Whitening-Rotation Based MIMO Channel Estimation 2/25/2019 CWC Research Review - ‘03 Whitening-Rotation Based MIMO Channel Estimation Aditya Jagannatham UCSD

TX Rx A MIMO Communication System: r- receive t - transmit Receiver 2/25/2019 A MIMO Communication System: Rx Transmitter Receiver = Antenna TX t - transmit r- receive Each channel is characterized by a Complex fading Coefficient hij represents the channel between the ith receiver and jth transmitter Arranging these as a matrix we get a ‘Flat Fading’ Channel Matrix ‘H’

Estimating H is the problem of Channel Estimation 2/25/2019 System Model: MIMO System H where System Model Estimating H is the problem of Channel Estimation

H Problem Statement Blind Outputs Data MIMO System Training 2/25/2019 Problem Statement Blind Outputs Data MIMO System H Training Training Output Statistical Information

Issues in Channel Estimation 2/25/2019 Issues in Channel Estimation 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 As the diversity of the MIMO system increases, the operating SNR decreases. - Calls for more robust estimation strategies * Constellation Size = 4

ESTIMATION STRATEGIES Training Based Estimation 2/25/2019 ESTIMATION STRATEGIES Training Based Estimation MIMO System H Training Blind Outputs Data Training Output Constraint Solution + denotes pseudo-inverse

H Blind Estimation MIMO System Entirely Data !! 2/25/2019 Blind Estimation MIMO System H Entirely Data !! Estimate channel from DATA No Training Necessary Uses information in source statistics

Training Blind Training Vs Blind Estimation Increasing Simplicity 2/25/2019 Training Vs Blind Estimation Training Blind Increasing Efficiency Increasing Simplicity

SemiBlind Estimation – ‘Whitening-Rotation’ 2/25/2019 SemiBlind Estimation – ‘Whitening-Rotation’ Goals : Use as few training symbols as possible 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

W can be estimated Blind from output Data 2/25/2019 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 How do we estimate Q ??

Estimating – ‘Q’ the rotation matrix 2/25/2019 Estimating – ‘Q’ the rotation matrix Solution : Estimate Q from the training sequence ! Advantages Unitary matrix Q parameterized by a significantly lesser number of parameters than M. r x r unitary - r2 parameters r x r complex - 2r2 parameters As the number of receive antennas increases, size of H increases while that of Q remains constant - size of M is r x t - size of Q is t x t

Parameter Sizes of Matrices 2/25/2019 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.

‘ROSE’ – Rotation Optimization SemiBlind 2/25/2019 ‘ROSE’ – Rotation Optimization SemiBlind Minimize the ‘True-Likelihood’ : subject to : Goal : 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

2/25/2019 Simulations Fading coefficients (entries of H) are circular Gaussian random variables (Rayleigh Fading) Input data is 16 QPSK. Different H sizes ( 4 X 4, 8 X 4 et al.) have been considered Input SNR  13 - 14 dB ( ) Error is. Estimation error Vs different pilot lengths is plotted for a fixed total length (N)

H is 8 X 4, SNR = 13 dB, N (Total # Samples) = 400 2/25/2019 Simulation Results H is 8 X 4, SNR = 13 dB, N (Total # Samples) = 400 ROSE performs better for very low Pilot lengths ( 20 symbols approximately)

ROSE performs better for all pilot lengths 2/25/2019 Simulation Results Total Optimization ROSE performs better for all pilot lengths

Conclusions A Semi-Blind algorithm has been proposed 2/25/2019 Conclusions A Semi-Blind algorithm has been proposed Motivation for the formulation has been presented. Its performance has been studied through simulations.

ROSE now performs better up to PILOT length 60 symbols. 2/25/2019 Low Power Scenario H is 8 X 4, Additional - 6db Fade on Channel ROSE now performs better up to PILOT length 60 symbols. Performance (as compared to Training) improves as SNR decreases