Improved LMS Algorithm for Adaptive Beamforming

The application of the constrained least mean square (LMS) algorithm to adaptive beamforming and its analysis has been studied by many authors [1]- [4].The algorithm updates the array weights employing a noisy estimate of the required gradient.In its usual form an estimate of the required gradient is made by multiplying the array output with the receiver outputs [1], [2].This is referred to as the standard algorithm throughout this paper.The structured gradient algorithm studied in [4], exploits the structure of the array correlation matrix (ACM) for estimating the gradient.For a linear array of equispaced receivers, immersed in a homogeneous noise eld, the ACM has a Toeplitz structure.i.e. the entries along each diagonal are equal.The noisy estimate of the ACM, used in the standard algorithm to calculate the gradient, is not constrained to have this structure.The structured gradient algorithm uses an estimate of the ACM constrained to have the same structure as the exact ACM.The standard LMS algorithm and the structured gradient algorithm are useful when all the receiver outputs are accessible.In the absence of that, perturbation algorithms [3], [5] are used to estimate the required gradient by ' ' array.The result presented in the paper shows that the performance of the algorithm is not sensitive to look direction signal.This algorithm performs better than the recursive least square algorithm in the presence of a strong look direction signal.