Sphere Decoding Algorithm for MIMO DetectionMotivationMotivation contd.Problem FormulationProblem Formulation contd.ML solutionExperimentExperiment: Brute Force SearchExperiment: Sphere Decoding AlgorithmSlide 10Slide 11OptimizationsSphere Decoding Algorithm for MIMO DetectionArslan ZulfiqarMotivationFuture mobile applications includeMobile TVHigh Speed InternetFuture wireless systems need to provideHigh Data RateHigh Quality of Service (QoS)Key challengesHostile propagation environmentBandwidth is a limited resourceHow do we meet these challenges?Multiple-Input multiple-output (MIMO) systemsMotivation contd.How can MIMO help?Spatial MultiplexingDiversityMIMO has been proposed in modern wireless standardsIEEE 802.11nIEEE 802.16e (WiMax)3GPP LTETradeoff: Increased complexity of the decoder!Problem FormulationSimple model of a communication system:1s2sMs1ˆs2ˆsˆMsChannelTX vectorRX vectorEstimateChannelMIMODecodingsxHˆHˆsM complexsymbols to be transmittedM transmitantennasN receiveantennasM decodedsymbols = + x Hs vHow do we do this?Problem Formulation contd.First, convert the problem involving complex quantities to one that involves real quantities dimensions scale by 2.Optimal ML solution= � = + x Hs v : 1n �x : 1m �s : 1n �v : n m�H2m M=2n N=ModelDimensions2argmin || ||mL�= -ss x Hs$DML solutionHow do we compute ?Brute force searchSearch over all Smart search: Sphere decoding algorithmThis algorithm finds a subset of that lie in a sphere around 2argmin || ||mL�= -ss x Hs$DssxExperiment64-QAM constellationQAM alphabet set = ={-7,-5,-3,-1,1,3,5,7}4x6 MIMO systemSNR considered:15dB,18dB,20dBInputs to MIMO decoder:received vector channel matrix LDxHExperiment: Brute Force SearchML equation:Total number of possibilities for 8ˆ8 16777216= =s2argmin || ||mL�= -ss x Hs$D~16 minutes!Experiment: Sphere Decoding AlgorithmML equation: Proposed by Fincke and PohstPick a radius such that, 2argmin || ||mL�= -ss x Hs$Dd22|| ||d -�x HsdxiHsExperiment: Sphere Decoding AlgorithmExperiment: Sphere Decoding AlgorithmOptimizationsParallel tree traversalLook ahead transformation Schnorr-Euchner
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