COURSE PROJECT REPORTENEE 624 FALL 2001A Study of a various Beamforming TechniquesAndImplementation of the Constrained Least MeanSquares (LMS) algorithm for BeamformingVikas.C.RaykarGraduate StudentDepartment of Electrical and Computer EngineeringUniversity of Maryland, College [email protected] 01TABLE OF CONTENTS0.Abstract...............................................................................21.Introduction to Beam forming.............................................32.Beamformer Classification...................................................43.Simple Delay and Sum Beamformer....................................54.Constrained LMS algorithm (Frost Beamformer)................75.Adaptive Algorithm for Frost Beamformer.........................126.Simulation setup................................................................147.Simulation results..............................................................20 8.Conclusion.........................................................................27References............................................................................28APPENDIX : MATLAB Scripts .2C h a p t e r 0ABSTRACTA Beamformer is an array of sensors which can do spatialfiltering. The objective is to estimate the signal arriving fromthe desired direction in the presence of noise and otherinterfering signals. A beamformer does spatial filtering in thesense that it separates two signals with overlappingfrequency content originating from different directions. Theaim of the project was to study the different beamformingtechniques and use the Constrained Least Mean Squares(LMS) filter for spatial filtering. An array of microphones wassimulated in MATLAB and a simple delay and sumbeamformer was implemented. The results were comparedwith that of a single microphone and it was observed thatbeamforming definitely gives a significant SNR improvement.A Constrained least mean square algorithm (also known asFrost Beamformer) was derived which is capable ofiteratively adapting the weights of the sensor array tominimize noise power at the array output while maintaining achosen frequency response in the look direction. Theadaptive version of the Frost beamformer was simulated inMATLAB and it was observed that there was a significantimprovement in the SNR as compared to the simple delayand sum beamformer.34C h a p t e r 1INTRODUCTION TO BEAMFORMINGSpatially propagating signals encounter the presence ofinterfering signals and noise signals. If the desired signal andthe interferers occupy the same temporal frequency band,then temporal filtering cannot be used to separate the signalfrom the interferers. However the desired and the interferingsignals generally originate from different spatial locations.This spatial separation can be exploited to separate thesignals from the interference using a beamformer. Abeamformer consists of an array of sensors in a particularconfiguration. The output of each sensor is properly filteredand the filtered outputs of all the sensors are added up.Typically a beamformer linearly combines the spatiallysampled waveform from each sensor in the same way a FIRfilter linearly combines temporally sampled data. When lowfrequency signals are used an array of sensors can synthesizea much larger spatial aperture than that practical with asingle physical antenna. A second very significant advantageof using an array of sensors is the spatial filtering versatilityoffered by discrete sampling. In many applications it isnecessary to change the spatial filtering function in real timeto maintain effective suppression of interfering signals.Changing the spatial filtering function of a continuousaperture antenna is impractical. Typical uses of5beamforming arise in RADAR, SONAR, communications,imaging, Geophysical exploration, Biomedical and also inacoustic source localization.6C h a p t e r 2BEAMFORMER CLASSIFICATIONBeamformers are classified as either data independent orstatistically optimum, depending on how the weights arechosen. The weights in a data independent beamformer donot depend on the array data and are chosen to present aspecified response for all signal and interference scenarios.The weights in a statistically optimum beamformer arechosen based on the statistics of the array data to optimizethe array response. The statistics of the array data are notusually known and may change over time so adaptivealgorithms are typically used to determine the weights. Theadaptive algorithm is designed so the beamformer responseconverges to a statistically optimum solution.The weights in a data independent beamformer are designedso that the beamformer response approximates a desiredresponse independent of the array data or data statistics.This design objective is same as that for a classical FIR filterdesign. The simple Delay and sum beamformer is an exampleof the data independent beamforming. In statistically optimum beamformer the weighs are chosenbased on the statistics of the data received at the array. Thegoal is to optimize the beamformer response so that the7output signal contains minimal contributions due to the noiseand signals arriving from directions other than the desireddirection. The Frost beamformer is a statistically optimumbeamformer. Other statistically optimum beamformers areMultiple Side lobe Canceller and Maximization of the signalto noise ratio.8C h a p t e r 3DELAY AND SUM BEAMFORMERThe underlying idea of sum-and-delay beamforming is thatwhen an electromagnetic signal impinges upon the apertureof the antenna array, the element outputs, added togetherwith appropriate amounts of delays, reinforce signals withrespect to noise or signals arriving at different directions.The delays required depend on the physical spacing betweenthe elements in the array. The geometrical arrangement ofelements and weights associated with each element arecrucial factors in defining the array's characteristics. In delay-and-sum beamforming, delays are inserted aftereach microphone to