Optimum Linear Filtering Maximizes the Signal-to-Interference plus Noise Ratio (SINR)

The problem:

• We have N “channels” of data containing signal, noise, and interference

• We want to maximize E{SINR} by linearly combining the channels

The solution:

y = wHx, where w = aC-1s

adapted

output

(scalar)

weight

vector

(N x 1)

unadapted

data

(N x 1)

arbitrary

scalar

(I+N)

covariance

matrix

(N x N)

signal

“steering

vector”

(N x 1)

THIS IS AN IMPORTANT RESULT THAT HAS MANY APPLICATIONS

BEYOND ADAPTIVE BEAMFORMING!

“signal to interference-plus-noise ratio”

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