Minimum Mean-Square Error (MMSE) Weights (Part 3)

On the previous page, the MMSE weights were obtained as: The above equation requires knowledge of the autocorrelation matrix and the vector , both defined here. The inverse of the autorcorrelation matrix is often estimated using the Sample Matrix Inverse (SMI) method. The estimate is denoted with a bar overhead. It uses K snapshots (or samples) of the input vector X to determine the estimate: Assuming the desired signal is uncorrelated in time with the noise and interference (a reasonable assumption), the vector can be simplified to: The above equation states the the vector can be determined if the direction of the signal (given by ) and the signal power () are known. These parameters can be estimated using a training sequence to calibrate the array (training or known bits are often sent to calibrate a digital system to optimize transmission). Using the above equation, the optimal weights can be rewritten as: The optimal value of the Mean-Squared Error (MSE) can be evaluated using the formula for the mse and substituting in the optimal weights: The fundamentals of this method have been presented. In the next section, we'll look at an example that illustrates the utility of this method.