Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Smart antennas and MAC protocols in MANETLili Wei2004-12-02ContentsSmart antennas – basic concepts and algorithms•Background knowledge•System model•Optimum beamformer design•Adaptive beamforming algorithms•DOA estimation methodSchemes using directional antennas in MAC layer of ad hoc network•Vaidya scheme1•Vaidya scheme2•Nasipuri scheme•Bagrodia schemePart I : Smart antennas-- basic concepts and algorithmsBackground KnowledgeBasic challenge in wireless communication:---- finite spectrum or bandwidthMultiple access schemes:FDMATDMACDMASDMASpatial Division Multiple Access ---- Uses an array of antennas to provide control of space by providing virtual channels in an angle domainDirectional AntennasSectorised antenna1) switched beam system•Use a number of fixed beams•Select one of several beams to enhance receive signals2) adaptive array system•Be able to change its antenna pattern dynamically;Smart antennaSystem Modelcdclsintfjcetmtx21)()( dd)(22)()(tfjcetmtx))1((2))1(()(MtfjMceMtmtxUniform Linear Array of M elementsSystem Model)()( tmtmtfjcetmtx21)()( cdjetxtxsin212)()(Narrow Band array processing Assumption:cdMjMetxtxsin)1(21)()(sin)1(2sin22sin21cccdMjdjdjeeeSArray response vectorArray response vectorSystem ModelThe Beam-former Structure)()()(1*tXwtxwtyHiMiiMwwww21)()()()(21txtxtxtXM)(1tx)(2tx)(txM12M*1w*1w*Mw)(tyA simple example Design a beamformer with unit response at 600 and nulls at 00, -300, -750Optimum Beamformer Design)()()(111tntitx )()()(222tntitx )()()( tntitxMMM12M*1w*1w*Mw)(tySignal in AWGN and Interference)()()()( tntitXtr SetmtXtfjc2)()(  HtrtrER )()(   HNItntitntiER )()()()()()( trwtyHOptimum Beamformer DesignMaximum SINR beamformerSRSSRwNIHNISINR11maxUnder different criterionsMean-Square-Error optimum beamformer 2)(tmEP SPRwMMSE1Optimum Beamformer DesignMinimum-Variance-Distortionless-Response beamformerSRSSRwHMVDR11Under different criterionMaximum Likelihood optimal beamformerSRSSRwNIHNIML11Practical IssuesIn practice, neither R nor RI+N is available to calculate the optimal weights of the array;In practice, direction of arrival (DOA) is also unknown.IssuesSolutionAdaptive beamforming algorithms – the weights are adjusted by some means using the available information derived from the array output, array signal and so on to make an estimation of the optimal weights;DOA estimation methodsAdaptive Beamforming AlgorithmsBlock diagram of adaptive beamforming systemAdaptive Beamforming Algorithms1. SMI Algorithm (Sample Matrix Inverse)2. LMS Algorithm (Least Mean Square)3. RLS Algorithm (Recursive Least Square)4. CMA (Constant Modulus Algorithm)Adaptive Beamforming Algorithms1. SMI Algorithm (Sample Matrix Inverse)NiHiiNrrNR11ˆEstimate R using N samples:nrrRnnRHnnnn 1ˆ1ˆnnHnnHnnnnnrRrnRrrRRnnR111111111ˆ)1()ˆˆˆ1ˆ,....2,10ˆ10kccIRUse matrix inversion lemma:Then:SRwnn1ˆAdaptive Beamforming Algorithms2. LMS Algorithm (Least Mean Square)**1)(nnnnnHnnnnerwdwrrwwnnHnndrwe •Need training bits and calculate the error between the received signal after beamforming and desired signal;•The step size u decides the convergence of LMS algorithm;•Based on how to choose u, we have a set of LMS algorithm, “unconstraint LMS”, “normalized LMS”, “constraint LMS”.According to orthogonality principle (data| error) of MMSE beamformer:  0)()()(* tdwtrtrEHSolution:3. RLS Algorithm (Recursive Least Square)Adaptive Beamforming Algorithms)()(ˆ*111nnHnnnndwrrnRww  Given n samples of received signal r(t), consider the optimization problem—minimize the cumulative square errornkkkne02min10 Solution:•In some situation LMS algorithm will converge with very slow speed, and this problem can be solved with RLS algorithm.Adaptive Beamforming Algorithms4. CMA (Constant Modulus Algorithm) Assume the desired signal has a constant modulus, the existence of an interference causes fluctuation in the amplitude of the array output. Consider the optimization problem:222)(21min AtrwEHSolution:)(221ArwwrrwwnHnnHnnnn•This is a blind online adaptation, i.e., don’t need training bits•CMA is useful for eliminating correlated arrivals with different magnitude and is effective for constant modulated envelope signals such as GMSK and QPSKDOA Estimation Method1. MF Algorithm (Matched Filter)2. MVDR Algorithm 3. MUSIC Algorithm (MUltiple SIgnal Classification)DOA Estimation Method1. MF Algorithm (Matched Filter)The total output power of the conventional beamformer is:  wRwwtrtrEwtrwEtyEPHHHH )()()()(22•The output power is maximized when •The beam is scanned over the angular region say,(-900,900), in discrete steps and calculate the output power as a function of AOA•The output power as a function of AOA is often termed as the spatial spectrum•The DOA can be estimated by locating peaks in the spatial spectrum•This works well when there is only one signal present•But when there is more than one signal present, the array output power contains contribution from the desired signal as well as the undesired ones from other directions, hence has poor resolution0Sw 2. MVDR AlgorithmDOA Estimation Method This technique form a beam in the desired look direction while taking into consideration of forming nulls in the direction of interfering