EVM simulation and analysis in digital transmitter

Available online at www.sciencedirect.comScienceDirectThe Journal of ChinaUniversities of Posts andTelecommunicationsEL SEVIERDecember 2009, 16(6): 43- -48www.sciencedirect.com/science/journal/10058885www.buptjournal.cn/xbenEVM simulation and analysis in digital transmitterTAN Xiao-heng (8), LI Teng-jiaoCollege of Communication Enginering, Chongqing University, Chongqing 40044 ChinaAbstractThe error vector magnitude (EVM) is extensively applied as a metric for digital transmitter signal quality compliance inmodern communication systems. This article is focused on the effects of local oscillator (LO) phase noise and nonlinear distortionof power amplifier on EVM. This article contributes to below aspects. First, the relationships between EVM and two effects, LOphase noise and nonlinear distortion of power amplifer, are derived and expressed. Second, to simplify the expression, thethird- order intermodulation distortion (IMD3) is used to calculate the EVM. Then, an expression for the EVM is derived based onthe digital transmitter model that considers local oscillator phase noise and nonlinear distortion of power amplifier. Finally, themath formula of bit error rate (BER) versus EVM is given which can be easier and more useful to predict BER, according toanalysis of the relationship between EVM and signal to noise rate (SNR), inspired by the works of Rishad, Md. Shahriar andAHM, 2006. Simulations are carried out to display the performance of EVM based on these relationships.Keywords power amplifirs, EVM, phase noise, nonlinear dstortion, IMD31 Introductioninfluence on EVM caused by several factors has been studiedseparately, but it has not acquired the general expression [4].SNR, BER and EVM are common performance metrics forAuthors in Ref. [5] analyze the combined effects of themodern communication systems.Amongthem,BERseveral factors on EVM in the traditional wireless analogperformance against SNR is the popular performance criterioncommunication system, but the formulas are processedused in today's communication systems. However, with theapproximately and it is complicated to obtain the value ofdevelopment of modern communication systems, and the useEVM. In this article, the work is focused on the effects of LOof different digital modulation types, EVM has graduallyphase noise and nonlinear distortion of power amplifier onbecome a quite importantEVM based on one type of wireless digital transmitter model.because it contains information about both amplitude andWhen considering the influence of nonlinear distortion ofphase errors in the signal [1-2]. This additional informationpower amplifier on EVM, a IMD3 is used to calculate EVMcan allow a more complete picture of channel distortion and iswhich makes the calculation more conveniently andmore closely related to the physics [3].efficiently. Based on the vector composition of phase noiseand third-order intermodulation product, improvement hasof digital transmitter in engineering applications, and it isbeen done for the deduced general expression for EVMvery useful for the radio designer. While there have been acompared with Refs. [4- -6].number of simulations and measurements of EVM [3-5], aIn this article, a digital transmitter model based on thegeneral analytical expression relating EVM to the LO phasesoftware design radio in Sect. 2 is first briefly introduced.noise and nonlinear distortion of power amplifier has not beenFollowing this, in Sects. 3 and 4 the relationship between thelisted, to the author's knowledge. For example, Ref. [3] onlyEVM and two main factors is analyzed, including localanalyzes the influence on EVM with phase noise. Theoscillator phase noise and non-linear power amplifier. Finally,the general expression to calculate EVM is given when thereReceived date: 28-10-2008are both phase noise and non-linear of power amplifier in Sect. 5,Corresponding author: TAN Xiao- heng, E- mail: txh@ cqu.edu.cnDOI: 10.1016/S1005- 88508960287-3and the relationships among EVM, SNR and BER are中国煤化工MHCNMH G44The Journal of China Universities of Posts and Telecommunications2009analyzed in Sect. 6.The model of digital transmitter is comprised of aquadrature modulator, as shown in the block diagram of Fig. 1.2 Digital transmitter model and EVMThe base-band mapping and the digital up-conversion (DUC)are realized by FPGA or digital signal processor (DSP). Themodulated intermediate frequency (IF) signal is convertedarray (FPGA), analog to-digital converter (ADC), digital-to-into analog signal through the high-speed DAC. After filteringanalog converter (DAC) and the theoretical maturity ofby the band-pass filter (BPF), the analog IF signal enters intosoftware radio, the communication system is always realizedthe analog mixer to shift the frequency to radio frequency (RF).in digital ways. The digital processing part is located asThe RF signal is transmitted by the antenna after powerclosely as possible to the antenna to minimize the analogamplifier.elements in digital transmitter.-Mapping }:Duc}-DAc}-[ BPF ]-Amlg mixar}-BrF]-Power apirFig.1 Model of digital transmitterBecause of the total digitization of quadraturecarrier frequency, and the unit is dBc/Hz. Another definitionup-conversion, the transmitter can avoid problems includingis the rms phase noise, which can be calculated by thein-phase and quadrature (IQ) phase shift deviation, I/Qintegration of single-sideband phase noise spectrum density inamplitude imbalance, frequency error, and I/Q zero offset.a certain extent of frequency, and the unit is degree. The latterTherefore, it only needs to consider the effects of LO phaseindicates the total phase stability of the LO within thenoise and nonlinear distortion of power amplifier on EVM ininformation bandwidth (BW) [5].the digital transmitter.EVM is an important performance metric of the modulationphase noise can be expressed as follows:precision, and EVM is a measure of errors between theSrndea(t)= I()cos(ot) + Q()sin(@ft)measured symbols and expected symbols. EVM representswhere I(t) is the in-phase baseband signal, Q(t) is thethe dispersion degree of constellation points, and is definedquadrature baseband signal, and @。is carrier frequency. Ifby the following formula [7]:the LO phase noise exists, the transmiting radio frequency一2|s.-s。signal can be expressed as follows:Emm=M台，(1)Sspas()= I()cos(@ot + 0())+ Q()sin(@,1 + 0())(3)Eq. (3) indicates the phase offset 0() ， which introducesM台a phase shift in the in-band frequencies. In Ref. [3] anwhere Ems represents the root-mean-square (rms) EVM,equation relating EVM and LO phase noise is given:S。is the actual normalized constellation point of nth symbolin the stream of measured symbols, Som is the correspondingEms=E+2-2exp|之(4)ideal normalized constellation point of the nth symbol, and Mis the number of constellation points for different modulationwhere E、/N。 represents the SNR，E、 is the energy pertypes. For example， M =4 for quadrature phase shiftsymbol，N。 is the noise power spectral density， σkeying (QPSK) and M =16 for 16-quadrature amplituderepresents the rms phase noise. Approximating exp(-o2/2)modulation (16 QAM).by 2-order Taylor series expansion, Eq. (4) is simplified to:3 EVM and local oscillator phase noiseEms=六+σ2(5)LO phase noise is known as random frequency fluctuationsγNaround its center frequency. Phase noise is measured in theUsually, SNR is very high at the transmitting terminal, thusfrequency domain. There are several ways of defining LOone can get the effect by phase noise on EVM:phase noise. The common definition is expressed as a ratio ofEphase=Ems≈σ(6)noise power to carrier signal power, and the noise power isFig. 2 shows the EVM variation with the LO phase noise bymeasured in a 1 Hz bandwidth at a given offset from the中国煤化工MHCNMH GIssue 6 .TAN Xiao-heng, et al. / EVM simulation and analysis in digital transmitter45Eq. (5) at different SNR. Fig. 3 shows the EVM variation withinput signal, a is the linear gain, a3 and as are the thirdthe LO phase noise by Eq. (6). Comparing Fig. 2 with Fig.3,itnd fifth order nonlinear coefficients. a, az and as areshows that the curves present an approximate linear growth indecided by the characteristic of power amplifier.Fig.2 and the slope is roughly consistent with the curves in Fig. 3Assume that the input signal is v(1)= 2 A, cos(@ot) , whichwhen SNR is high. Assuming that SNR is 40 dB, EVM is 2%in Fig.2 and 19% in Fig.3 when the phase noise is 1° . Whenmeans the input signal is cosine carrier without modulation,the phase noise is 4.5° and SNR is 40 dB, EVM is 8% inand N is the number of the different cariers in the inputFig. 2 and 7.9% in Fig. 3. Therefore, at high SNR, Eq. (6) cansignal. By inputting it into Eq. (7) and only considering thereplace Eq. (5) as the simple estimation formula to calculate theIMD3 product, the following can be obtained:EVM caused by LO phase noise.V()=a{ Z4.cos(O) )+a, A4c0(o)](8)2-Consider the case of two tone intermodulation, whichmeans the input signals are two cosine waves with the sameamplitude and different frequency. Because of the non-linear干E/N=20 dBcharacteristic of power amplifier, the third-order intermodulation甘EN=25 dB+ E/N-=30dBproduct (20,-0) will be obtained when the two carrier* EJN。-35 dBsignals pass through the power amplifier. According to theconclusions in Ref. [8], the signal amplitude of the third-order0σ()intermodulation product is (3/4)aA at the frequencyFig.2 EVM variation with LO phase noise by Eq. (5)20, -@,. The Ig is defined as the ratio of this IMD3 product9power (P3) to the carrier power (P), and is usually expressedin dBc. The calculation formula is:4=101gp(9)Fig. 4 describes IMD3 variation with the normalized inputpower (Pm) of IS-IV satellite traveling-wave tube amplifier(TWTA), where the coefficient that a=1.65， az =-0.887,as =0.16 was used [8].σ(°)-10rFig. 3 EVM variation with LO phase noise by Eq. (6)-204 EVM and nonlinear distortion of power amplifier-30-The conclusions of Ref. [3] indicate that the relationship-40between EVM and nonlinear distortion of power amplifier canbe analyzed through power or Volterra series. The power-50-amplifier of the transmitter usually operates well below its 1 dBcompression point. Thus, among the nonlinear effects, the-15 -10-5third-order intermodulation interference is the majorP:/dBcontribution to EVM. Because IMD3 is the best parameter toFig. 4 IMD3 variation with normalized input powercharacterize nonlinear distortion of power amplifier, IMD3 isThe EVM caused by third. order intermodulation is just theused to calculate the EVM to simplify the expression.square root ratio of the third-order intermodulation productThe non-linear characteristic of the power amplifier can bepower to the desired RF carrier signal power [5], as follows: .expressed by the following series model [8]:V.(v)=av+aqv +asv'(7)Euome=. =10/20(10)where V。 is the RF output signal, v is the instantaneous RF中国煤化工MHCNMH G46The Journal of China Universities of Posts and Telecommunications2009Fig. 5 shows EVM variation with IMD3. When consideringthe influence of nonlinear distortion of power amplifier onEVM，it makes the calculation more conveniently andefficiently because of using IMD3 to calculate EVM.0fOtherwise, it needs more parameters to calculate EVM, such25Fas input power, output power, the 3rd interception point andthe 3rd intermodulation product power, though they are not是15-all easy to obtain.5 EVM and combined effects5In Eq. (3), while 0() has perturbation, the interference45-40-3530-25-20-15-10erm ASphase(t) caused by LO phase noise can beexpressed as follows:Fig. 5 EVM variation with IMD3Srphase(1)= Sphuxe()- SFdea()= I()cos(@o.t + 0()) + Q()sin(@,1 + 0())- I()cos(@,1)- Q(1)sin(@,1)= I()Ccos(@0,I + 0())-cos(qt)] + Q()[sin(ojt + ())- sin(gt)] =[()cos(a,t + 0()- co(o.1)]+ 20)sin(@.1 + 0(0)- sn(@.t)]g()=0(t)(n) cos(@.1 +0())-cos(@.,) + orsin(@. + 0()) - sin(@.1)0(t)≈[-()in(o,1)+ Q()cos(,)]0(t)(11)θ(t)In the case of slight non-linearity, according to the(0)=- 1(0)*+I(0)2(1)2AS Roninear'- cos(@,t)-relationship between the coefficient of the cubic term and the21p33rd interception point (Ip3) [9- -10], the series model is2(1)3 + 1()-Q()(16)modified as follows:y=x- :_2.(12) .Therefore，when there are both LO phase noise and3Ip3third-order intermodulation interference the RF signal can beIp3 is given by Ref. [9]:rewritten as follows:2qSpp()= Spidea(1)+ SsRpbuse(t)+ Sponincar(t)=(13)3 a3| 1I(1) + Q()0()I(t)3 + I(t)Q(t)|cos(oft)+Input Eq. (2) into Eq. (12):2Ip3Snonlinear'(t)= I(t)cos(ot) + Q(t)sin(opt)-Q()+ I(t)0(t)Q(t)3 + I(t)-Q()|sin(of) (17)7 -[()cos(ogt) + Q()sin(ot)](14)To get the vector relation between the ideal signal vectorIn Eq. (14), the component produced by the third term atand the two interference vectors, the interference vector@, is just the third order intermodulation products. Usingcaused by phase noise and the interference vector caused byproduct to sum formula to reduce the power of the third term,non- linearity, the baseband signal vector in Eq. (17) can beone can obtain:mapped into IQ plane. Then, three vector signals are obtained2r(1)+ I()Q2*(2).31I-[()o<(@,1)+ Q()in(o,)] =21prespectively as follows:Siouea()= (I(),Q())(18)cos(o.1)-Q*(1)+1'()Q()-sin(@1)+3()Q2(1)-1().Snas()= (0()Q(t),-0(t)I(t))(19)6Ip3Q*(1)-3172()Q()Sqolinew(t)=I(1)3 +I()Q()2_ Q()3 + 1(1)-Q0)(20)cos(30.1)+-sin(3o,t)(15)By comparing Eqs. (18)-(20), it is easy to find thatHence, the interference Sromlier(t) caused by the thirdinterference vector caused by LO phase noise is orthogonal toorder intermodulation at o， can be expressed as follows:中国煤化工MHCNMH GIssue 6 .TAN Xiao-heng, et al. / EVM simulation and analysis in digital transmitter47the ideal signal vector, while interference vector caused by thetheir unnormalized quantities, that is, Eq. (22) can behird order intermodulation is parallel to the ideal signalmodified as follows:vector. Because the two error vectors given by Eqs. (19) andEms≈E。(23)(20) are orthogonal and independent to each other, the totalerror vector power equals to the sum of the two error vectors'power. When considering the combined effects of phase noiseTo establish relationship between BER and EVM, SNR inand the third-order intermodulation interference, the generalEq. (23) can be expressed in terms of EVM as [7,11]:expression to calculate synthetic EVM is:(24)Ems =VEFhase + Enninerr(21)By expressing EVM in a logarithmic form, the relationship .where Ense can be calculated by Eq. (6) and Enr iner canbetween SNR and EVM can be obtained as follows:be calculated by Eq. (10).Fig. 6 shows EVM variation with the combined effcts ofEms≈20lg(25)E|=-10(号,)六。phase noise and third-orderintermodulation interference.(VN,Fromig. 66, it is easy to obtain the EVM value of the digitaltransmitter when the combined effects on EVM includingConsidering multi-ary QAM modulation with coherentboth LO phase noise and nonlinearity of power amplifier aredetection, while carrier frequency and phase are both perfectrecovery，the BER of digital multi-ary modulation irconsidered.Gaussian white noise channel can be shown as [7]:lrc_E1lbM4(0(-(V2M -1)N。i 20-ric.3_ E1bM(26)V 2(M-1) N。10where E。is the energy per bit, and No is the noise power_10_2-30~spectral density. Defining E,/N。 as the signal to noise ratio forthe M-ary modulation system, taking E、/N。 =(E,/N)lb MdBc”-50_--600and E、/No≈1/Ems into Eq. (26), one can now relate theFig. 6 EVM variation with the combined effectsBER directly with the EVM as follows:6 Relationships among EVM, SNR, and BERR-=2(一+)(V2(M-1)E2，It is evident that EVM is essentially the normalized error_3__ 1magnitude between the measured constellation and the ideal1 - 2(l-im√2(M-1)E2 )(27)constellation [7]. For Gaussian noise model, EVM can also bedefined in terms of noise in-phase component, ηk andFig.7 shows the BER versus SNR performance of differentquadrature component, no.x as:modulation types. Because of the relationship between BER1/2and EVM in Eq. (27), the BER versus EVM curve, as shown片2maP +InasPlin Fig. 8, shows the inverse ratio relationship that existsT台P。(22)between BER and EVM (EVM is given by logarithmic form).where P。 is the power of the normalized ideal constellationComparing Fig. 8 with Fig. 7, it is easy to find that the curvesin the two figures are symmetrical with the axis of ordinate,or the transmitted constellation, T is the number of symbolswhich means EVM (dB) is the minus value of theused to calculate the mean square value of EVM. For T>>Mcorresponding SNR (dB) with the given BER. For example,(M is the number of constellation points for differentwhen QPSK modulation is adopted and BER is 10- , SNR ismodulation types), the ratio of normalized noise power to10 dB from Fig. 7, and EVM is10 dB from Fig. 8.the normalized power of ideal constellation can be replaced by中国煤化工MYHCNMH G48The Journal of China Universities of Posts and Telecommunications200910transmitter specifications to meet desired EVM performance.Extended relationships among the bit error rate, signal tonoise rate and error vector magnitude are given, then10-2predicting BER with EVM instead of SNR can save th心10necessary closed loop equipment in the conventional methodand shorten the measure time. However, only the relationship10=+OPSKbetween EVM and transmitter imperfections in Gaussian安16QAM105---64 QAM 'white noise channel is discussed. The effect of different士256 QAMfading channel and that of using EVM adaptive M ary10 - 5101520253035modulation systems instead of BER- adaptive systems are now/dBbeing considered as an extension of the work.Fig. 7 BER vs. SNR performance curvesAcknowledgements10°This work was supported by the National Natural ScienceFoundation Project of CQ CSTC of China (2008BB2168).References .<1031. Hassun R, Flaherty M, Matreci R, et al. Efective evaluation of link10-案QPSKquality using error vector magnitude techniques. Proceedings of 1997。16 QAMWireless Communications Conference (WCC'97), Aug 11-13. 1997,女64 QAMBoulder, CO, USA. Piscataway, NJ, USA: IEEE, 1997: 89-94女256 QAM2. Wang A K, Ligmanowski R, Castro J, et al. EVM simulation and analysis10-35 -30-25 -20-15 -10一 -5 0techniques. Proceedings of IEEE Military Communications Conference(Milcom'06), Oct 23- 25, 2006, W ashington, DC, USA. Piscataway, NJ,USA: IEEE, 2006: 1-7Fig.8 BER vs. EVM performance curves3. Georgiadis A. Gain, phase imbalance, and phase noise effects on errorvector magnitude. IEEE Transactions on Vehicular Technology, 2004,Extended relationships among the bit error ration, signal to53(2): 443- -449noise ration and error vector magnitude are shown in Figs. 7FanX L, Zheng J H, Chen L. EVM testing and analysing in TD SCDMA.and 8. As shown in Figs. 7 and 8, due to normalization, theJournal of Chongqing University of Posts and Telecommunications:Natural Science Edition, 2005, 17(2); 156- 159 (in Chinese).EVM (dB) is the minus value of the corresponding SNR (dB)with the given BER, and an inverse relationship betweentransmitter imperfections mathematically and graphically. Analogthem is maintained. Because EVM can be directly measured6. LinF L, Chen s F, Chuang H R. Computer simulation of nonlinearusing vector signal analyzer (VSA), it can save the extraeffects of RF power amplifiers based on EVM and ACPR for digitalcalculation that may be required to find out the BER.wireless communications. Electronics Letters, 2000, 36(2): 77-79Predicting BER with the value of EVM can save the7. Shafk R A, Rahman S, Islam A R. On the extended relationships amongEVM, BER and SNR as performance metrics. Proceedings of the 4thnecessary closed loop equipment in the conventional method,International Conference on Electrical and Computer Engineeringand shorten measure time. In addition, according to the(ICECE'06), Dec 19- -21, 2006, Dhaka, Bangladesh. Piscataway, NJ, USA:IEEE, 2006: 408 411relationship between EVM and SNR, SNR can be easily8. LiH H, Cai J M, Gan Z M, et al. Satellite communication system.obtained by measuring EVM.Beijing, China: Post & Telecom Press, 1994 (in Chinese)9. Carvalho N B, Pedro J C. Compact formulas to relate ACPR and NPR to7 Conclusionstwo- tone IMR and IP3. Microwave Journal, 199, 42(12): 70-840. Wang X F. How to estimate ACPR index and intermodulation products.International Electronic Elements, 2004(10): 73- -76 (in Chinese)In this article, the effects of transmitter imperfections such1. Gharaibeh K M, Gard K G, Steer M B. Accurate estimation of digitalas nonlinear distortion of power amplifier and LO phase noisecommunication system metrics - SNR, EVM and ρ in a nonlinearamplifier environment. Proceedings of the 64th ARFTG Microwaveon system EVM are analyzed mathematically and graphically.Measurements Conference, Nov 30- Dec 3, 2004, Orlando, FL ,USA.Equations relating EVM to these imperfections are given forPiscataway, NJ, USA: IEEE, 2004: 41-44radio designers to predict transmitter EVM easily andeffectively. These equations can also be used to determine(Editor: WANG Xu-ying)中国煤化工MHCNMH G