Multiple-Input-Multiple- Output (MIMO) SystemsTopicsAspirationsAspirations (Mathematical) of a System DesignerAntenna ConfigurationsMIMO Antenna ConfigurationData UnitsShannon’s Capacity (C)Spectral EfficiencyMIMO System ModelTypes of ChannelsFading ChannelsChannel Matrix HCapacity of MIMO ChannelsCapacity (contd)MIMO Design CriterionDiversitySpatial MultiplexingPractical SystemV-BLAST – Spatial Multiplexing (Vertical Bell Labs Layered Space-Time Architecture)V-BLAST (Experimental Results)Alternate ReceiversD-BLAST – a little of both (Diagonal Bell Labs Layered Space-Time Architecture)Alamouti’s Scheme - DiversityComparisonsOrthogonal Frequency Division Multiplexing (OFDM)OFDM Spectral EfficiencyMIMO-OFDMIEEE 802.11 MAC (DCF Mode)MIMO-Based SolutionsMIMO-Based Solutions MIMA-MAC ProtocolSimulation ResultsSummary/ConclusionsReferencesMultiple-Input-Multiple- Output (MIMO) SystemsBasic principles, Algorithms and Networking ApplicationsHARISH GANAPATHYTopicsMotivations for the development of MIMO systemsMIMO System Model and Capacity StudiesDesign Criterion for MIMO Systems (Diversity Vs Spatial Multiplexing)Some actual architectures based on these criterionMIMO-OFDMNetworking Applications: MAC protocol for MIMO PHY layerConclusionsAspirationsHigh data rate wireless communications links with transmission rates nearing 1 Gigabit/second (will quantify a “bit” shortly)Provide high speed links that still offer good Quality of Service (QoS) (will be quantified mathematically)Aspirations (Mathematical) of a System DesignerHigh data rate Quality Achieve “Channel Capacity (C)”Minimize Probability of Error (Pe) Real-life Issues Minimize complexity/cost ofimplementation of proposedSystemMinimize transmission powerrequired (translates into SNR)Minimize Bandwidth (frequencyspectrum) UsedAntenna ConfigurationsSingle-Input-Single-Output (SISO) antenna systemTheoretically, the 1Gbps barrier can be achieved using this configuration if you are allowed to use much power and as much BW as you so please!Extensive research has been done on SISO under power and BW constraints. A combination a smart modulation, coding and multiplexing techniques have yielded good results but far from the 1Gbps barrierchannelUser data streamUser data streamMIMO Antenna ConfigurationUser data streamUser data stream..12MT...12MR.....channelUse multiple transmit and multiple receive antennas for a single userNow this system promises enormous data rates!Data UnitsWill use the following terms loosely andinterchangeably,Bits (lowest level): +1 and -1Symbols (intermediate): A group of bitsPackets (highest level): Lots and lots of symbolsShannon’s Capacity (C)Given a unit of BW (Hz), the max error-free transmission rate is C = log2(1+SNR) bits/s/HzDefine R: data rate (bits/symbol)RS: symbol rate (symbols/second)w: allotted BW (Hz)Spectral Efficiency is defined as the number of bits transmitted per second per HzR x RSbits/s/Hz W As a result of filtering/signal reconstruction requirements, RS ≤ W. Hence Spectral Efficiency = R if RS = WIf I transmit data at a rate of R ≤ C, I can achieve an arbitrarily low PeSpectral EfficiencySpectral efficiencies of some widely used modulation schemesThe Whole point: Given an acceptable Pe , realistic power and BW limits, MIMO Systems using smart modulation schemes provide much higher spectral efficiencies than traditional SISOScheme b/s/HzBPSK 1QPSK 216-QAM 464-QAM 6MIMO System Modely = Hs + nUser data stream..User data stream....ChannelMatrix Hs1s2sMsy1y2yMyTransmitted vector Received vector..h11h12Where H = h11 h21 …….. hM1 h12 h22 …….. hM2h1M h2M …….. hMM . . …….. . MTMRhij is a Complex Gaussian random variable that models fading gain between the ith transmit and jth receive antennaTypes of ChannelsFading ChannelsFading refers to changes in signal amplitude and phase caused by the channel as it makes its way to the receiverDefine Tspread to be the time at which the last reflection arrives and Tsym to be the symbol time periodTime-spread of signalFrequency-selectiveFrequency-flatTsymTspreadtimefreq1/TsymOccurs for wideband signals (small Tsym)TOUGH TO DEAL IT!TsymTspreadtimefreq1/TsymOccurs for narrowband signals (large Tsym)EASIER! Fading gain is complex GaussianMultipaths NOT resolvableChannel Matrix HIn addition, assume slow fadingMIMO Channel ResponseTaking into account slow fading, the MIMO channel impulse response is constructed as,Time-spreadChannel Time-variance Because of flat fading, it becomes,a and b are transmit and receive array factor vectors respectively. S is the complex gain that is dependant on direction and delay. g(t) is the transmit and receive pulse shaping impulse response•With suitable choices of array geometry and antenna element patterns, H( ) = H which is an MR x MT matrix with complex Gaussian i. i. d random variables•Accurate for NLOS rich-scattering environments, with sufficient antenna spacing at transmitter and receiver with all elements identically polarizedCapacity of MIMO Channelsy = Hs + nLet the transmitted vector s be a random vector to be very general and n is normalized noise. Let the total transmitted power available per symbol period be P. Then,C = log 2 (IM + HQHH) b/s/Hzwhere Q = E{ssH} and trace(Q) < P according to our power constraintConsider specific case when we have users transmitting at equal power over the channel and the users are uncorrelated (no feedback available). Then,CEP = log 2 [IM + (P/MT)HHH] b/s/HzTelatar showed that this is the optimal choice for blind transmissionFoschini and Telatar both demonstrated that as MT and MR grow, CEP = min (MT,MR) log 2 (P/MT) + constant b/s/HzNote: When feedback is available, the Waterfilling solution is yields maximum capacity but converges to equal power capacity at high SNRsCapacity (contd)The capacity expression presented was over one realization of the channel. Capacity is a random variable and has to be averaged over infinite realizations to obtain the true ergodic capacity. Outage capacity is another metric that is used to capture thisSo MIMO promises enormous rates theoretically! Can we exploit thispractically?MIMO Design CriterionMIMO Systems can provide two types of gainSpatial Multiplexing Gain Diversity Gain• Maximize transmission rate (optimistic approach) • Use rich scattering/fading