Asymptotic properties of an adaptive beam former algorithm

The asymptotic properties of a recursive adaptive beam former algorithm are studied. Both decreasing-gain and constant-gain cases are treated. For the case of decreasing gain the mean square convergence result is obtained, whereas for constant gain a sharp bound is derived, and asymptotic analysis for the normalized error is carried out. The analysis provides a clear picture of the local behaviour of the iterates near the optimal value. A sequence of scale deviations or normalized errors is shown to converge to a Gauss-Markov diffusion process which satisfies a stochastic differential equation.<
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