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

Previous: MMSE (Part 2)
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Weighting Methods

On the previous page, the MMSE weights were obtained as:

optimal weights for minimizing the MSE

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:

sample matrix inversion method

Assuming the desired signal is uncorrelated in time with the noise and interference (a reasonable assumption), the vector antenna arrays can be simplified to:

phased antenna array

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:

weighting methods

The optimal value of the Mean-Squared Error (MSE) can be evaluated using the formula for the mse and substituting in the optimal weights:

optimal value for MSE in phased arrays

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.

Next: MMSE (Part 4)

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