CWC Research Review 03 WhiteningRotation Based MIMO Channel

CWC Research Review - ‘ 03 Whitening-Rotation Based MIMO Channel Estimation Aditya Jagannatham UCSD Jump to first page

TX Transmitter r- receive t - transmit A MIMO Communication System: Rx Receiver = Antenna Each channel is characterized by a Complex fading Coefficient q hij represents the channel between the ith receiver and jth transmitter q Arranging these as a matrix we get a ‘Flat Fading’ Channel Matrix ‘H’ q Jump to first page

System Model: MIMO System H Syste m where Model p. Estimating H is the problem of Channel Estimation Jump to first page

Problem Statement Blind Outputs Data MIMO System H Training Output Statistical Informati on Jump to first page

Issues in Channel Estimation p As the number of channels increases, employing entirely training data to learn the channel would result in poorer spectral efficiency. -Calls for efficient use of blind and training information p As the diversity of the MIMO system increases, the operating SNR decreases. * Constellation Size = 4 - Calls for more robust estimation strategies Jump to first page

ESTIMATION STRATEGIES Training Based Estimation Blind Outputs Data MIMO System H Training Output Training Constrai nt Solution + denotes pseudo-inverse Jump to first page

Blind Estimation MIMO System H Entirely Data !! q Estimate channel from DATA q No Training Necessary q Uses information in source statistics Jump to first page

Trainin g Blind Increasing Efficiency Increasing Simplicity Training Vs Blind Estimation Jump to first page

Semi. Blind Estimation – ‘Whitening-Rotation’ Goals : q Use as few training symbols as possible q Use total information – Training + Blind Total Information Key Idea : H is decomposed as the product of -A ‘Whitening’ Matrix W and a ‘Rotation’ Matrix Q Jump to first page

Procedure Estimating W : W can be estimated Blind from output Data Output Correlation = Estimate Output Correlation Estimate W such that, Q is the non-minimum phase part and cannot be estimated using Second Order Statistics. Q ? ? How do we estimate Jump to first page

Estimating – ‘Q’ the rotation matrix Solution : Estimate Q from the training sequence ! Advantage s Unitary matrix Q parameterized by a significantly lesser number of parameters than M. As the number of receive antennas increases, size of H increases while that of Q remains constant r x r unitary - r 2 parameters - r x r complex - 2 r 2 parameters - size of Q is t x t size of M is r x t Jump to first page

Parameter Sizes of Matrices # of Parameters “Accuracy can be improved by estimating only Q from training data while estimating H blind without employing training information” - CR Bound for Channel Estimation error is proportional to the number of parameters. Jump to first page

‘ROSE’ – Rotation Optimization Semi. Blind Goal : Minimize the ‘True. Likelihood’ : subject to : Procedure Step 1: Minimize the ‘Modified. Likelihood’ : Step 2: Employ this estimate of Q to minimize the True likelihood Step 3: Using the estimate of Q compute jointly optimal estimates of W, Q Jump to first page

Simulations p Fading coefficients (entries of H) are circular Gaussian random variables (Rayleigh Fading) p Input data is 16 QPSK. p Different H sizes ( 4 X 4, 8 X 4 et al. ) have been considered p Input SNR 13 - 14 d. B ( ) p Error is. p Estimation error Vs different pilot lengths is plotted for a fixed total length (N) Jump to first page

Simulation Results H is 8 X 4, SNR = 13 d. B, N (Total # Samples) = 400 ROSE performs better for very low Pilot lengths ( 20 symbols approximately) Jump to first page

Simulation Results Total Optimization ROSE performs better for all pilot lengths Jump to first page

Conclusions r A Semi-Blind algorithm has been proposed r Motivation for the formulation has been presented. r Its performance has been studied through simulations. Jump to first page

Low Power Scenario H is 8 X 4, Additional - 6 db Fade on Channel ROSE now performs better up to PILOT length 60 symbols. Performance (as compared to Training) improves as SNR decreases Jump to first page