A structured gradient algorithm for adaptive beamforming

The constrained least‐mean‐square (LMS) algorithm uses a noisy estimate of the required gradient to adaptively estimate the weights of an optimal antenna array. The gradient is estimated by multiplying the array output with the array receiver outputs. An alternative scheme for estimating the required gradient is proposed in this paper. The new scheme uses a structured estimate of the array correlation matrix to estimate the gradient. This structure reflects the structure of the exact array correlation matrix and is obtained by a spatial averaging of the elements of the noisy array correlation matrix used in the standard algorithm. It is shown that the estimated gradient is unbiased and the array weights converge to the optimal weights in the mean sense. Furthermore, the weights estimated by the structured gradient algorithm are less noisy than those estimated by the standard algorithm.