ANALYSIS AND SIMULATION OF QSP BEAMFORMER

Vol.24 No.6JOURNAL OF ELECTRONICS(CHINA)November 2007ANALYSIS AND SIMULATION OF QSP BEAMFORMER'Shi ShuangningShang YongLiang QinglinLiang Bin'(School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China)(School of Electronics Engineering and Computer Science, Shihezi University, Shihezi 832003, China)Abstract The real Direction Of Arrival (DOA) varies with time in mobile communication system. Insuch situation, the performance of conventional beamformers will be degraded obviously. QuantumSignal Processing (QSP) beamformer is insensitive to DOA errors, thus it can achieve stable outputperformance in such circumstance. This letter verified the effectiveness and feasibility of the QSPbeamformer by simulation results.Key words Beanforming; DOA error; Quantum Signal Proessing (QSP); Impact factorCLC index TN911.23DOI 10.1007/s11767-006 0266-3I. IntroductionDOAs of the signals are {,,j = 1,..J respec-Beamformingl12, which is the key technology oftively. The receiver antenna array is composed of Mthe smart antenna, is getting more and more at-elements. Suppose that the Additive White Gaus-tention as the smart antenna is adopted in the 3rdsian Noise (AWGN) at each array element isgeneration mobile communications. Conventional{n(t),m = 1,2,..,M} with the same variance o2,beamforming, such as Capon beamformer, is widelythen the vector form of the received signals isused since it only needs Direction Of Arrival (DOA)(t)= A8()+n()= _a(,)i(t)+n(t) ()of the interested signal and can be easily imple-mented. But in mobile environment the DOAs varywhere a(0,)= (())-.a,(,)]T is the steeringwith time because of the mobility of the users,vector corresponding to the signal from DOA 0,,which results in instable output performance of thex()= [x...xw()"，A= [a()... a(0])], 8()=conventional beamformerl3-5. Adaptive algorithm,()..i(t)]", and n(t)= [n(t)... n(t)]".as a choice in such environment, is restricted in theAccording to the principle of beanforming,application by the convergence speed as well.after adjusting the weight vector w of the array, wePresented in Ref.[6], the Quantum Signal Proc-can get the output signal of the beamformer, whichessing(QSP) beamformer is based on quantumis denoted as: y(t) = w"x(t). With this method, thesignal processing framework, and is discussed as ajamming can be reduced and the expected signalsnew method of solving this problem. It can providecan be better separated.not only good but also stable output performanceIn the mobile environment, because of the moin such environment because of its insensibility forbility of the user, random errors exist on a fixedrandom perturbations on the DOAs of signals.estimation of some DOA, and make the realII. Signal Model4] .steering vector different with the ideal steeringAssume that there are J narrow-band station-vector. We denote the errors as a Gaussian randomary signals in far field {i(t),j = 2...,J}, and thevector 0。, which is an addition for the ideal DOA.The mean of0。 is 0 and the standard deviationManuscript received date: December 7, 2006; revised date:is σg。So the real steering vector is not a(0,),March 31, 2007.but a(0; +0,), and the real data at the receiverSponsored by the National Natural Science Foundation ofcan be written asChina (No.60302006 and No.60462002).Communication author: Shi Shuangning, born in 1980,中国煤化工,，)(t)+n() (2) .male, Ph.D. candidate. School of Electronics Engineeringand Computer Science, Peking University, Bejing 100871,:THCNM H G;:iance of recevedChina.data based on Eq.(2) is not accurate and it will leadEmail: shnsh@pku.edu.cn.SHI et al Analysis and Simulation of QSP Beamformer813to the loss of the output performance.Capon beamfomer, because the ()-1/2 is moreIII. Performance Analysis of the QSPstable than ()-' when () changes slightly.In order to validate the stable performance ofBeamformerQSP beamformer, we present the simulation asFor conventional Capon beamformer, thefollows.weight vector w is denoted as w= μR-a(0,),Simulation environment We utilize a four-where R is the covariance of the received data, andelement Uniform Linear Array (ULA) with thethe output of the beamformer is good when theelements separated by half-wavelength interval andDOAs of the signals are known accurately. But theassume that the expected signal comes from theDOA errors exist in mobile environment, the con-direction of 0”, and an interference signal comesventional Capon beamformer can not obtain thefrom the direction of 15°, and Signal to Interferenceoptimal value of w timely, and then the outputRatio (SIR) is 0dB. The impact factor of the ex-performance of the beamformer will be degradedpected signal isqn = 0.1 and 92 = 0.9. The result isobviously.shown in Fig.1.QSP beamformer6 is a new kind of beamformerbased on quantum signal processing framework",Its principle can be expressed as follows:Assume that there are J steering vectors{a(,),1≤j≤J} in Hilbert space H. When agroup of vectors {a(0,),1≤j≤J} are given, we出1◆Caponcan construct a group of vectors {w(0,), 1≤j≤J}万10F Capon 01whose element is orthogonal to each other, whichapproach to the given group of vectors {a(0,),- QSP 01日QSP 031≤j≤J} under least- square constraint as close as51015202530possible. Furthermore, we introduce different im-SNR (dB)pact factors {g;,1≤j≤J} for different signals,which satisfy 9n +92 +...+9j=1 then the vec-Fig.1 The output SINR of the bearnformerstors {w(0,), 1≤j≤J} should make the followingequation minimumIn Fig.1, the output Signal to Interference andNoise Ratio (SINR) curves of the two beamformersLs := E:,(a(,)- w),)0(,)- w0,)are drawn. When DOAS of all signals are stable andj=l(3)accurately known, Capon beamformer presents itss.t(w,(,)=2*6excellent performance as curve Capon shows in91+q2+...+q=1Fig.1, and there is a performance gap between thecurve QSP which represents the output perform-where C is a constant value greater than zero, δance of QSP beamformer and curve Capon. Alongindicates that the vectors should be orthogonal tewith the SNR goes higher, the gap goes wider.each other and the constant q; denotes the impactThe curve Capon 01 and the curve Capon 03factor of the jth signal. After calculation we canrepresent the outputs of Capon beamformer in thegetsituation where the DOA errors exist withu= a(,)Q(QA'AQ)",{..g}.variagYHCNMH Glarger, especiallyFrom Eq.(4), we know that the stability of w inwhen ue binn Ibulgu. Imeallwillte, the performanceQSP beamfomer is better than the one in theof the QSP beamformer is only degraded partly814JOURNAL OF ELECTRONICS (CHINA), Vol.24 No.6, November 2007because curve QSP 01 and curve QSP 03 are very{2] Barry D. van Veen and Kevin M. Buckley. Beam-close to curve QSP, which means that performanceforming: A versatile approach to spatial filtering.of QSP beamformer is more stable than that ofIEEE ASSP Magazine, 5(1988)2, 4 24.Capon beamformer.3] Anyi Wang, Zheng Bao, and Linrang Wang. Remnediesof the estimation errors and perturbation errors.IV. ConclusionsJourmal of Xidian University, 261999)5, 614 618 (inIn this letter, how to deal with the randomChinese).ertors on a fixed estimation of some DOA in mobile王安义,保铮,张林让.阵列估计误差和扰动误差引起environment is discussed. Conventional beam-方向图畸变的校正，西安电子科技大学学报,former like Capon beamformer will be degraded261999)5, 614- 618.badly in such environment. However, QSP beam-[4] B. D. Carlson. Covariance matrix estimation error8former which is based on QSP frarnework canand diagonal loading in adaptive arrays. IEEE Trans.on AES, 24(1988)7, 397 401.present good and stable output performance in theenvironment, because it theoretically depresses the5] C. Chou and J. H. Lee. Robust adaptive arraybeamforming under steering vector errors. IEEEeffect caused by the perturbation on DOA. TheThans. on AP, 45(1997)1, 169-175.final simulation results have been presented to il-lustrate the effectiveness of the proposed QSP6] Shuangning Shi, Shubo Ren, Yong Shang, QinglinLiang, and Haige Xiang. 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