretical notes on parametrical PSD estimation are given in the following further details can be found in 45 Suppose that the discrete parametric stationary process X has a PSD that is completely determined by k parameters a d2 ay namely S f 8S f a a a l 1 1 Given a time series that can be regarded as a realization of this process 1f the parameters of S can reasonably be estimated from this data by 45 d then S f S f d 1 2 is a reasonable estimate of S f An autoregressive model of order p AR p 1s the most widely used f
38. ation of the transmitter on function and the moment after which the frequency of the carrier always remains within 1 kHz of its steady state frequency f 42 Chapter II Performance Evaluation The standard prescribes that ta shall not exceed 25 ms Instantaneous power and frequency trajectories are evaluated by suitably processing the matrix obtained at the end of the previous step Instantaneous power of the signal as a function of time can in particular be calculated by summing the values along each column of the matrix and multiplying the result by the frequency resolution which is equal to As the maximum value of the power spectrum is in each time instant associated to the instantaneous frequency of the signal the frequency trajectory can be evaluated by applying a proper peak location algorithm to the matrix 24 Specifically for each column the row index in correspondence of which the power spectrum reaches its maximum is collected in an array which consequently accounts for the evolution versus time of the frequency of the analyzed signal No demodulation is thus needed to gain the desired instantaneous power and frequency trajectories Transmitter attack time 15 finally measured according to its definition 1 4 3 Performance assessment Typical evolutions of power and frequency transients are given by the standard 61 The authors have synthesized a signal characterized by such trajectories to properly sele
39. butions the proposed method which is addressed to transmitter testing allows for the automatic evaluation of the amount of each I Q impairment 76 Chapter III Impairments Detection and Evaluation Specifically the original measurement procedure implemented by the method can be summarized as follows The RF output signal 15 first demodulated to gain the symbols related to all sub carriers Then for each sub carrier but the so called DC an algebraic equation system derived from the aforementioned model and involving both impairments amounts and in phase and quadrature components of symbols conveyed by the sub carrier and related mirror one is solved in order to evaluate gain imbalance and quadrature error amounts Concerning voltage offsets their estimates are achieved by particularizing the same equation system to the DC sub carrier Measurement results for each impairment are finally obtained by averaging the different estimates A number of experimental tests on OFDM signals are conducted to highlight the good performance of the method III 4 2 Problem statement A OFDM modulation A simplified OFDM implementation diagram is sketched in Fig III 15 Input serial bit sequence 15 parallelized into K groups to each of which a QAM 15 applied The K complex sequences of QAM symbols Co n C n modulate orthogonal carriers For a given n Co n Cj n Ck 1i n can be regarded as the FFT coefficients of the t
40. cant as it often occurs In particular the results achieved provide evidence of the same accuracy as the method presented in Section III 2 whereas measurement time is significantly reduced 0 2 Gain imbalance g 0 500 1000 1500 2000 2500 3000 symbols Fig III 14 Symbol by symbol estimation of gain imbalance 75 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters III 4 I Q impairment detection and evaluation on OFDM transmitters III 4 1 Introduction Orthogonal Frequency Division Multiplexing OFDM is an emerging technology for high data rate transmission 85 86 87 which 1s expanding its application field to a variety of broadband communication schemes OFDM is in particular adopted in the European standards for Digital Audio Broadcasting DAB 9 and Digital Video Broadcasting Terrestrial DVB T 12 More recently different Wireless Local Area Network W LAN and Metropolitan Area Network MAN standards in the USA and Europe have converged on OFDM to achieve high data rates 7 8 88 Detection and evaluation of I Q impairments affecting an OFDM modulator on the basis of their effects on the RF output signal is not a trivial extension of procedures designed for generic I Q modulators The measurement method based on clustering presented in Section IIIL 2 as well as that proposed in 67 have proved to be effective with regard to generic QAM transmitters and in the pr
41. ches 1 take advantage of proper sampling strategies developed during the research activity that 15 object of the thesis 58 which grant alias free sampling and a digital downconversion of the RF signal and 11 process the instantaneous power trajectory suitably evaluated In particular to gain the instantaneous power trajectory the first approach time domain approach averages the quadratic values of the samples over a carrier period while the second time frequency approach applies TFRs 23 59 The two approaches do not require any demodulation of the signal under test and do not need special purpose high performance instrumentation only a processing unit and a DAS are in fact needed 5 gag dB xe ss Trig Free ALAR ms 2 FA ms Fig II 5 Envelope power of a W CDMA signal its high variability is due to the noise like nature of the signal 33 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 882 Las B 1z Percentage of time Hale en oe 0 0001 2 B Ae 15 88 dB Relative power level Fig II 6 Power CCDF curve of the signal referred to in Fig II 5 1 3 2 Proposed Approaches As stated above the two proposed approaches gain a measure of the CCDF from the instantaneous power trajectory In particular no analog downconversion and or demodulation of the signal under test are needed both approaches in fact simply process the sample
42. component I c equal to 0 15 A 2 Quadrature error In the case that only quadrature error occurs the error vector 15 given by EV 2 yy o SINE j Ypo cos 1 III 20 which can be approximated as follows when lt lt 1 EV 9 yy o IIL 21 hence Re EV x Re EV j IIL 22 Yobo A 3 Offset Finally a straightforward relation links the error vector to the voltage offsets c and cg when other impairments are negligible EV fse Cr J 4 23 The values of c and cg can therefore be evaluated respectively as c Re EV per 111 24 and 68 Chapter III Impairments Detection and Evaluation Co Im EV 111 25 B Two impairments B 1 Gain imbalance and quadrature error Fig IIIL 7 shows a QPSK constellation diagram in the presence of gain imbalance and quadrature error in such cases the analytical expression for the error vector EVeain g is EV 47 8 Yona 1 sind j yuo 1 g cos 1 IIL26 If 1 relation III 26 reduces to EV aing TE Yn 7 Ymo 1 8 9 J 8 Yu IIL27 Consequently g and can be obtained respectively from Im EV g Im EV ang 11 28 Yob o and Re EV E Ref EV ang 8 Yons 29 8 B 2 Gain imbalance and offset c When gain imbalance and c are present at the same time the error vector EVgaincr can be written as EV am 2 11 30 Therefo
43. concurring results 51 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 52 Chapter III Impairments Detection and Evaluation CHAPTER III I Q IMPAIRMENTS DETECTION AND EVALUATION III 1 Introduction Proper functioning of RF digital transmitters mainly relies upon the performance of the I Q modulator they are normally equipped with Impairments in the I Q modulation section also called I Q impairments such as gain imbalance quadrature error and voltage offsets can severely degrade the quality of transmitter output signal with a consequent reduction of transmission efficiency Detection of I Q impairments and evaluation of their amount 1s therefore crucial for transmitter troubleshooting and in every stage of transmitter lifecycle A significant part of the research activity at the basis of this thesis has been devoted to that three different solutions for I Q impairments detection and evaluation are presented in the following each of which 15 designed to be particularly effective in one or more cases of practical interest The proposed solutions have been extensively tested on telecommunication signals to assess their performance 2 A measurement method based on clustering III 2 1 Introduction Due to the high degree of integration direct access to the I Q modulation section of a digital transmitter 1s precluded only the transmitter output signal generally at radiofreque
44. correctly attained through a common threshold decision rule when one or more representative points are outside their correct decision region Named yopp ligtjQia the ideal baseband signal unaffected by I Q impairments the signal expression at IF III 2 can be rewritten as yy t 6 L 0 cosQ fet 1 B eg Qu 2 sin 27 fit 9 1 6 where Gg gt G 15 supposed An equivalent expression is yy t 2 c c5 1 B sin 9 D t B sin 9 Q 1 cos 27 fet III 7 Co 1 P cos t 1 5 cos 9 Q t sin 2774 Despite their non linear combination all the impairments are estimated without previously separating them thus overcoming one of the limitations of ETSI guidelines In detail the coordinates Or Og of the barycentre of the set of representative points 1 Q are first evaluated It is worth highlighting that the barycentre can be different from the origin of the axes because of the presence of impairments With reference to the discrete time version of the expression III 7 the following equations for the barycentre coordinates can be derived O c t co 1 B sin 11 5 and Op c 1 B cos III 9 Subsequently taking into account III 8 and 11 9 the substitution of the ideal coordinates 7 into the time discrete version of the expression III 7 yields 1 B singQ I k 1 2 M III 10 and 58 Chapter III Impairments Detection
45. ct the value of each parameter involved in the evaluation of the considered TFRs e g window function scaling factor chirp rate and bending factor A Test Signal As highlighted by the standard common features characterizing the time domain evolution of real power and frequency trajectories during transmitter transients are overshoot and ringing Suitable test signals should assess the capability of the method to accurately measure power and frequency trajectories exhibiting such features In detail some significant points characterizing the evolution versus time of power and frequency that 1s respectively significant values of instantaneous power and frequency are fixed in correspondence of certain time instants elapsed from the initiation of the transmitter on function The whole trajectory is then synthesized by interpolating between and re sampling data at the same rate that is intended to be used in the generation process In particular piecewise cubic interpolation allows the significant points to pass through unchanged Finally test signals are accomplished by imposing the so synthesized trajectories to sinusoidal carriers As an example typical instantaneous frequency and power trajectories of the adopted test signals utilized to assess the performance of the method are shown respectively in Fig II 11 and Fig IL 12 Steady state power and frequency values P and f are chosen equal to 43 Performance Evaluation and Troub
46. cussed In particular a measurement method capable of estimating gain imbalance quadrature error and voltage offsets has been presented and its performance experimentally assessed The main advantages of the method are its capability of 1 univocally revealing each symbol deviation from its ideal position even when impairment combination leads some symbols outside their own original decision region and 11 separating different simultaneous I Q impairments thus overcoming a major limitation of ETSI guidelines 62 Chapter III Impairments Detection and Evaluation A suitable measurement station has been set up with the aim of assessing the performance of the method through a number of experiments on different types of signals and with regard to different impairment combinations and amounts The experimental activity has proved effectiveness and repeatability of the proposed method experienced values of A and o are in fact lower than few percents Experimental results give also evidence of the robustness of the method with regard to the possible presence of interfering tones or phase jitter in such critical conditions in fact A and o are generally lower than 6 and 9 respectively 3 A measurement method based on error vector analysis III 3 1 Introduction To estimate most common impairments gain 1mbalance quadrature error and voltage offsets that affect the I Q modulator in a digital transmitter through mea
47. d different sub carrier modulation patterns 1 e modulation patterns characterizing the symbols Co n C n have been considered QPSK 16 QAM and 64 QAM A Measurement station and operative procedure A suitable measurement station has been set up which the same as in Fig III 11 It consists of 1 a processing and control unit namely a personal computer 11 a digital RF signal generator Agilent Technologies E4432B 55 250 kHz 3 GHz output frequency with AWG capability 14 bit vertical resolution 1 Megasample memory depth 40 MHz maximum sample clock and iii a VSA Agilent Technologies 4460A 52 7 MHz 4 0 GHz input frequency range I Q signal demodulation personality they are all interconnected by means of an IEEE 488 standard interface bus The following operative steps have been taken Baseband signals have digitally been synthesized through a suitable algorithm running on the processing and control unit I Q impairments of known amount are imposed on the digital sequence of samples Impairments have been assumed to be constant in the observation interval Generated samples have been downloaded into the volatile memory of the AWG operating the D A conversion and RF up conversion VSA has been employed to demodulate the RF signal and extract baseband components To this end the VSA has been synchronized to the signal generator they have shared the same 10 MHz reference clock I and Q components
48. digital transmitter based on I Q modulation 1s shown in Fig I 1 The waveform depicted at the input of the transmitter is to be intended as digital that 1s either representing the quantized discrete time version of an analog signal e g voice coming out of an analog to digital converter or consisting of digital data Input data usually undergoes source coding and channel coding Source coding generally involves compression which aims at removing redundancy thus allowing a more efficient spectral utilization 13 14 15 16 Channel coding consists in introducing controlled redundancy that can be exploited by the receiver to face problems due to noise and interference encountered by the transmitted signal through the channel in a word channel coding provides protection from errors 17 18 Burst errors can sometimes occur for instance in the class of channels characterized by multipath and fading To face burst errors interleaving of coded data is usually adopted The symbol encoder maps groups of input serial bit stream into the I and Q waveforms that is into symbols of the I Q plane peculiar to the specific communication system Examples of symbol mapping performed by the symbol encoder are reported for instance in Section 4 5 of 10 and Section 9 of 11 The symbol Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Encoder Source Coding Channel Coding Fig I 1 Block diagram of
49. e sample rate characterizing the acquired signal and its local characteristics have been expressed in terms of slope chirp rate and curvature bending factor given by respectively the first and second order finite difference 47 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Finally a number of frequency and power transient measurements have been carried out to determine the optimal mother chirplet scaling factor a which is the value that minimizes rmse given in II 35 In particular the plot of rmse values versus a exhibits a minimum equal to 0 021 in correspondence of a mother chirplet scaling factor equal to 4 0 1 4 4 Tests on real transmitters Once optimal parameter combinations have been singled out the proposed method has been applied to real transmitters operating in the range 30 1 GHz to which ETSI standard 61 1s addressed In particular attack times of 1 a transmitter intended to be part of a bug and 11 a walkie talkie have been measured A Bug transmitter The transmitter under test has been set to a steady state carrier frequency f equal to 75 827 MHz Its output signal has been sampled at 250 kS s so as to center the sampled signal at 77 kHz A short pre trigger has been imposed in order to capture the whole power and frequency transients Fig II 16 plots the evolution versus time of the acquired signal whereas Fig IL17 and Fig IL18 respectively show ins
50. e which is given in input to the next stage of the proposed method The value of in step 3 is chosen as the result of a number of tests on simulated and emulated signals The rationale for the choice relies upon the consideration that for a Gaussian AR p process the De i terms for k gt p are approximately independently distributed with zero mean and a variance equal about to 1 N 48 25 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Signal digitization amp 4 34 YES S f 2 S f k amp k 1 4 k 1 k 1 lt t lt N Power a k amp k 1 8 k 1 k 1 lt t lt N Mgasurempn Dnk n I lt m lt k l1 1 8 2 T e SOP 2 k j2anyfT E ME Pme Fig II 1 Flow chart diagram of the PSD estimation routine 26 Chapter II Performance Evaluation C Power measurement Once the PSD of the analyzed signal has been estimated power measurement can be carried out by means of very straightforward algorithms In particular average power channel power and occupied bandwidth measurements are taken into account Average power 15 evaluated by integrating the estimated PSD over the whole frequency span analyzed With regard to channel power the frequency interval centered at the tune frequ
51. e drawn between CCDF curves measured at the antenna port for lower amplitudes of the transmitted signal 1 5 2 I Q impairments Fig I 4 shows the I Q section of a digital transmitter whose input 1s represented by the I and Q discrete time signals provided by the symbol encoder and whose output feeds the IF filter I Q impairments can be caused by differences between the I and Q paths of the modulator The most common are 1 gain imbalance 11 quadrature error and 11 voltage offsets Difference between gains of the amplifiers on the I and Q separate paths can induce a distortion on the I Q diagram similar to that shown in Fig I 5 where gain on the Q path 15 clearly higher The effect of gain imbalance 15 definitely more evident when IF section 15 implemented in an analog way A phase shift between the two carriers modulated by signals on the I and Q paths not exactly equal to 7 2 rad is responsible for a quadrature error whose effects on the I Q diagram are depicted in Fig I 6 Finally DC offsets possibly introduced in 12 Chapter I Transmitter Testing and Troubleshootin 0 rad IF Local Oscillator Fig I 4 I Q section of a digital transmitter the I and Q paths for instance added in the amplifier determine a translation of the I Q diagram Fig I 7 I Q impairments cause an increase in the error probability because they reduce the minimum distance of symbols from decision region boundaries this is visible i
52. e partial autocorrelation coefficient 1s attained as h 11 12 and the k parameters k ox are then calculated according to 22 Chapter II Performance Evaluation Prk E EE E L lt m lt k l 1 13 2 2 re Of c oS 1 6 1 14 It is worth noting that even though Levinson Durbin recursions grant a significant reduction of computational burden the need to estimate the autocovariance sequence in order to solve system II 9 there still exists A key role in the recursive procedure is in fact played by the partial autocorrelation coefficient estimated according to II 12 1 2 5 Proposed method From an operative point of view the proposed method can be divided into three stages each of which is described in the following A RF signal downconversion and digitization As it happens with vector signal analyzers VSA and performance spectrum analyzers PSA the input RF signal is first downconverted to a suitable IF and then digitized by means of a data acquisition system DAS the bandwidth of which has to include all the significant spectral content of the downconverted signal B Power spectral density estimation Let X X2 Xy be the samples of the downconverted signal A proper digital signal processing based approach based on Burg s solution 1s applied to the acquired samples in order to derive an estimate of the PSD of the downconverted signal In particular
53. ecifications is digitized according to the following procedure the optimal sampling frequency f 1s provided by the algorithms presented in 58 and a sinusoidal signal at frequency f 1s generated by the synthesized signal generator to drive the DSO sampling clock external clock Subsequently the CCDF is measured through the application of the proposed approaches to the acquired samples B Optimal choice of time frequency parameters As stated before spectrogram results depend on the particular window function adopted for STFT in II 29 an optimal choice of the type and size of the window has to be made To this aim preliminary measurements on test signals have been carried out considering rectangular Hanning and Blackman windows which are some of the most common ones different window sizes have been taken into account too The optimal window type and size have been singled out as those that minimise the rmse root mean square error between the CCDF measured by applying the proposed approach and that given by the VSA which has Processing and Synthesized Signal Data Acquisition Digital RF control unit Generator System Signal Generator mE M E External RF signal 9 clock signal IEEE 488 INTERFACE BUS Fig II 8 Measurement station 37 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters been taken as the reference curve Even though both curves to be compared have been evaluated
54. ed by the ice A eo Re EV jose ReiEV y Pov are computed same Yobo 4 Then impairment amounts can be estimated by observing that Ael 2Y po Sing due to the symmetry of the constellation Specifically arcsin III 40 Y bb Q and c Re EV yy o sin IILA1 III 5 4 Performance assessment The method has been validated through a wide experimental activity carried out on signals characterized by different types of digital modulation schemes Both high and low cardinality signal spaces have been taken into consideration In particular the following test signals have been adopted 1 WCDMA signals which characterize UMTS the European proposal for a third generation communication system and 11 16 QAM and 32 QAM signals peculiar to DVB standards 10 11 A Measurement station A suitable measurement station has been set up Fig III 11 It consists of 1 a processing and control unit namely a personal computer 11 a digital RF signal generator Agilent E4432B 55 250 kHz 3 GHz output frequency with AWG capability 14 bit vertical resolution 1 MS memory depth 40 MHz maximum generation frequency and 111 a VSA Agilent 4460A 52 7 MHz 4 0 GHz input frequency range I Q signal demodulation personality these are all interconnected by means of an IEEE 488 standard interface bus Taking advantage of the features of the chosen RF generator impairments having
55. ency of the monitored channel and whose extent 1s as wide as the channel spacing of the specific system is first established then the desired power 15 obtained by integrating the PSD over the aforementioned frequency interval Concerning occupied bandwidth it 15 defined as the frequency interval centered at the tune frequency of the monitored channel over which the integral of the estimated PSD equals 99 of the average power Occupied bandwidth 1s calculated as the difference fz f between the two frequency values f and f which make each of the two frequency intervals f2 f 2 and 0 f contain 0 5 of the average power 1 2 4 Performance assessment The proposed method has been validated through an extended experimental activity In particular WCDMA and DVB S signals have been taken into consideration the former have been synthesized by means of a proper arbitrary waveform generator whereas the latter have been received through a professional satellite station A Measurement station A suitable measurement station shown in Fig IL 2 has been set up to assess the performance of the method It consists of 1 a processing and control unit namely a personal computer 2 a digital storage oscilloscope DSO LeCroy LC 584AL 49 8 bit resolution 1 GHz bandwidth 8 GS s maximum sample rate 3 a spectrum analyzer Agilent Technologies HP8594E 50 9 kHz 2 9 GHz input frequency range channel power and occupied bandwidth
56. er and Receiver in Pulse Amplitude Modulation Proc IEEE vol 53 pp 248 259 March 1965 J W Smith The Joint Optimization of Transmitted Signal and Receiving Filters for Data Transmission Systems Bell Syst Tech J vol 44 pp 1921 1942 December 1965 F Hlawatsch F Boudreaux Bartels Linear and quadratic time frequency signal representations IEEE Signal Processing Magazine vol 9 No 2 pp 21 67 Apr 1992 90 References 24 25 26 27 28 29 30 31 32 33 34 35 36 B Barkat B Boashash Instantaneous frequency estimation of polynomial FM signals using the peak of the PWVD Statistical performance in the presence of additive Gaussian noise IEEE Trans Signal Processing vol 47 pp 2480 2490 Sept 1999 L Cohen Time Frequency Analysis Prentice Hall 2000 B Boashash Estimating and interpreting the instantaneous frequency of a signal Proc IEEE vol 80 No 4 pp 520 568 Apr 1992 Mann and S Haykin Chirplets and Warblets Novel Time Frequency Methods Electronics Letters vol 28 no 2 pp 114 116 January 1992 L Angrisani P Daponte and M D Apuzzo A measurement method based on time frequency representations for testing GSM equipment JEEE Trans Instrum Meas vol 49 pp 1050 1056 Oct 2000 Testing and troubleshooting digital RF communications transmitter designs Application Note 1313 Agile
57. eral instruments as recommended by the standard 1 4 2 Proposed method The proposed method is mandated to the measurement of wireless transmitter attack time without demodulating its output signal and without needing special purpose instrumentation The method based on digital signal processing consists of three fundamental stages which are described in the following 1 sample rate selection and signal digitization 11 TFR application to gain instantaneous power and frequency trajectories and 111 measurement of power and frequency transients A Sample rate selection and signal digitization First the transmitted signal has to be digitized by the DSO at the sample rate provided by one of the algorithms presented in 58 In particular the algorithm receives in input some information on the signal such as its bandwidth and carrier frequency and then outputs the minimum sample rate f that satisfies user s requirement in terms of spectral allocation of the sampled signal It is so possible to digitally downconvert the input signal thanks to a sampling 41 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters frequency much lower than the carrier frequency with consequent benefits in terms of frequency resolution Equivalently it is possible to analyze a larger time interval given the number of samples B TFR application To evaluate instantaneous power and frequency trajectories a TFR has
58. esence of multiple I Q impairments The method based on the analysis of EV 15 particularly timesaving and grants the same performance as the former but is applicable only in the presence of one or two predominant impairments Such methods however as well as troubleshooting procedures proposed by major manufacturers and based on the analysis of I Q diagram 29 are designed for traditional RF digital transmitters and cannot be profitably applied to OFDM transmitters OFDM transmitters in fact exploit a multicarrier modulation scheme I and Q components of which are respectively the real and imaginary part of the outcome of an IFFT Inverse Fast Fourier Transform As a consequence not only are actual positions of symbols on the I Q diagram of a certain carrier generally called sub carrier affected by impairment amounts but they also depend on symbols conveyed on the so called mirror sub carrier A new method for I Q impairment detection and evaluation in OFDM transmitters 15 presented hereinafter To rightly account for major effects induced on RF output signal by mirror sub carrier interference in the presence of I Q impairments a proper analytical model is exploited A similar model is at the basis of a method recently proposed for the compensation of I Q impairments in OFDM receivers 89 While the latter is only interested in evaluating the overall effect of impairments on the received signal and does not separate different impairment contri
59. esents time By visualizing the matrix along a time frequency plane the evolution versus time of the power spectral contents of the analyzed signal can be observed By summing the values along each column the instantaneous power of the signal as a function of time can be calculated It is worth noting that spectrogram results depend on the particular windowing function 35 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters adopted The results of the experimental activity aimed at singling out the optimal tuning of window parameters are given in the next subsection C CCDF curve determination Finally the mean and peak signal power levels are evaluated and the CCDF is measured by determining a set of levels distanced one to another of 0 01 dB between the mean and the peak signal power level and calculating the percentage of time during which the signal 1s above each level For the sake of clarity Fig II 7 shows the evolution of the instantaneous power of a 3G signal versus time The bold line represents the mean power level while the thin solid one represents a power level of 1 0 dB above the mean The value of CCDF x for x 1 0 dB is evaluated as the ratio of the time during which the signal is above the thin dotted line to the observation interval IT 3 3 Performance assessment A suitable measurement station has been set up in order to validate the approaches with regard to real 3G signals ch
60. fact that E 0 for k gt 0 implies that E 4Y E amp DE tnp HeYa Es op 18 P 21 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Hence by observing that s s equation II 6 evaluated for k 0 1 p leads to the so called augmented Yule Walker equations 09 Sp l c po uM Sp Ap _ 0 B 1 9 Sy Sp i 50 Pp p 0 In the presence of a time series that is a realization of a portion X X2 Xy of any discrete parameter stationary process with zero mean X an AR p model could be fit by replacing s with ps uet gt 10 t l and solving system 11 9 by inversion The better the arbitrary stationary process X 15 approximated by an AR p stationary process the more reasonable is this procedure Concerning this given the values of X X 2 X k of a stationary process X with zero mean the best linear prediction of the value of X 1 9 the one that minimizes the mean square error 47 1s B k X 4 gt nXm 11 1 1 m 1 also named the forward predictor of of length k To avoid matrix inversion a time consuming task system 1 9 can be solved through Levinson Durbin recursions 47 which take advantage of a nice property of parameters Qi p Q2 p 0 and Oy Equation II 11 induces in fact a recursive procedure at the k th stage of which given the estimates Or ca amen ee 0 E an estimate of th
61. fiers The information provided by CCDF curves in fact allows designing the amplifier on the basis of the particular signal expected in input e g a Quadrature Phase Shift Keying QPSK modulated input signal will impose different design requirements than a 32 Chapter II Performance Evaluation 64 QAM Quadrature Amplitude Modulation one Vice versa given the amplifier gain versus input power the CCDF curve can be useful to determine the optimal input signal level Concerning testing and troubleshooting CCDF curves are an excellent tool for quantifying compression effects if a signal is linearly amplified in fact its CCDF does not vary while compression due to non linearity would result in a decrease of the CCDF For the sake of clarity Fig IIL 5 shows the envelope power of a WCDMA signal Its CCDF curve is given in Fig II 6 the percentage of time the signal spends above each power level specified by the x axis estimates the probability for that particular power level Instruments that perform CCDF measurements currently available on the market are high performance spectrum analysers such as VSAs and PSAs which demodulate the RF signal under test and then evaluate its CCDF curve by processing the samples of the baseband components Two alternative digital signal processing approaches for CCDF measurements based on original algorithms that are directly applied to the samples of the RF signal are presented hereinafter Both approa
62. g I 2 Transmitter testing Different tests are carried out at different stages of the design of a digital communication transmitter Individual components the transmitter is made of are at first tested individually in order to verify their conformance to requirements and specifications After assembling the transmitter strict conformance tests are carried out in order to verify system requirements along with design robustness and grant interoperability of products made by different manufacturers Conformance tests are usually performed at antenna port through an ideal receiver Possible causes of degradation must consequently be inferred from measurement results at the antenna port Measurements on the transmitted signal are carried out in different domains time domain frequency domain and modulation domain Time domain analysis is required for instance on transmitters implementing TDMA Time Division Multiple Access techniques in order to measure burst shaping and timing it is also performed on the RF signal envelope at the output of spectrum analyzers operating in zero span mode and on demodulated I and Q components Crucial information on spectral occupancy out of band emissions and possible interference are provided by the analysis in the frequency domain which 15 carried out through analog or FFT Fast Fourier Transform based spectrum analyzers Modulation domain analysis can be carried out by comparing the demodulated signal
63. g which could result more reliable and or repeatable and or efficient than the publicized ones Regarding reliability efforts have been dedicated to design methods providing smaller difference between expected and measured quantities of interest Concerning repeatability a smaller dispersion of the results of successive measurements carried out in a very short time under the same operating conditions and following the same measurement procedure has been sought As for efficiency one or more of the following goals not necessarily independent of one another have been pursued i reduced measurement time ii reduced cost of measurement equipment iii increased measurement automation iv less a priori information on the system under test and increased flexibility intended as the capability of adapting with minor modifications to newer standards and systems All the proposed methods have been extensively tested by applying them to simulated emulated and real communication signals Measurement results have been analyzed and compared to those achievable through the application of existing methods and or instrumentation available on the market The Ph D thesis is organized as follows In Chapterl the model of a typical radiofrequency digital transmitter 1s introduced and its main functional blocks are described moreover the most significant measurements involved in transmitters testing and troubleshooting are reported Chapter II de
64. have been taken 1 The baseband signal has been synthesized in digital form by means of a suitable algorithm running on the PC 2 Calibrated I Q impairments have been introduced on the digital sequence of samples impairments have been assumed to be constant in the observation interval 59 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters downloading IEEE 488 ESG E4432B LeCroy Fig III 5 Measurement station 3 The generated samples have been downloaded into the memory of the AWG which has operated the conversion in analog form 4 The analog modulated signal has been digitized by the DSO the acquired samples have been transferred to the PC 5 The PC has demodulated the signal and evaluated I Q impairments through the proposed algorithms b Experimental results Three sets of experiments have been carried out In each set for a given amount of I Q impairments involved about one hundred signals characterized by the same baseband modulation with different bit sequences have been considered in order to achieve a reliable analysis In particular in the first set of experiments a single impairment has been considered In the second set two simultaneous impairments have been imposed on the synthesized signal with the aim of analyzing the influence of an interfering impairment when the measurement of the other impairment 1s addressed The last set of experiments has been foc
65. ide signal bandwidth 1 5 6 DAC impairments Although a DAC should ideally output a series of delta impulses impulses of a certain width are observed in practice A sin x x function in the frequency domain must therefore be compensated for a correct functioning of the system otherwise a distortion in the spectrum of transmitted signal occurs 1 5 9 Burst shaping impairments In TDMA systems a burst modulator is present in the block diagram of the transmitter before the final amplification stage If burst parameters are not in accordance with specifications harmful interference can occur Overshoot on power up frequency drift amplitude droop and erroneous burst width are only some of the potential problems that can be experienced Time domain measurements and TFR based measurements can help troubleshooting this kind of impairments 17 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 18 Chapter II Performance Evaluation CHAPTER II PERFORMANCE EVALUATION II 1 Introduction The chapter presents some original measurement methods for performance evaluation of RF digital communication transmitters Power measurement CCDF curve estimation and transient evaluation which are some of the most significant measurements carried out to assess transmitter performance are in particular dealt with For each measurement a state of art 1s discussed the proposed method 1s described details ab
66. igital transmitter under analysis is demodulated and the K complex sequences C o n C n provided by the FFT block are extracted The measurement algorithm in fact operates on such sequences Let us drop index n and consider the OFDM symbol at the output of the FFT block at a generic time instant namely C o According to III 45 real and imaginary parts of coefficients C are respectively A i4 M Lp B max k 1 0 1 B e 111 46 k 2 k 2 h 2 k h I Q and B 1 2 B A A max k 1 0 c 10 47 80 Chapter III I O Impairments Detection and Evaluation The first step consists in estimating C A jB for k 0 1 K 1 through typical threshold comparisons B Gain imbalance and quadrature error evaluation Some terms in III 46 and IIL 47 are present only when k 0 as accounted for by max k 1 0 which is equal to 1 if k 0 and null else Index k 0 identifies the first entry of the IFFT and is therefore often referred to as DC sub carrier index In other words possible voltage offsets on I and Q branches have effect only on DC sub carrier as expected Taking into account that symbols related to all sub carriers except the DC are processed in order to get an estimation of gain imbalance and quadrature error In detail for each sub carrier except the DC III 46 and 11 47 can be rewritten to yield the following system of two linear equations
67. ignal attained through the spectrum analyzer Anritsu MS2687B very critical measurement conditions are highlighted 3 Fig II 5 Envelope power of a W CDMA signal its high variability is due to the noise like nature ot the eo ed lote t mi ten ed tet d iHa besten cdd pseudo 33 Fig II 6 Power CCDF curve of the signal referred to in Fig II5 uessseesssse 34 Fig II 7 Evaluation of the CCDF from the instantaneous power trajectory the bold line is the mean power level while the thin dotted line 1s 1 dB above The value of CCDF x with x 1 dB is computed as the ratio between the duration of all the time intervals indicated by the arrows and the overall duration of the signal 36 Pio S Measurement SEO occisi nt oti vant esi Devant taeda pu a eene 327 Fig II 9 Comparison between the CCDF provided by the VSA and those provided by a the time domain approach and b the time frequency approach when different values of the sampling frequency f and therefore of the ratio p are taken into account Details of low and high power levels are given in al a2 b1 b2 39 Fie Ir 0 e Standard measurement S rea c 4 Fig IIL 11 Instantaneous frequency trajectory of the test 44 Fig II 12 Instantaneous power trajectory of the test
68. ime sequence co n c1 n c n which constitutes an OFDM symbol Real and imaginary parts of the complex sequence resulting from the serialization of the IFFT output are respectively I and Q component feeding the I Q modulator Their expression in complex form 15 K 1 12 1 n jO 9 C Ge K m 0 1 Kl k 0 ro MODULATOR Fig 111 15 Basic OFDM modulation scheme du Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters B OFDM signals affected by I Q impairments As it 15 evident from Fig III 16 I Q diagram of an OFDM signal appears as a messy agglomeration of symbols rather than a more familiar geometrical shape This is the reason why no qualitative information on impairments affecting the modulator can be obtained from its analysis in contrast to what happens for other modulation formats Expressions of sequences and Q which an ideal receiver would recover through its FFT block are I 1 cos 2n z B sin 22k n k 0 Kai m 11 43 A sin c z B cos c zj t Cg k 0 K 1 Q DD sin c z B cos c z Co 44 k 0 In expressions 111 43 and 111 44 Gr gt Gg 1 is assumed A and are respectively the real and imaginary part of Cj cos and sin 9 are approximated with the first terms of their Maclaurin series and index n is dropped since the same considerations can be done f
69. in Section II 2 shows that the values of A and o 9o respectively included in the ranges 0 9 6 7 and 1 0 9 0 concur with those experienced in Section II 2 which are included in 1 0 4 5 and 1 5 6 6 The method based on EV is operational even for short input data streams In particular when it is compared to the real time RLS algorithm proposed in 67 the same experimental standard deviation of the measurement results is typically accomplished for a 5 times shorter input data stream which allows a 5 time reduction of the measurement time Its fast execution is much more evident when it is compared to the method loaded by the clustering pre processing described in Section III 2 especially in the presence of a high signal space cardinality III 3 5 Conclusion An original method for estimating I Q impairments in digital transmitters has been presented It exploits the results of EV measurements and is appropriate in various stages production installation and maintenance of transmitter life cycle Simple and original algebraic expressions which relate the amount of occurred impairments to EV components represent the core of the method and allow overcoming typical limitations of measurement approaches proposed by leading manufacturers or suggested by measurement guidelines An extended experimental activity has shown the reliability and effectiveness of the proposed method when only one or two I Q impairments are signifi
70. in the variables Gand e p 9 IILA8 where A A B B o zl AP A i 111 49 B B A Ay and ASA OD aet 50 D B The idea is to obtain an estimation of gain imbalance and quadrature error respectively po and gi for each k As well known if det o 0 system 11 48 has a univocal solution and impairment estimates are A A A A B B B B po 2 aa 9 IIL 51 A 4 B B 4 A J 5 B det 6 52 81 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters It is worth noting that the case det 0 is not infrequent especially with regard to I Q diagrams characterized by low cardinality det o is in fact always null when sub carriers are QPSK modulated Nevertheless when det 9 0 it is still possible to estimate either gain imbalance or quadrature error provided that one of the columns of III 49 is identically null In this case in fact system III 48 collapses into two equations in the same variable which are theoretically linearly dependent As an example if o 9 0 III 48 reduces to B B g 2 4 A 111 53 A A 6 2 B B In actual situations a slight difference between the two equations in system III 53 can occur due to non idealities that have effect on the terms A and B at the output of the FFT block To contemplate this case the
71. ing are described following the classification given in 29 I 2 1 In band measurements A In channel measurements Channel bandwidth It 15 good practice first to perform a channel bandwidth measurement In most cases of interest depending on the baseband filter specifications the 3 dB bandwidth approximates the symbol rate its measurement can therefore reveal major errors in transmitter design Carrier frequency Carrier frequency measurements are of great importance Not only can frequency errors result in possible interference but they can also be responsible for possible problems in the carrier recovery process at receiver side Channel power Channel power is the average power of the signal in the channel according to the acceptation given in Section I 2 It is usually measured as the integral of power spectrum density over the frequency band of interest although the measurement method depends on the particular communication standard 30 31 32 Occupied bandwidth Occupied bandwidth 15 defined as the frequency interval centered at the tune frequency of the monitored channel over which the integral of the power spectral density equals x of the average power where x 15 usually chosen equal to either 95 or 99 Peak to average ratio Peak to average power ratio PAR 15 the ratio of the peak envelope power to the average envelope power of a signal during a given period of time CCDF curves PAR only ta
72. ixed receivers ETSI European Standard EN 300 401 v 1 3 3 2001 Digital Video Broadcasting DVB Framing structure channel coding and modulation for 11 12 GHz satellite services ETSI European Standard EN 300 421 v 1 1 2 1997 Digital Video Broadcasting DVB Framing Structure Channel Coding and Modulation for Cable Systems ETSI EN 300 744 Ver 1 3 1 1998 Digital Video Broadcasting DVB Framing structure channel coding and modulation for digital terrestrial television ETSI European Standard EN 300 744 v 1 5 1 2004 J G Proakis Digital Communications 3rd ed New York McGraw Hill 1995 C E Shannon A Mathematical Theory of Communication Bell Syst Tech J vol 27 pp 379 423 July 1948 C E Shannon A Mathematical Theory of Communication Bell Syst Tech J vol 27 pp 623 656 October 1978 D A Huffman A Method for the Construction of Minimum Redundancy Codes Proc IRE vol 40 pp 1098 1101 September 1952 C E Shannon Communication in the Presence of Noise Proc IRE vol 37 pp 10 21 January 1949 D Slepian Key Papers in the Development of Information Theory IEEE Press New York 1974 H Nyquist Certain Topics in Telegraph Transmission Theory AIEE Trans vol 47 pp 617 644 1928 I Gerst J Diamond The Elimination of Intersymbol Interference by I put Pulse Shaping Proc IRE vol 53 July 1961 D W Tufts Nyquist s Problem The Joint Optimization of Transmitt
73. kes into account the signal mean and the peak value and 15 strongly dependent on the duration of the signal More generally characterizing a signal by providing Chapter I Transmitter Testing and Troubleshooting information on just one power level e g the peak can be not sufficient This 15 particularly true for modern digital telecommunication systems which adopt more and more complex modulation schemes CCDF Complementary Cumulative Distribution Function curves provide a statistical description of power levels of an RF signal 33 A CCDF curve is in fact a plot of relative power level expressed in decibel dB versus probability Specifically CCDF x represents the probability that the signal envelope power is at least x dB above the average power Fig I 2 shows the CCDF curve of a digitally synthesized CDMA Code Division Multiple Access signal consisting of a single data channel 100 155 D OT 55 0 001 0 0 5 1 5 2 2 5 3 3 5 4 dB over avg power dB Fig I 2 CCDF curve of a CDMA signal Timing measurements Timing measurements are common on TDMA systems As transmitters in TDMA systems generate bursty signals turn on and turn off phases can introduce interference with adjacent frequency channels A set of measurements are usually carried out including burst width rise time fall time peak power and duty cycle in order to characterize the bursts Modulation quality measurements Modulation qua
74. l processing approach that operates on the transmitter output signal properly digitized by means of a DAS In particular it 15 based on a suitable clustering procedure mandated to the correction of the distorted pattern of received symbols and on an original measurement algorithm which faces the problem of separating the effects of different impairments acting at the same time in order to proceed to an accurate evaluation of their amount The method consists of three fundamental stages signal demodulation clustering and Fig III 1 I Q diagram for QPSK signal Fig III 2 I Q diagram for 16 QAM signal 54 Chapter III Impairments Detection and Evaluation impairment amount evaluation In particular signal demodulation detects the actual positions that symbols affected by impairments have on the I Q diagram The clustering procedure suitably pre processes the recovered symbols to univocally reveal the deviation of each of them from its ideal position on the I Q diagram Finally the contribution of each impairment to the deviations of all symbols is singled out and correctly evaluated according to a straightforward measurement algorithm 1II 2 2 Impairments affecting modulators I Q modulator combines I and Q signals coming from the baseband stage Due to potential different behavior exhibited by the I and Q paths 29 several impairments can take place which show up as anomalies in the transmitted signal
75. leshooting of Radiofrequency Digital Transmitters respectively 0 dBV and 25 kHz Fig II 13 shows the evolution versus time of the test signal which will be generated in analog form related to the initial transient B Experimental Setup The measurement station set up for assessing the performance of the method consists of a DSO a processing and control unit namely a PC and an AWG that provides the emulated signal All instruments are interconnected by means of an IEEE 488 standard interface bus The digitally synthesized signal 1s downloaded into the internal memory of the AWG which converts it in analog form The synchronization pulse emitted by the AWG at the beginning of the generation is routed to the trigger channel of the DSO which performs a single acquisition at a sample rate equal to 100 kS s The acquired samples are then transferred to the PC which applies the proposed method to measure the transmitter attack X 10 Instantaneous frequency trajectory 9 4 5 4 N 35 i 3 D D 25 LL 2 15 1 0 5 0 0 005 0 01 0 015 0 02 0 025 Time 5 Fig II 11 Instantaneous frequency trajectory of the test signal Instantaneous power trajectory 20 Power dB V7 30 40 798 0 005 0 01 0 015 0 02 0 025 Time s Fig II 12 Instantaneous power trajectory of the test signal 44 Chapter II Performance Evaluation Test signal V 0 0 0 005 0 01 0 015 0 02 0 025 Time s Fig II 13 Ev
76. lis Levinson s Algorithm Wold s Decomposition and Spectral Estimation SIAM Review N 27 pp 405 441 S M Kay J Makhoul On the Statistics of the Estimated Reflection Coefficients of an Autoregressive Process IEEE Trans on Acoustic Speech and Signal Processing vol 31 No 6 1983 pp 1447 1455 http www lecroy com tm products Scopes LCSeries LC684D XL TecnicalSpecificatio ns asp http www home agilent com cgi bin pub agilent Product cp Product sp NAV ID 536898379 536881805 00GLANGUAGE CODE eng amp CONTENT KEY 100000215 5Vo3aepsgo3apro amp ID 1000002155993aepsgVo3apro amp COUNTRY CODE US 92 References 51 52 LL 53 54 55 LL 56 57 LL LLL 58 59 60 61 LL 62 65 MS2687B Spectrum Analyzer Data Sheet Anritsu Catalog No MS2687B E A 1 4 00 2005 Agilent E4406A Vector Signal Analyzer Data Sheet Agilent Technologies Literature no 5968 3030E 2005 Agilent PSA Series Spectrum Analyzers Data Sheet Agilent Technologies Literature no 5980 1284E 2005 Agilent E4416A E4417A EPM P Series Power Meters and E Series E9320 Peak and Average Power Sensors Data Sheet Agilent Technologies Literature no 5980 1469E 2005 Agilent ESG A and ESG D RF Signal Generators Data Sheet Agilent Technologies Literature no 5989 4074EN 2005 http www eutelsat com Designing and Testing 3GPP W CDMA Base Transceiver Stations Application Note Agilent Techn
77. lity measurements involve the demodulation of the transmitted signal through an ideal receiver and the comparison of the demodulated signal to an ideal one The measurements to carry out depend on the particular modulation scheme and standard The Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters most common are EVM Error Vector Magnitude 32 34 phase and frequency error 31 coefficient rho p and code domain power 30 Error vector EV is defined as the vector difference between the actual and ideal symbol position on the I Q plane Fig I 3 Its magnitude EVM is a key modulation quality metric in most modern communication systems 35 since most impairments and non idealities of the transmitter affect its value Besides providing quantitative information on modulation quality a thorough analysis of EVM can help detecting which are the most significant impairments and non idealities of the transmitter under test this feature is discussed later in this chapter as it turns out to be useful in troubleshooting With regard to communication systems like GSM which characterized by constant envelope modulation formats modulation quality is determined by analyzing the I Q phase and frequency errors The phase error is determined by comparing the actual and reference phase trajectories whereas the mean gradient of the phase error evolution versus time is the frequency error Problems in the baseband secti
78. m characterizing the transmitter under test the output signal is suitably digitized and demodulated If the signal is outside the bandwidth of the data acquisition system a prior downconversion stage 15 required As nominally identical symbols are slightly spread the acquisition of a number of i i i I I I I I I B I I B I I EC I I a I I I I I I I I I I I I x E x X NL x I I I I I I b f 8 eo eae c eee ac I I I I I I I I I I I I zx i X 2x X 2x i X 2x X I I I I I I Aff vicis I I I I I I E I m E I m E I x I x I E I I I I I I I I I I I I aif ah ety ope er eee eee irre ae eget bee re Bem ect ea ac ee en ee sa ree ap ee nee were sence eee Oliver eee eg ee Em pet ee eee eg ees gee oe l l l l I dh I Li mx x 0X x X AE X EE I I I I I I I I I I E I Lj I ES LJ I I d I d I I I E i X i 2 i zx 2 i zx i 25 i X I I I A T por EE mene L fem E ann ene Sp end MN NEUE men c UR I I I I I I aL 4 aL 4 X a i X X X X X bd I I I I I I 1 7 eee ee ee d d I I I I I I I I I I I I x p x X x E x x 5 x p x I I I I I I I I I I I I BT gpeesemes emo mmm yo m UNI vence dE y Boum I I I I I 8 5 D X D A c TIMES I I I
79. made 83 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters available by the VSA have been transferred to the control and processing unit via the IEEE 488 bus The proposed measurement algorithm running on the processing and control unit has provided the estimates of the detected I Q impairments B Results Table IIL6 and Table 7 summarize the results obtained for each sub carrier modulation pattern taken into account They also gives the range of values within which amounts of imposed impairments have been chosen Results are given in terms of minimum and maximum values of difference between imposed and measured impairment amount A Table IIL 6 and experimental standard deviation o Table 7 Both A and o are expressed in percentage relative terms Gain imbalance is normalized to the value of Q branch gain Go and voltage offsets c and cg are normalized to the nominal peak value of the baseband component From the analysis of the values accounted for in Table III 6 and Table III 7 the following considerations can be drawn Table III 6 Measurement results difference between imposed and estimated values Range of values of imposed 1 0 impairments 0 05 0 30 HT 0 05 0 30 0 18 0 93 0 77 0 05 0 30 0 10 0 55 0 30 Table III 7 Measurement results experimental standard deviation Range of values of imposed I Q impairments 84 Chapter III
80. mulation Results IEEE Communications Letter vol 5 No 3 March 2001 pp 88 91 K Voelker Apply Error Vector Measurements in Communications Design Microwaves amp RF Dec 1995 J K Cavers and M W Liao Adaptive compensation for imbalance and offset losses in direct conversion transceivers JEEE Trans Veh Technol vol 42 pp 581 588 Nov 1993 R Hassun M Flaherty R Matreci and M Taylor Effective evaluation of link quality using error vector magnitude techniques Proc IEEE Wireless Commun Conf 1997 pp 89 94 M Heutmaker The error vector and power amplifier distortion Proc of IEEE Wireless Communications Conf 1997 94 References 79 80 81 82 83 84 85 86 87 88 89 T Nakagawa and K Araki Effect of phase noise on RF communication signals in Proc of IEEE Veh Tech Conf 2000 vol 2 2000 pp 588 591 H Ku and J S Kenney Estimation of error vector magnitude using two tone intermodulation distortion measurements Proc IEEE MTT Microwave Symp Dig vol 1 2001 pp 17 20 J L Pinto and I Darwazeh Phase distortion and error vector magnitude for 8 psk systems Electronic Letters vol 37 pp 437 438 2001 A Georgiadis Gain Phase Imbalance and Phase Noise Effects on Error Vector Magnitude IEEE Transactions on Vehicular Technology vol 53 No 2 March 2004 pp 443 449 S Hori T Kumagai T Sakat
81. n Fig I 5 Fig I 6 and Fig I 7 where red dots represent the nominal symbol positions and blue crosses correspond to the actual symbol positions due to impairments An analytical model for the effects of such impairments on the demodulated signal is presented in III 2 Amplitude Q Aff 247 Amplitude IL Fig I 5 Effect of the presence of gain imbalance for a 64 QAM signal constellation with unitary maximum I Q component value 13 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Amplitude Q 8 7 6 7 4T 247 0 2 Af 6 7 of Amplitude Fig I 6 Effect of the presence of quadrature error for a 64 QAM signal constellation with unitary maximum I Q component value Amplitude Q 8 7 6 7 4i T 247 0 2 AT Bf of Amplitude Fig I 7 Effect of the presence of positive offsets on the in phase and quadrature components for a 64 QAM signal constellation with unitary maximum I Q component value The presence of I Q impairments can be inferred by analyzing the EVM although it is difficult to determine which impairment is present without a look at the I Q diagram 14 Chapter I Transmitter Testing and Troubleshooting 1 3 3 Incorrect symbol rate An incorrect symbol rate 1s a defect of the symbol encoder which can affect the ability to correctly interpret symbols at receiver side Its presence can be deduced from the evolution versus time of EVM which exhibits
82. n digitized at different sampling frequencies with the aim of investigating the role of the parameter p For each signal and each given sampling frequency several acquisitions have been made and the related CCDF curves have been evaluated Then the measurement result for the considered signal has been expressed in terms of the average CCDF curve which has Table II 4 Average values of rmse between measured and reference CCDF curves WINDOW SIZE 2F 3T 4 T EM c Homing 099 ww pus ux aur 38 WINDOW TYPE Chapter II Performance Evaluation been obtained by calculating the average value for each abscissa 1 6 for each power level For the sake of brevity Fig II 9 shows the outcomes of the application of the two approaches to a 3G signal modulating a carrier at 449 4 MHz in particular Fig II 9a 1s related to the time domain approach while Fig II 9b refers to the time frequency approach The two figures compare the CCDF curves gained through the proposed approaches when different sampling frequencies have been utilized to the CCDF curve provided by the VSA In all the cases the digitized signal has been downconverted to 21 4 MHz with different values of the integer p Specifically in each figure 1 the dashed line 1s the CCDF curve achieved when the RF signal is sampled at f 428 MS s p 20 11 the dotted line is related to a sampling 0 00194 sierra vsa
83. n transceiver characterization 75 35 76 as it provides information on the overall modulated signal quality bearing traces of possible causes of signal distortion ranging from I Q impairments to phase noise and power amplifier non linearity 77 78 79 80 81 82 83 B I Q impairments model Expression 111 2 for the IF signal y t at the output of an I Q modulator affected by such impairments can equivalently be rewritten as yy G e c Yp 0 cosQ fist III 14 G 1 g co Ym 9 0 sinQz frt where g 15 the semi difference between the gains on the two branches normalized to their average value G 1 9 G G g 111 15 G and 64 Chapter III Impairments Detection and Evaluation G G p J 11 16 In the case of unity average gain G 1 relation 11 14 yields the following expression for the equivalent baseband signal affected by impairments z 7 s 1 1 g 1357 t J 1 g Cg ee t el 11 17 C Limits of currently available proposals As stated above the analysis of the constellation diagram suggested by troubleshooting procedures of leading manufacturers is effective only in the case that no more than two impairments simultaneously affect the I Q modulator Indeed in the presence of one or two impairments it provides only qualitative information For the sake of clarity Fig III 7 shows the constellation diagram of a QPSK
84. nal appreciation goes to each and every member of the group from leading professors to technicians and young researchers with whom I have had the occasion of exchanging ideas and cooperating I would like to direct a very special thank to Prof Antonio Langella the dean of our group whose incomparable expertise firm guidance fruitful help and personal dedication are of immeasurable value Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters I am also personally grateful to Prof Nello Polese for his valuable teachings and precious encouragement Prof Aldo Baccigalupi for his human support and helpful suggestions and Prof Felice Cennamo for his motivation and his kindness A warm thank to my dear colleagues and friends Mauro D Arco Nicola Pasquino Rosario Schiano Lo Moriello Annalisa Liccardo and Alessandro Masi with whom I have cooperated exchanged ideas and had a lot of fun too It 15 also my sincere desire to acknowledge Antonio Grillo Umberto Cesaro and Alessandro Teotino for their help and availability Last but not least I must give immense thanks to my parents and my sister for the unconditional support they have provided me through my entire life and to my beloved Angela the greatest joy in my life who illuminates my existence and makes every day a special day with her love VI Contents CONTENTS ne er een re rere ce emt l CHAPTER I
85. nals Proposed method 29 65 0 0007 29 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Table II 2 Comparison of measurement results obtained in the experiments on downlink WCDMA signals VSA 43 29 IE mI sem pee pm pom The results of the proposed method are compared to those provided both by the method based on non parametric estimation 44 and other instruments included in the measurement station Specifically the power meter and VSA have executed respectively average and channel power measurements whereas the spectrum analyzer and PSA have provided both occupied bandwidth and channel power values From the analysis of the results the following considerations can be drawn Concurrence of measurement results achieved through different methods and instruments 1s experienced Repeatability of the proposed method is comparable to that of the method based on non parametric estimation experimental standard deviations are very similar to each other Experimental standard deviation of the proposed method is significantly lower than dBm b3 uA 61 62 63 64 65 66 67 68 69 70 7l Frequency MHz Fig II 3 PSD of a WCDMA signal estimated through the proposed approach 30 Chapter II Performance Evaluation that characterizing measurements carried out through the spectrum analyzer It 15 even lower with respect to VSA and PSA which are specifically addressed to this kind of
86. ncy 53 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters is often available for the analysis Unfortunately the overall effect observable on the output signal is normally due to different simultaneous impairments which must be separated one from the other In addition combined impairments could drive one or more symbols out of their own decision regions causing impairment evaluation to fail The aforementioned problems do not seem to be adequately faced by standard measurement guidelines 34 and test and measurement solutions proposed by major manufacturers 29 57 32 In particular 1 neither rules for distinguishing the specific contribution of each impairment in the output signal are provided 11 nor the possibility of symbols outside their own decision regions 1s taken into account In particular the occurrence of condition 11 may make inapplicable troubleshooting procedures 29 and measurement methods presented 1n the literature 67 which are based on a decision directed strategy This is particularly critical when constellation diagrams are characterized by high cardinality as the minimum distance d between ideal symbol position and decision region boundary decreases with cardinality see Fig III 1 and Fig III 2 An original measurement method for a comprehensive evaluation of I Q impairments also in the aforementioned critical conditions is presented hereinafter It follows a digital signa
87. nded result D Chirplet optimal parameter choice To exploit CT s capabilities its parameters must be suitably tuned according to the local characteristics of the analyzed signal Table II 5 Results achieved with optimal windows IMS freq Optimal length rmse FMSC yo V TMSC fred firms TMSC pol Prms kHz Gaussian 0 136 0 91 96 Hanning Hamming Chapter II Performance Evaluation x 107 Instantaneous frequency measured trajectory 4 5 a nominal trajectory Frequency Hz n3 0 0 005 0 01 0 015 0 02 0 025 Time s Fig II 14 Instantaneous frequency trajectory gained when optimal values of STFT parameters are used Measured solid line and nominal dotted line trajectories are compared Instantaneous power trajectory Power dB measured trajectory nominal trajectory 0 005 0 01 0 015 0 02 0 025 Time s Fig II 15 Instantaneous power trajectory gained when optimal values of STFT parameters are used Measured solid line and nominal dotted line trajectories are compared With regard to window type the 37 tap Gaussian window which has come out to be optimal for STFT has been used also for CT Concerning chirp rate c and bending factor b their values have been determined from the analysis of a reference frequency trajectory The same frequency trajectory considered for STFT optimization has been used for the purpose In detail 1t has been digitized at the sam
88. nt Technologies Literature No 5968 3578E 2002 Understanding CDMA measurements for base stations and their components Application Note 1311 Agilent Technologies Literature no 5968 0953E 2000 Understanding GSM EDGE Transmitter and Receiver Measurements for Base Transceiver Stations and Their Components Application Note 1312 Agilent Technologies Literature No 5968 2320E 2002 Understanding PDC and NADC Transmitter Measurements for Base Transceiver Stations and Mobile Stations Application Note 1324 Agilent Technologies Literature No 5968 5537E 2000 Characterizing Digitally Modulated Signals with CCDF Curves Application Note Agilent Technologies Literature No 5968 6875E 2000 Digital Video Broadcasting DVB Measurement Guidelines for DVB Systems ETSI Tech Report 101 290 Ver 1 2 1 2001 Using Error Vector Magnitude Measurements to Analyze and Troubleshoot Vector Modulate Signals Product Note 89400 14 Agilent Technologies Literature No 5965 2898E 2000 L Angrisani M D Apuzzo M D Arco New digital signal Processing approach for transmitter measurements in third generation Telecommunications systems IEEE Trans Instrum Meas vol 53 No 3 pp 622 629 June 2004 9 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 37 38 39 40 41 42 45 44 45 46 47 48 49 50 Comparing power me
89. od performance of the method differences between imposed and measured impairment amounts and experimental standard deviations generally lower than 6 have been experienced Moreover no dependence on the particular modulation pattern adopted on sub carriers to characterize measurement results 7 7 7 Y A 7 Yj 7 Y 2 Yj A f 7 NNNNNNN SOY RY RA Fig 111 19 Measurement results for QPSK sub carrier modulation in the presence of gain imbalance and quadrature error a difference from imposed and measured amounts and b experimental standard deviation concerning gain imbalance measurements c difference from imposed and measured amounts and d experimental standard deviation concerning quadrature error measurements All differences and experimental standard deviations are expressed in percentage relative terms 86 Chapter IV Conclusion CHAPTER IV CONCLUSION This Ph D thesis has dealt with performance evaluation and troubleshooting of radiofrequency digital communication transmitters The original contribution has consisted in the proposal of innovative measurement methods based on digital signal processing and addressed to power measurement CCDF curve evaluation transient measurement and I Q impairment detection and evaluation Suitable measurement stations have been set up to experimentally test all the proposed methods and assess their performance Experimental outcomes including comparison
90. ologies Literature No 5980 1239E 2003 L Angrisani M D Arco R Schiano Lo Moriello M Vadursi Optimal sampling strategies for band pass measurement signals Proc of XIII IMEKO Intern Symposium on Measur for Research and Industry Appl Athens Greece 29 Sept 01 Oct 2004 pp 343 348 L Angrisani M D Apuzzo M D Arco New digital signal processing approach for transmitter measurements in third generation telecommunication systems IEEE Trans on Instr and Meas vol 53 n 3 pp 622 629 June 2004 C Balz CCDF determination a comparison of two measurement methods News from Rohde amp Schwarz n 172 pp 52 53 2001 Electromagnetic compatibility and Radio spectrum Matters ERM Land mobile service Radio equipment intended for the transmission of data and or speech using constant or non constant envelope modulation and having an antenna connector Part 1 Technical characteristics and methods of measurement ETSI EN 300 113 1 v 1 5 1 September 2003 Measuring Transmitter Transients with the 89400 Series Vector Signal Analyzers Product Note 89400 5 Agilent Technologies Literature No 5962 9493E 2000 Measuring Frequency Settling Time for Synthesizers and Transmitters Rohde amp Schwarz Literature Application Note No IMAI5 OE 1999 93 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 64 65 66 67 68 69 70 71 72 75 74
91. olution versus time of the test signal time C STFT optimal window function STFT results depend on the particular window function adopted Hence an optimal choice of the type and size of the window 1s desirable Common window functions such as Gaussian Hanning Hamming and Blackman have been considered 66 Different window sizes have been taken into account too In particular measurements have been carried out using all possible combinations of the four considered window types and window sizes ranging from 20 to 120 samples For each parameter combination frequency power and combined rmse have been evaluated which are defined respectively as 1 33 1 34 rmse rmse Y rmse Em E 5 35 where fi and P i are the nominal frequency and power trajectories and f i and P i are the measured ones Moreover firms and Pims are respectively nominal frequency and power rms values 45 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters The optimal window function 15 the one characterized by the lowest rmse For each type of window function Table II 5 indicates the optimal window length along with related values of rmse Results reported in Table 5 show that each window actually provides the same minimum rmse Therefore any of the considered windows can equivalently be utilized provided that the respective optimal length is selected In the experiments a 37 tap Ga
92. ombinations of imposed impairment amounts The following considerations arise The lower the impairment amount the higher the values of A and o The existence of a sensitivity limit for the method can be inferred When different impairments are simultaneously present measurement results for one of them are influenced but not compromised by the amounts of the others It 15 generally true and evident from Fig III 19 that the higher the amount of quadrature error the higher the values of A and o experienced with regard to gain imbalance measurements The dual case is equally true and evident from the same figure III 4 5 Conclusion A new method for the evaluation of I Q impairments in OFDM transmitters has been presented The method is based on a suitable analytical model that properly accounts for the way I Q impairments affect the RF output signal taking into account the effect of mirror sub 85 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters carrier interference The analytical model exploited and with the original measurement procedure implemented allow overcoming key limitations of other solutions mainly designed for traditional transmitter testing and troubleshooting Moreover the method does not require particular test input sequences thus allowing non intrusive measurements Results of a wide experimental activity carried out on laboratory OFDM signals have given evidence of the go
93. on of the transmitter and distortion introduced by the output amplifier are possible causes of phase error A stable frequency error is due to a difference between specified and actual carrier frequency whereas short term instability of the local oscillator is one of the possible causes of unstable frequency error Coefficient 15 one of the modulation quality metrics used in CDMA systems It 15 the ratio of correlated power to total power transmitted when a single code channel 15 transmitted The transmitted energy that does not correlate behaves as added noise with 0 p d _ Actual symbol position eee of Error Vector measured Error Vector 9 4 Phase of Error Vector Lo Ideal symbol position reference Fig I 3 Error vector definition 10 Chapter I Transmitter Testing and Troubleshooting consequent potential interference on other channels Code domain power measures the fraction of total power transmitted in each code channel of a CDMA system it 1s evaluated through code correlation algorithms B Out of channel measurements Adjacent Channel Power Ratio Adjacent Channel Power Ratio ACPR is defined as the ratio of the average power in the adjacent channel to the channel power It gives information about the interference of the signal under examination on adjacent channels As ACPR depends on the statistics of the transmitted signal care must be taken to perform ACPR measurements with sense S
94. or any OFDM symbol Expressions III 43 and III 44 yield I e c 1 8 c jc 11 45 G component component Fig III 16 I Q diagram of an OFDM signal 78 Chapter III Impairments Detection and Evaluation K where x is the complex conjugate of x and h mod K k K that is the remainder of From expression III 45 another significant difference between OFDM and classical QAM modulation emerges If both channel and receiver are assumed to be ideal the actual positions of received symbols on any of the K I Q diagrams related to a single sub carrier also depend on the symbols transmitted on the so called mirror sub carrier referred to as A Consequently for a given amount of I Q impairments actual symbol positions are not univocally determined As a Clarifying example let us suppose that the complex symbols Co n C n at the input of the IFFT block be QPSK modulated and let C o n C n C k j n be the n th OFDM symbol recovered by an ideal receiver at the output of the FFT block Fig III 17 depicts the diagram related to the generic k th sub carrier achieved from the sequence C ie n t n 1 2 n stands for time when quadrature error and gain imbalance affect the transmitter possible symbol locations on the diagram turn out to be 16 instead of 4 Let us now consider one of the 4 symbols in the original QPSK diagram For a given
95. ory depth 40 MHz maximum sample clock or the output of a low noise downconverter 52 dB gain 0 7 dB noise figure fed by the satellite signal received through a 1 790 m diameter parabolic antenna All the instruments except the satellite station are interconnected by means of an IEEE 488 standard interface bus B Laboratory wideband signals WCDMA test signals have been generated by exploiting the AWG capability of the digital RF generator Both uplink and downlink signals have been considered The RF signal is given in input to the spectrum analyzer Anritsu MS2687B which operates in zero span mode to downconvert it to 66 MHz intermediate frequency The downconverted signal 1s digitized by the DSO at 200 MS s and a record of 32 768 acquired samples is retrieved Measurement algorithms are then applied to the acquired samples in order to evaluate average power channel power and occupied bandwidth C Real wideband signals Experiments have been carried out also on real telecommunication signals In particular two different DVB S signals RAJ International 4 and BBC Prime have been taken into account which are emitted respectively by Hot Bird 1 transponder number 8 and Hot Bird 28 Chapter II Performance Evaluation 3 transponder number 27 satellites 56 RAI International 4 signal is in particular characterized by a central frequency equal to 11 381 GHz a symbol rate equal to 4 4 Msymbol s and a FEC Forward Error
96. out the experimental setup are given and experimental results are commented on in order to assess the performance of the method II 2 Power measurement II 2 1 Introduction Power measurement in digital wireless communication systems 1s not an easy task This is particularly true in the presence of spread spectrum and or wideband signals due to their noise like nature and high crest factor peak to average power ratio Repeatability problems usually accompanied by low accuracy are in fact often experienced in power measurements involving the integration of the power spectral density PSD of the RF signal over a specified 19 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters frequency range 30 36 37 38 39 channel power occupied bandwidth and adjacent channel power ratio measurements are relevant examples 2 40 41 42 43 With the aim of overcoming the aforementioned problems a method for power measurement in digital wireless communication systems has recently been published 44 which 15 based on non parametric solutions for spectral estimation The main limit of the method is its heavy computational burden which can compromise its use in production and testing stages of digital wireless equipment Reducing measurement time while granting the same good repeatability as that provided by the use of non parametric PSD estimators 1s still an open issue To this end the utiliz
97. pecifically test signals must be accurately chosen because the results of ACPR measurements made on the same transmitter can significantly vary depending on the statistics of the signal As an example higher values of PAR can be responsible for more interference similarly the number of data channels in CDMA systems have direct impact on the power statistics of the signal and therefore on ACPR It has to be said that adjacent channel power measurements are differently named and carried out according to different communication standards 30 31 32 Spurious It can happen that spurious emissions due to combination of signals in the transmitter fall within the band of the communication system Standards usually define power levels spurious that in band emissions must not reach in order to avoid interference with other frequency channel of the system 1 2 2 Out of band measurements Spurious and harmonics Spurious emissions outside the system frequency band are due to transmitter non linearities They can be responsible for interference with other communication systems 1 5 Transmitter troubleshooting Conformance of a transmitter with the standard is verified through tests which can be performed at the antenna port as well as at other sections of the transmitter Since impairments that can occur at different parts of the system are responsible for performance 1 Performance Evaluation and Troubleshooting of Radiofrequenc
98. perimental standard deviation o in percentage relative terms related to c amplitude imbalance and d quadrature error 61 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters Table III 1 Results of experimental tests on signals affected by different combinations of impairments Imposed impairments A 9o B rad CI CQ B c P rad ci From the analysis of the results the following considerations can be drawn The proposed method provides good results in terms of difference between imposed and measured impairments A 1s in fact always inferior to 5 It also offers satisfying repeatability since o is inferior to 7 for quadrature error measurements and lower than 4 with regard to all the other impairments Both A and o values 1 decrease upon the increasing of the amount of the impairment and 11 increase upon the increasing of the amount of the other impairments The performance of the method is slightly worse for higher I Q diagram cardinality The method 15 capable of detecting and evaluating the amounts of more than two impairments that simultaneously affect the modulator and its range of application is not limited to I Q diagrams characterized by low cardinality 1 2 9 Conclusion A new digital signal processing approach aimed at troubleshooting transmitters in QAM based telecommunication systems has been dis
99. power measurement results obtained in the experiments On B SS Saks cor E 31 Table II 4 Average values of rmse between measured and reference CCDF curves 38 Table II 5 Results achieved with optimal windows eese 46 Table II 6 Measurement results related to the 49 Table II 7 Measurement results related to the 1 8 50 Table III 1 Results of experimental tests on signals affected by different combinations of eeu RE eens EcL EIE DH d T EM cc Ub EE 62 Table IIL 2 Impairment amounts for WCDMA signals sees T2 Table III 3 Impairment amounts for DVB signals eese 73 Table III 4 Measurement results for WCDMA signals eese 74 Table 5 Measurement results for DVB 75 Table III 6 Measurement results difference between imposed and estimated values 84 Table III 7 Measurement results experimental standard 84 101
100. re g is given by g Im EV ane 111 31 Ybb O and c can be obtained from Re y Re EV ane J 8 Yoo _ 11 32 69 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters B 3 Gain imbalance and offset co When gain imbalance and cg are present at the same time the error vector EVgainco has the following expression a DEBE co L 8 X45 011 33 Impairments can thus be estimated as e OUR 34 and J 8 wo Q 14 2 l l B 4 Quadrature error and offset co The combination of quadrature error and cg leads to the following expression for the error vector EV 4 0 EV Yung 8ind J cg Ying COSH Ying 111 36 Therefore impairment amounts can be estimated as Ref EV atan 5 11 37 Im EV Yano and Re EV 39 sing B 5 Quadrature error and offset cl If quadrature error and offset c jointly act the error vector is expressed as EV C Xp o SING J Yo o 054 1 39 and to estimate the amount of the considered impairments the following steps have to be taken 1 Received symbols are separated into groups characterized by the same y o 70 Chapter III Impairments Detection and Evaluation 2 For each group the average of Re EV 7 namely Re EV ee 15 computed 3 Differences Aree between Re p of the two groups characteriz
101. s The proposed methods are based on digital signal processing and operate in time frequency time frequency and modulation domains Besides being based on rigorous methodological approaches the proposed methods take advantage of a wide experimental activity All the proposed methods are extensively tested by applying them to simulated emulated and real communication signals Measurement results are analyzed and compared to those achievable through the application of existing methods and or instrumentation available on the market M Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters IV Acknowledgements ACKNOWLEDGEMENTS Many are the persons I would like to thank for their support and concrete help in the development of this work Two of them Prof Massimo D Apuzzo and Prof Leopoldo Angrisani have their names written at the bottom of the front page as my tutors though they deserve to be put at the very top I express my personal gratitude to them whose continuous inspiration and scientific support have been driving factors to accomplish this goal A sincere thank goes to Prof Giovanni Miano who has coordinated the Ph D course with competence and devotion It has been my pleasure and luck to work in the unique workgroup of Electrical and Electronic Measurements of the University of Naples Federico II It 15 a very special scientific and research group of which I am proud to be part My perso
102. s of the RF signal Specifically they consist of three steps 1 signal digitization 11 instantaneous power trajectory evaluation and 111 CCDF curve determination A Signal digitization First the RF signal s t is digitized by a DAS at the sampling frequency provided by one of the algorithms presented in 58 The role played by such algorithm is quite important it lets the user choose the integer ratio p between the sampling frequency fs and the frequency at which the spectrum of the digitized signal will be centered and then outputs the minimum value of the sampling frequency that satisfies such requirement It 1s so possible to digitally downconvert the input signal thanks to a sampling frequency much lower than the carrier frequency with consequent benefits in terms of frequency resolution Equivalently it is possible to analyse a larger time interval given the number of samples Moreover as it will be clear soon with regard to the time domain approach it grants the advantage of acquiring an integer number of samples per carrier period 34 Chapter II Performance Evaluation B Instantaneous power trajectory evaluation gt Time domain approach The first proposed approach moves from the following consideration the carrier frequency is higher than the symbol rate or chip rate with regard to 3G signals 2 and consequently one symbol modulates several carrier periods It therefore makes sense to average the square
103. seems to be considerable above 3 dBm is on the contrary irrelevant In other words the discrepancy between the two curves that appears to be significant over 3 dBm 1s referred to power levels that are seldom reached by the RF signal In conclusion low values of p p 4 5 are generally preferable even though higher values have also provided good results Similar outcomes have been experienced with regard to other considered signals II 4 Transmitter transient measurement II 4 1 Introduction As well known typical functioning of wireless transmitters generally involves power and or frequency transients Both transients are experienced at the transmitter switching on and similarly during bursty transmissions Another example is provided by TDMA and spread spectrum systems where rapid and continuous carrier power changes intended to maximize spectrum utilization and battery life naturally determine power transients Moreover frequency transients occur when transmitters switch from one channel to another The main problem connected with transmitter transients is possible interference to other stations To avoid such interference transmitter attack time 1 6 the time it takes to switch its output power on should be short enough The standard issued by ETSI European Telecommunication Standard Institute on electromagnetic compatibility and radio spectrum matters includes a section on measurements of transmitter transient behavior
104. signal when a gain imbalance g 0 1710 and a quadrature error 7 32 rad are jointly present dots are the actual symbol positions while crosses are the expected ideal ones Although it can be clearly stated from a look at the dashed diagram that a rotation and an unevenness between the two axes are simultaneously present no quantitative information can be gained concerning the impairment amounts At the same time analytical relations suggested in 34 are of no use since the required separation of the effects of different impairments is impractical t Fig III 7 Effect of joint gain imbalance and quadrature error on the constellation diagram of a QPSK signal and are respectively equal to 0 1710 and 7732 rad 65 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 1II 5 3 Proposed method Besides overcoming the limits of manufacturers troubleshooting procedures and measurement guidelines the proposed method aims at estimating the amount of I Q impairments that affect a digital transmitter in a reduced measurement time It 1s in particular effective when one or two impairments are predominant and received symbols do not cross the boundaries of their original decision regions which are very frequent conditions with digital transmitters troubleshooting The fundamental stages of the method can be summarized as follows The presentation order given below reflects a typical exec
105. signals Regarding measurement time the proposed method comes out to be much more convenient and effective The application of the proposed method takes in fact from about 4 to 14 of the time needed to apply non parametric estimation whatever the configuration adopted With regard to real signals the proposed method has proved effective and exhibited good performance even in very critical measurement conditions Fig II 4 Table II 3 Comparison of channel power measurement results obtained in the experiments on DVB S signals RAI International 4 BBC Prime u dBm o dBm u dBm o dBm 52681 01 Mar 2005 10 44 36 Ref Level 54 00dBn DET Pos Peak 10dB Tracc A Center 1 632 50GHz Fig II 4 PSD of Rai International 4 signal attained through the spectrum analyzer Anritsu MS2687B very critical measurement conditions are highlighted 3l Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters 1 2 9 Conclusion A new method for power measurement in digital wireless communication systems has been presented It is based on parametric spectral estimation following Burg s solution Besides overcoming repeatability problems which often affect such measurement the method copes with the long convergence time that is the main limitation of an alternative method based on non parametric spectral estimation and presented in 44 The performance of the method h
106. surements performed at its RF output leading manufacturers suggest looking at the constellation diagram of the transmitted RF signal 29 Besides being impracticable when more than two impairments are present at the same time this solution allows only qualitative estimation of impairment amount because no appropriate relations are put at user s disposal ETSI measurement guidelines concerning DVB provide on the contrary useful relations which are however effective only in the case that a single impairment affects the I Q modulator 34 Two different methods allow overcoming the aforementioned limitations the method proposed in 67 and the one presented in the previous section Both of them are capable of separating and estimating all I Q impairments simultaneously present In particular the presented in the previous section assures better accuracy for high signal space cardinality and works properly even when received symbols are outside their correct decision regions whereas the method described in 67 is more accurate in the case of a low cardinality Computational load of both methods however could be too heavy also in some uncomplicated situations very frequent in practice such as those in which only one or two impairments are predominant and received symbols do not cross the boundaries of their original decision regions To grant lighter computational burden and consequently reduced test and measurement time in such uncomplica
107. tantaneous frequency and power trajectories provided by the method when CT is applied Very similar trajectories are obtained through STFT The measurement has been repeated after tuning transmitter steady state carrier frequency f to 85 817 MHz when the signal sampled at 250 kS s is centered at 67 kHz Table H 6 enlists achieved results expressed in terms of power and frequency transient duration respectively t and t and transmitter attack time ta which is equal to max t t in accordance to the standard definition Results show that attack time is basically Evolution versus time of the acquired signal 3 5 Amplitude V 0 0 002 0 004 0006 0 008 0 01 0 012 0014 0016 0 018 Time s Fig II 16 Evolution versus time of the signal acquired from the bug transmitter 48 Chapter II Performance Evaluation Instantaneous frequency trajectory Frequency Hz 0 0 0 002 0004 0 006 0008 O01 0 012 0 014 0 016 Time s Fig II 17 Instantaneous frequency trajectory obtained through the use of CT of the signal at the output of the bug transmitter Instantaneous power trajectory 20 0 0 002 0 004 0 006 0 008 0 01 20 012 0014 0 018 0 018 Time 5 Fig II 18 Instantaneous power trajectory obtained through the use of CT of the signal at the output of the bug transmitter determined to frequency transient No significant discrepancy in the results emerges when the adopted TFR is either CT or STFT differences bet
108. tations introduced in the previous section the continuous line vectors represent the ideal signal y while the dashed line vectors represent the signal with impairments Zp and the dotted line vectors represent the EV A 1 Gain imbalance When only the gain imbalance g is present the error vector can be written as 66 Chapter III I O Impairments Detection and Evaluation EV x 1 8 E 0 6 ybb X 04 i02 08 06 2 1 2 0 4 ybb 75 Pa 0 6 d i E 0 8 1 puc 04 06 08 ES b bb y S zbb s a WE Fig III 8 EV components due to a gain imbalance equal to 0 1146 1 w E 0 8 wW v ybb zbb X 4 0 2 lema 2 ia yb Z D 4 2 0 5 zbb 4 4 2 04 06 08 1 mr Fig III 9 EV components due to a quadrature error equal to 7716 rad EV gain and therefore g can be estimated as Ybb Q kp yg e 8 F Imo Amy EV gain 18 19 Ybb 1 The operators Re x and Im x respectively give the real and imaginary part of input x 67 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters EV EV N A zbb E a E NM ybb M L pbb N 0 4 3 2 02 02 04 06 08 1 f 0 2 S ET A 0 4 S zbb 7 M zbb ybb 9s 0 5 ht is 1 y EV EV Fig III 10 EV components due to a voltage offset on
109. ted situations a new and straightforward measurement method 1s proposed hereinafter After a preliminary analysis of the constellation diagram with the aim of singling out the predominant one or two I Q impairments the method provides for the 63 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters calculation of the error vector for each transmitted symbol The amount of the detected I Q impairments is then evaluated through the application of original and simple algebraic relations which involve the components of the error vector and the considered impairments 1II 5 2 Theoretical background A Error Vector As well known an I Q modulator allows a discrete set of symbols to be represented by a specific constellation diagram on a bidimensional space namely the I Q plane Impairments affecting the transmitter system non idealities as well as thermal noise can result in a deviation of the actual symbols from their ideal positions on the diagram EV 1s defined as the vector difference between the actual and ideal symbol position on the I Q plane Fig I 3 its components along the I and Q axes are generally referred respectively to as the EV real and imaginary part Several international standards specifications and technical literature 29 34 70 71 72 73 74 consider the magnitude of the error vector EVM a key metric for RF transmitter testing and troubleshooting EVM 15 also important i
110. terest and its group delay should be constant across the same bandwidth A typical impairment that can affect IF filters 1s ripple in the frequency response which causes a degradation of the I Q diagram accounted for by EVM 1 3 6 Local oscillator instability Instability of local oscillators LO may induce interference with other channels Both I C diagram and phase error evolution versus time give evidence of LO instability 1 5 7 Interfering tones An interfering tone can disturb the transmitted signal if it falls within the signal s bandwidth while it can cause interference with other channels or systems if it is outside of the signal bandwidth While the frequency domain analysis of the transmitted signal frequency can clearly give evidence of the latter case 1t could be of no utility in the former since the tone could be masked inside the spectrum On the contrary the I Q diagram can reveal circles around nominal positions of the symbols if the tone amplitude is not too small Circles due to 16 Chapter I Transmitter Testing and Troubleshooting a tone of small amplitude may in fact be confused with noise A good method to measure amplitude and frequency of interfering tones is to perform a spectral analysis of the EV As shown in Fig I 10 the tone stands out of the magnitude spectrum of the EV Magnitude of Error Vector Spectrum Fig I 10 Magnitude spectrum of EV in the presence of an interfering tone ins
111. the optimal AR model order p along with estimates 9 53 pO of the parameters 4i p Qp p Op that appear in 11 4 are assessed Burg still uses relations II 13 and II 14 but estimates the partial autocorrelation coefficient on the basis of observed data rather than estimated autocovariance sequence Specifically the approach followed to estimate consists in minimizing a certain sum of prediction errors namely N 53 hr E E k emt x 15 t k 1 where k and k are the so called observed order k forward and backward prediction errors whose expressions are respectively 23 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters k k X gt bpp Xim kt1 lt t lt N 11 16 m l and k Crk k SAk gt mk t kam k l lt t lt N 1 12 m By substituting 11 13 into expressions 11 16 and II 17 and rearranging observed order k forward and backward prediction errors can be calculated in terms of order k 1 errors according to 6 1 1 kt lt t lt N 18 and 4 k amp _ K 1 G amp 6 k 1 lt t lt N 11 19 Function SS in II 15 can then be equivalently written as a quadratic function of dy ies 53 UT Ay 2h B Aid 1 20 whose coefficients are N A gt E k 1 e k 1 1 21 t k 1 and N B 2 k 1 amp k 1 11 22 t k 1 The value of dy y that minimi
112. to an ideal reference as it will be shown in the following a number of possible impairments and non idealities that are responsible for signal distortion in the modulation domain can be inferred by modulation domain measurements Finally a potentially powerful tool in transmitter testing is constituted by time frequency representations TFRs 23 24 25 26 27 28 TFRs which are implemented through digital signal processing algorithms account for the evolution of signal spectral content versus time and can provide some advantages in terms of measurement efficiency and costs Their use is at the basis of some of the measurement solutions presented in the following sections of the thesis Measurements on digital communication transmitters are classified into in band and out of band measurements In band measurements are carried out within the frequency band occupied by the particular communication system and are further divided into in channel and out of channel measurements In such classification the channel is to be intended as the Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters frequency channel the transmitter 1s operating in and it does not necessarily coincides with the common meaning of channel in a communication system which can refer also to a particular timeslot or code In the next two sections a brief description of most common measurements in digital communication transmitter test
113. two equations in 11 53 are separately solved and is calculated as the average of their solutions Therefore system 11 485 is solved for those ke 1 K 1 that verify either det zo or II 2 0 Estimates po and are then averaged to obtain a 6 S measure of gain imbalance p and quadrature error db for that particular OFDM symbol C Voltage offset evaluation The final step of the proposed method consists in the estimation of voltage offsets The values of B and db attained at the previous step are substituted into equations III 46 and 11 47 which are evaluated for k 0 yielding A 1 B A c By 111 54 and B B 111 55 An estimate of c and cg can be obtained by simply inverting the two linear equations 11 54 and 111 55 which are split with regard to the variables c and co 82 Chapter III I O Impairments Detection and Evaluation AER III 56 1 2 B B 1 57 Assuming time invariant impairments the procedure is repeated for successive OFDM symbols 1 e for successive values of time variable n and I Q impairment amounts evaluated for various symbols are averaged to achieve the desired measurement result III 4 4 Performance assessment A number of laboratory tests on OFDM signals have been carried out to experimentally assess the performance of the method To this end different combinations of impairment types and amounts an
114. unctional form for PSD estimation A stationary AR p process Y with zero mean satisfies the equation 20 Chapter II Performance Evaluation Y Pip Pp Yi ques Et 1 3 where 4i 5 0 05 are p fixed coefficients and 6 is a white noise process with zero mean and variance Oy The process 6 is often called the innovations process associated with the AR p process and Op is called the innovations variance The PSD for a stationary AR p process is given by o T SU i 2 Lf Ef 11 4 3 bn pe m l S where T l f 15 the sampling interval between values in the process and fyw 1 2T is the Nyquist frequency The two main rationales for this particular class of parametric PSD functions can be so synthesized first it can be shown that any continuous PSD can be approximated arbitrarily well by an AR p PSD if p is chosen large enough 46 and second there exist efficient algorithms for fitting AR p models to time series Consequently assumed that p 15 known to form an AR p PSD estimate it 1s necessary to properly estimate the p 1 parameters 4i Q2p Pp p and 6 The question 1s how to estimate them If both sides of equation are multiplied by Y the equation P 2 11 5 m 1 is yielded By taking expectations we have p Sk X npk E amp Y 1 6 where sp E YY 1 7 is the autocovariance sequence The plausible
115. unts ensure that the generated symbols do not cross the boundaries of their decision boxes on the I Q plane This is the reason why impairment amounts for DVB signals are lower than the corresponding ones for WCDMA signals as it is evident for gain imbalance and voltage offsets Table III 2 Impairment amounts for WCDMA signals Single Double 72 Chapter III I O Impairments Detection and Evaluation Table III 3 Impairment amounts for DVB signals Go G dB 0 5 2 0 0 5 2 0 o rad 0 052 0 122 0 035 0 069 0 02 0 12 0 02 0 08 002 0 12 0 02 0 08 As an example Fig III 12 Fig III 13 and Fig III 14 refer to a 32 QAM signal generated at a symbol rate equal to 1 5 Msymbol s with an imposed gain imbalance g equal to 0 129 In particular Fig III 12 and Fig III 13 give respectively the I Q polar diagram and baseband I x Agilent 01 19 04 15 50 10 Basic pa n Ch Freq 1 00000 GHz Waveform Time Domain 1 0 Polar Sample Intvl 66 6 M Urigin fa V Fig III 12 I Q polar diagram of a DVB signal in the presence of gain imbalance x Agilent 01 19 04 15 55 14 Basic Ch Freq 1 00000 GHz Waveform Time Domain Ref 0 00 V I Q Waveform Fig III 13 I and Q waveforms related to the signal in Fig III 12 73 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters and Q waveforms 10 samples per symbol
116. used on the most general situation in which gain imbalance quadrature error and I Q offsets were all simultaneously present For the sake of brevity only the results attained in the second and the third sets of experiments are given Results are expressed in terms of difference A between imposed and measured impairment values averaged over the one hundred measurements and experimental standard deviation o 60 Chapter III Impairments Detection and Evaluation With reference to the second set of experiments Fig III 6 shows the results attained on 64 QAM signals simultaneously affected by gain imbalance and quadrature error Specifically it provides a histogram representation of A and o related respectively to gain imbalance Fig III 6 a c and quadrature error Fig III 6 b d measurements as functions of imposed impairment amounts Table enlists results achieved on 64 QAM signals with regard to the most general case when all the impairments were simultaneously present both A and o are expressed in percentage relative terms Difference A496 Difference A496 A MME 0 0654 0 0872 rad Experimental standard deviation c 476 0 1309 d E g 9 3 0 25 2 0 15 N ANN 1 0 WAY m Fig III 6 Difference A c in percentage relative terms between measured and imposed a amplitude imbalance A and b quadrature error ex
117. ussian window has been utilized as it comes out to be the optimal choice with regard to both power and frequency rmse In particular optimized TFR provide an rmse value equal to 0 032 thus showing the efficacy and reliability of the proposed method 6 14 and Fig II 15 show a superposition of measured and nominal power and frequency trajectories when the optimal window function 15 utilized In particular Fig II 14 1s related to frequency transient whereas Fig II 15 accounts for power transient In both figures the solid line is the measured trajectory and the dotted line is the nominal one Looking at the figures significant differences between measured and nominal trajectories can be appreciated at the beginning of two trajectories This 15 not an unexpected result due to the very low power level characterizing the signal at the beginning of the transient in fact the random quantization noise introduced by DSO significantly degrades the acquired signal The maximum value in the corresponding columns of the TFR matrix is thus related to the aforementioned noise rather than to the input signal For the same reason the measured power trajectory significantly differs from the nominal one during the first portion of the signal As a consequence rmse values which are at the basis of the window function choice are calculated excluding the first portion of instantaneous trajectories in order to avoid worthless outcomes and achieve the inte
118. ution order a Demodulation The RF output of the digital transmitter under analysis 1s demodulated in order to recover the time domain evolution of its baseband I Q signals and accordingly actual and nominal position of transmitted symbols on the constellation diagram b Impairment detection The actual constellation diagram should be analyzed in order to detect the presence of I Q impairments and establish whether one or two impairments prevail To this end suitable approaches can be exploited 84 c Impairment evaluation For each transmitted symbol the real and imaginary part of the error vector are first calculated and then put into original algebraic relations which allow the estimation of the amount of the occurred impairments The measurement result 1s finally obtained as the average of all gained estimates according to the size of the considered set of consecutive symbols With regard to the last stage different relations are given depending upon which impairment or pair of impairments is singled out as predominant For the sake of clarity details concerning all proposed relations are separately given below A Single impairment Fig III 8 Fig III 9 and Fig III 10 show the effects on the I Q diagram of a QPSK of the presence of respectively 1 a gain imbalance g equal to 0 1146 11 a quadrature error equal to 7 16 rad and 111 a normalized voltage offset on component I c equal to 0 15 With reference to the no
119. ween related results are in fact within 2 STFT is therefore preferable because its computational burden is much lower than that characterizing the CT Table II 6 Measurement results related to the bug transmitter 75 827 MHz 85 817 MHZ 49 Performance Evaluation and Troubleshooting of Radiofrequency Digital Transmitters B Walkie talkie The proposed method has been applied also to measure the attack time of a walkie talkie when receiving a sinusoidal 20 kHz signal in input The steady state carrier frequency f of the transmitter under test 15 equal to 30 225 MHz Its output signal has been sampled at fs 200 kS s the sampled signal being consequently centered at f 8 The evolution versus time of the acquired signal is shown by Fig II 19 Measurement results for both TFRs are reported in Table 7 expressed in terms of transmitter attack time ta and frequency and power transient durations f and 1 In this case power transient is longer than frequency one and therefore determines the walkie talkie attack time which 15 largely within the limits imposed by the standard Table II 7 also shows that the difference between transient durations measured through the application of CT and that provided by the use of STFT 1s inferior to 2 STFT is therefore preferable because its computational burden is much lower than that characterizing the CT Evolution versus time of the acquired signal 0 3 0 2 0 1 0 1
120. y Digital Transmitters not meeting standard s requirements during test stages it 1s important to single out the sources of impairment Nevertheless this is not an easy task mainly because larger and larger parts of modern communication systems are implemented digitally and because some of the parts of the transmitter are not accessible Major manufacturers adopt and suggest troubleshooting procedures designed to help recognize and troubleshoot possible problems from measurements performed at antenna port Such procedures designed to have a minimum impact on the time to market rely on the ability to infer possible impairments from a look at the signal or at the instrument display In this section some relevant examples of how possible problems affecting the transmitter can be singled out from the analysis of transmitted signal are given 1 3 1 Compression If instantaneous power level of the signal at the input of the power amplifier which represents the final block in Fig I 1 1s too high the amplifier can be driven into saturation and signal compression can occur with consequent non linear distortion on the transmitted signal Compression can be inferred for instance by comparing the CCDF curves of signals at the input and at the output of the amplifier If compression occurs the output CCDF denotes lower probability of reaching high power values In case the input section of the amplifier cannot be accessed comparison can b
121. zes SS can be therefore simply calculated as B Pek A 11 23 The flow chart in Fig II schematizes the algorithm implemented to assess the optimal AR order p and estimate the PSD In particular initialization of observed forward and 24 Chapter II Performance Evaluation backward prediction errors and innovations variance is first required Their initial values are chosen according respectively to e 0 0 X 11 24 and 1 N A 3 X37 1125 Successively starting from k 1 the routine evolves through the following steps 1 Auxiliary terms and B are calculated according to 11 21 and 1 22 2 An estimate of d is gained as in 1 23 3 A check on the estimated partial autocorrelation coefficient 1s performed In particular if 2 Un lt JN order p is put equal to k 1 and the routine halts otherwise it goes to the next step 4 Order k backward and forward prediction errors are evaluated according to II 18 and 1 19 5 Estimations of 4 m 1 2 k 1 and o are calculated according to II 13 and 14 6 Order k estimate of the PSD se f is evaluated in accordance to 11 4 2 e X 7 k 2 11 26 gt bape re 7 Index k is incremented by 1 and the routine 15 re executed from step 1 When the routine halts the AR model order p 15 set equal to k 1 and the current PSD estimate S f becomes the final PSD estimat

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