Analysis of constrained LMS algorithm with application to adaptive beamforming using perturbation sequences

Adaptive antenna array processing employing a constrained least mean square algorithm requires an unbiased estimate of the gradient of the output power with respect to the array weights. There are a number of schemes for obtaining an unbiased estimate of this gradient. As the covariance of the estimated gradient with each method is different, the transient and the steady state behaviour of the algorithm is different in each case. In this paper the transient and the steady state behaviour of the weight covariance matrix is analysed and the exact expressions for the misadjustment are derived when the required gradient is estimated using perturbation sequences. The necessary and the sufficient condition for the diagonalization of the weight covariance matrix is derived.