Minimum MeanSquare 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 MeanSquared 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.

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