1. A Semi-Blind Technique for MIMO Channel Matrix Estimation Aditya Jagannatham and Bhaskar D. Rao The proposed algorithm performs well compared to its training based parallel for low pilot lengths. Its performance improves as the accuracy of computation of the whitening matrix increases. Typically the algorithm performs well in 1. Low SNR environments 2. When there are more receive than transmit antennas Summary: Semi-Blind What ? Semi-Blind refers to using a “pilot” signal of known input symbols along with “blind” outputs from unknown data symbols to estimate the channel matrix. Why ? In most practical scenarios training symbols are available Avoids “Convergence problems” Makes complete use of the training and blind information available. Robust algorithms for low SNR scenarios. Then, H TS = Y X † is the training based least-squares estimate of the channel matrix. It is the MLE and hence is optimal. However, it does NOT use blind information. Training only based estimation Let N channel outputs be observed. Of the inputs, are known “training” symbols. are “blind” outputs to unknown data symbols It is desired to make best use of complete available data to estimate H. If is the number of parameters required to parameterize a matrix G then, Since is defined by a much lesser number of parameters than, it can be determined with greater accuracy from the limited pilot data. As the number of receive antennas r increases, the size of increases while the size of (and hence, its complexity) remains constant. Advantages: When the whitening matrix is perfectly known, the error bound for estimating by the SB algorithm is: The error bound for the computation of employing the pilot signal based procedure is : When Simulation Results: Figure shows the error after the optimization of the ‘True-Likelihood’ cost function. H is 4X4, Data is 16-QAM, SNR =13dB The proposed procedure always performs better than the Training based one. Problem motivation Training only based estimation Semi-blind estimation Algorithm Performance bounds Simulations and observations Conclusions and future work Outline TxTx R # transmit antennas = t# receive antennas = r System Model: Multi-Input Multi-Output System University Of California, San Diego - Flat Fading Channel Matrix - Input Symbol Vector - Channel Output Vector - Additive White Gaussian Noise - Input is “white” = - Noise Covariance = M is unknown. “Channel Estimation” refers to determining this channel matrix. Plot shows the estimation error Vs pilot for an 8X4 matrix H, SNR = 13 dB and W is perfectly known. The proposed algorithm performs 4 dB better. This is expected because the parameter ratio is 64:16. Our work focuses on developing optimization procedures for steps 3,4 and 5. The Optimal matrix is first estimated as a solution to a simple modified likelihood. Using this as an initial estimate, the optimal for the actual cost function is determined, followed by a procedure for computing the jointly optimal estimates of Compute “blind” from output data. Factorize Find “Whiten” Output Compute initial by SVD “Refine” Estimate of Find jointly optimal W and Semi-Blind Algorithm Minimize the ‘True-Likelihood’ : subject to Goal : ‘Modified-Likelihood’ : Step 5: Minimize True Likelihood This has a ‘Closed-Form’ Solution The above likelihood has to be optimized for ‘JOINTLY’ optimal solution of W and Q 1. 2. 3. 4. 5. Step 3. Step 4. can be determined employing only output Assuming that noise power is known, can be computed “blind” from the output, without any knowledge of input. can then be computed using training data. However, since is a unitary matrix, the optimal solution has to be determined through a “constrained” optimization procedure. is a “whitening” matrix and is a unitary “rotation” matrix. Then Every matrix can be decomposed as: The semi-blind technique