Space/time/frequency methods in adaptive radar - New Jersey ...

67where k is a gain constant and R is the colored noise true covariance matrix. TheWiener filter can be interpreted as a cascade of a whitening filter for the interference,followed by a matched filter. This solution requires the knowledge of thetrue covariance matrix R.3.2.3 Sample Matrix InversionIn practice, the true covariance matrix of the interference R is unknown a priori andneeds to be estimated from a limited set of the secondary data (noise and interference)as given in Equation 3.8.Substituting R for the true covariance matrix, R, in Equation 3.18 yields thefollowing solutionThe covariance matrix used for this solution has been estimated from a finite numberof secondary samples. Therefore, this solution for the weights is not optimal.The conditioned signal-to-colored noise ratio (CSNR) is defined as the ratio ofthe actual signal-to-colored noise ratio (SNR) to the optimal SNR. The optimal SNRresults when the covariance is known. Colored noise refers to the white noise andinterference. If K 2N snapshots are used to estimate R in Equation 3.8, Reedet al.[15] showed that this solution in Equation 3.19 achieves a CSNR at the outputof the array with a mean of 0.5. A 3 dB loss with respect to the optimal SNR is aCSNR with a mean of 0.5. The CSNR is a random variable bounded between 0 and1 because the covariance matrix is estimated using Equation 3.8 and the resultingsignal-to-noise ratio is a random variable.3.2.4 Generalized Sidelobe Canceller (GSC)The Generalized sidelobe canceller (GSC) is a general form of a linearly constrainedadaptive beamforming algorithm[48]. It adapts to minimize mean square error (MSE)