Autocorrelation matrix of input signal (noise-corrupted signal) x(n), Φxx is [Note: Φd and Φm are autocorrelation matrix of desired signal and noise, respectively]

Φd∗Φm

Φd+Φm

Φd−Φm

Φd/Φm

The covariance is pretty fundamental here, Φd∗Φm