Adaptive Broadband Beamforming with Spatial-Only Information

ADAPTIVE BROADBAND BEAMFORMING WITH SPATIAL-ONLY INFORMATIONWei LiuCommunications Research GroupDepartment of Electronic and Electrical EngineeringUniversity of Sheffield,UKw.liu@Abstract.A novel adaptive broadband beamforming structure is proposed,where the tapped delay-lines in the traditional broadband beamforming structure are replaced by sensor delay-lines and only one coefficient is required for each of the received sensor signals.In this way,the high-speed analogue tapped delay-lines or digital sampling cir-cuits are not required any more for some broadband beam-forming applications and beamforming can be realized by simple analogue circuits.Since there is no temporal infor-mation employed for beamforming,it can be considered as a beamforming method with spatial only information.The effectiveness of the proposed method is verified by simula-tions.Keywords.Adaptive broadband beamforming,sensor delay-lines,tapped delay-lines.1.INTRODUCTIONBeamforming has found many applications in various ar-eas ranging from sonar and radar to wireless communica-tions[1].It is a signal processing technique to form beams in order to receive signals illuminating an sensor array from specific directions,whilst attenuating signals from other di-rections.The sensors in the array system can be positioned in space according to different patterns,e.g.along a straight line,around a circle,or on a plane.Such arrangements lead to linear arrays,circular arrays and planar arrays[1],respec-tively.In this work,we limit the discussion to linear arrays, however,it can be easily extended to the case of other array patterns.Fig.1shows a linear array system with M sensors,where a signal s l(t)arrives from the directionθl.The propagation delay between the sensor0and the sensor m is denoted by τm.The received array signals are given by x0(t),x1(t), ...,x M−1(t).For narrowband signals[2],to form a beam pointing to the direction of arrival(DOA)of the signal of in-terest,we can apply one coefficient to each of the received signals and then sum them up directly.For broadband sig-nals,however,such a configuration will not work well and normally we need to employ a tapped delay-line(TDL)sys-tem[3,4],as shown in Fig.2,where each of the received()xxM−1tm()tt()xFig.1:A linear array system with M sensors,where a signal s l(t)arrives from the directionθl.array sensorsFig.2:A general structure for broadband beamforming.array signals x m(t),m=0,1,...,M−1is processed by the following tapped delay-line,with an adjacent tap delay ofΔand the corresponding tap coefficients given by w m,j, m=0,1,...,M−1,j=0,1,...,J−1.There are in total J taps for each TDL.The length J of the TDLs is dependent on the bandwidth of the imping-ing signals[5].In general,the larger the bandwidth,the longer the tapped delay-lines[6].The TDL coefficients can be designed for maintaining afixed specified response for all signal/interference scenarios,which leads to the concept of a data independent beamformer[4].Alternatively,they can be chosen based on the statistics of the array data for5751-4244-0882-2/07/$20.00c 2007IEEEoptimising the array’s response,which forms a statistically optimum beamformer[4].Since the statistics of the array data are often not known or may change over time,adaptive algorithms may be used to determine these coefficients.In its discrete form,the TDL system is replaced by afinite im-pulse response(FIR)filter and adaptive algorithms can be realized by digital circuits.In both of the cases,the delaysbetween samples/taps gets shorter and shorter with increas-ing signal bandwidth and very high speed circuits need tobe employed.Recently,a rectangular array with afixed frequency in-variant property was proposed[7]and then further studied in[8].A special characteristic of this beamformer is that there are no TDLs involved and only one single weight isattached to each sensor.By examining its beam pattern,we canfind that this rectangular array is approximating the re-sponse of a frequency invariant linear array with TDLs[9] and the only major difference is that the tapped delays in [9]are replaced by new sensor delays.We therefore gener-alize the idea in[7]to the adaptive case and also to arbitrary beam patterns and sensor patterns.The advantage of this ar-rangement is that only one coefficient is required for eachreceived array signal and the adaptive beamforming process can be realized by very simple analogue circuits.Thus we can release the pressure for very expensive high-speed ana-logue tapped delay-lines or digital sampling circuits.Note in some extreme cases,the very short delays required in thetraditional system may not be able to be realized at all by the state of the art technology.The paper is organized as follows.The new adaptive broadband beamforming structure is proposed with two im-plementations discussed in Section2;simulation results aregiven in Section3,and conclusions drawn in Section4.2.ADAPTIVE BROADBAND BEAMFORMINGWITH SENSOR DELAY-LINESBased on our discussion in the previous section,we pro-pose to use sensor delays to replace the tapped delays in the general adaptive broadband beamforming structure of Fig.2.The new structure is shown in Fig.3,where each ofthe tapped delay-lines with length J is replaced by a sen-sor delay-line(SDL)with N sensors each,and the tem-poral delay between adjacent taps is thus replaced by thespatial delay between adjacent sensors due to signal propa-gation.In this new structure,there are in total M×N sen-sors,with the received sensor signals denoted by x m,n(t), m=0,1,...,M−1,n=0,1,...,N−1.As there is only one coefficient for each received sensor signal,thereare no TDLs involved and adaptive beamforming can be performed by very simple analogue circuits.Note that there is no temporal information used in the beamforming pro-cess.Therefore it is a broadband beamforming structure with spatial-only information.array sensors(t)x x(t)x(t)x(t)xFig.3:A general structure for the proposed broadband beamforming structure.In Fig.3,the output y(t)can be expressed asy(t)=w H x(t),(1) wherew=w∗0,0...w∗M−1,0w∗0,1...w∗M−1,1...w∗M−1,N−1T x(t)=[x0,0(t)...x M−1,0(t)x0,1...x M−1,1(t)...x M−1,N−1]T(2) Note the vector w contains the complex conjugate values of the original weight coefficients.Corresponding to the traditional TDL systems,the co-efficients for this new beamforming structure can be deter-mined in different ways,depending on the specific situation. Here we give two different adaptive implementation exam-ples.Thefirst one is the case for which a reference signal r(t)is available and the weights are adjusted to minimize the mean square error between the beamformer output y(t) and the reference signal r(t).This is the simplest case and its structure is shown in Fig.4.It is a classical adaptivefil-tering problem and can be solved by any existing adaptive algorithms such as the least mean square(LMS)or recursive least squares(RLS)algorithms,or their subband implemen-tations[10].However,we may not have the desired reference signal available in practice,but have some information about the DOAs of the signal of interest and/or the interference and also their bandwidth range.In this case,we can impose some constraints on the array coefficients and then adap-tively minimize the variance E{y(t)∗y(t)}of the beam-former output subject to the imposed constraints.This leads to the well-known linearly constrained minimum variance (LCMV)beamformer[11].The LCMV problem can be for-576Proc.of the200715th Intl.Conf.on Digital Signal Processing(DSP2007)e)(tFig.4:A general structure for thefirst implementation ofthe proposed broadband beamformer.Fig.5:A general structure for the LCMV beamformer, where C H w=f is the constraint imposed on the adaptive process.mulated asminww H R xx w subject to C H w=f,(3)where R xx is the covariance matrix of observed array data in x,C is the constraint matrix and f is the response vec-tor.The constraint will ensure that no matter how to ad-just the array coefficients,the resultant beamformer will have the desired response set out by the constraint equa-tion C H w=f.Fig.5shows a general structure for such a LCMV beamfomer.The constrained adaptive optimisa-tion in(3)can be conveniently solved using a generalised sidelobe canceller(GSC)[12],which performs a projection of the data onto an unconstrained subspace by means of a blocking matrix B and a quiescent vector w q as shown in Fig.6.Thereafter,standard unconstrained adaptive algo-rithms such as the LMS and RLS algorithms can be invoked to minimize the variance of y(t),which is given byy(t)=d(t)−w H a u(t),(4) whered(t)=w H q·x(t)with w q=C(C H C)−1f(5) andu(t)=B H x(t).(6) The blocking matrix B must satisfyc H B=0(7) to block the signal of interest in the lower branch.Fig.6:A general structure for the GSC.3.SIMULATIONSThe purpose of the simulations is to show that the proposed structure is capable of performing beamforming as success-fully as the traditional structure.Further analysis about itsperformance compared to the traditional method will be our future topic of research.(In[13],an analysis of this struc-ture for the case with a reference signal is provided.)More-over,we need to bear in mind that the new structure is pro-posed to avoid the very expensive high-speed circuits insome applications of the traditional beamforming structure,which may be at the expense of a not as good performance, or for some other cases where the tapped delays are so shortthat it can not be easily realized by the technique of the state of the art.In our simulations,the proposed SDL beamforming struc-ture with M=N=10is compared with the traditionalTDL structure with M=J=10.The spacing between adjacent sensors is half wavelength of the signal componentwith the highest possible frequency(corresponding to a nor-malised frequencyπ).The signal of interest comes from thebroadside and four interfering signals from the directions θ=20◦,40◦,−30◦,−60◦,respectively.All of the signals have a bandwidth of[0.4π;0.95π].The signal to interfer-ence ratio(SIR)is about−20dB and the signal to noiseratio(SNR)is about20dB.We use a normalised LMS al-gorithm with a stepsize of0.1for all of the simulations.In thefirst set of simulations,we assume a referencesignal is available and the implementation in Fig.4is used. The learning curves for the ensemble mean square output error are shown in Fig.7and we can see that they have a similar convergence speed.However,the steady state er-ror of the SDL system is much higher than that of the TDL one for the same stepsize.Interestingly,for the second im-plementation,i.e.no reference signal is available,which is more practical,as shown in Fig.6,the SDL system achieves a lower steady state error than the traditional TDL one,as shown in Fig.8.In both of the cases,the proposed SDL system has shown its capability of nulling out the interfer-ing signals.In the future,more research is needed to analyze the performance of the SDL system in details and compare it with the traditional method for different implementations.Proc.of the200715th Intl.Conf.on Digital Signal Processing(DSP2007)577iterationse n s e m b l e m e a n s q u a r e e r r o r /[d B ]Fig.7:The learning curves when a reference signal is avail-able for beamforming.Fig.8:The learning curves based on the GSC.4.CONCLUSIONSA novel adaptive broadband beamforming structure has been proposed,where the TDLs in the traditional broadband beam-forming structure are replaced by sensor delay-lines and only one coefficient is required for each of the received sen-sor signals.In this way,the high-speed analogue tapped delay-lines or digital sampling circuits are not required any more and broadband beamforming can be performed by sim-ple analogue circuits.Our simulations show that the new structure is capable of performing the beamforming task ef-fectively.In the future work,we will give a detailed analy-sis of this structure in terms of bandwidth performance and also compare it with the traditional method in all kinds of situations.5.REFERENCES[1]H.L.Van Trees,Optimum Array Processing,PartIV of Detection,Estimation,and Modulation Theory ,John Wiley &Sons,Inc.,New York,U.S.A.,2002.[2]M.Zatman,“How narrow is narrowband?,”IEE Proc.-Radar,Sonar Navig.,vol.145,no.2,pp.85–91,April 1998.[3]J.T.Mayhan,A.J.Simmons,and W.C.Cummings,“Wide-band adaptive antenna nulling using tapped de-lay lines,”IEEE Transactions on Antennas and Prop-agation ,vol.AP-29,pp.923–936,November 1981.[4]B.D.Van Veen and K.M.Buckley,“Beamforming:AVersatile Approach to Spatial Filtering,”IEEE Acous-tics,Speech,and Signal Processing Magazine ,vol.5,no.2,pp.4–24,April 1988.[5]E.W.V ook and pton,Jr.,“Band-width Performance of Linear Adaptive Arrays withTapped Delay-Line Processing,”IEEE Transactions on Aerospace and Electronic Systems ,vol.28,no.3,pp.901–908,July 1992.[6]L.Yu,N.Lin,W.Liu,and ngley,“Band-width performance of linearly constrained minimum variance beamformers,”in Proc.IEEE International Workshop on Antenna Technology ,Cambridge,UK,March 2007.[7]M.Ghavami,“Wideband smart antenna theory us-ing rectangular array structures,”IEEE Transactions on Signal Processing ,vol.50,no.9,pp.2143–2151,September 2002.[8]M.Uthansakul and M.E.Bialkowski,“Widebandbeam and null steering using a rectangular array of planar monopoles,”IEEE Microwave and Wireless Components Letters ,vol.16,pp.116–118,March 2006.[9]W.Liu and S.Weiss,“A new class of broadband ar-rays with frequency invariant beam patterns,”in Proc.IEEE International Conference on Acoustics,Speech,and Signal Processing ,Montreal,Canada,May 2004,vol.2,pp.185–188.[10]S.Haykin,Adaptive Filter Theory ,Prentice Hall,En-glewood Cliffs,3rd edition,1996.[11]O.L.Frost,III,“An algorithm for linearly constrainedadaptive array processing,”Proceedings of the IEEE ,vol.60,no.8,pp.926–935,August 1972.[12]L.J.Griffiths and C.W.Jim,“An alternative approachto linearly constrained adaptive beamforming,”IEEE Transactions on Antennas and Propagation ,vol.30,no.1,pp.27–34,January 1982.[13]N.Lin,W.Liu,and ngley,“Performance analysisof a broadband beamforming structure without tapped delay-lines,”in Proc.the International Conference on Digital Signal Processing ,Cardiff,UK,July 2007.578Proc.of the 200715th Intl.Conf.on Digital Signal Processing (DSP 2007)。