Weight vector fluctuations in adaptive antenna arrays with nonlinear function in a feedback loop

We present the results of statistical analysis of adaptive antenna arrays with nonlinear function in the feedback loop, which are adjusted by an algorithm for recurrent inversion of a sample estimate of the input-signal correlation matrix with allowance for the weight-coefficient fluctuations. Using the perturbation-theory methods in the first (Born) approximation, we obtain expressions for the correlation function and power of the output signal of an adaptive antenna array and a formula for the covariance matrix of the weight-coefficient vector. The weight-coefficient fluctuations are shown to result in signal distortions at the antenna-array output and appearance of additional terms in the statistical characteristics of the antenna array. These terms are second-order infinitesimals with respect to adaptation coefficient. Fluctuations are first-order infinitesimals and, thus, are much greater in an antenna array without nonlinear function in the feedback loop. It is also shown that the weight-vector fluctuations are anisotropic, i.e., they are absent in the constraint direction, minimal in the interference direction, and maximal in all other directions. © 2006 Springer Science+Business Media, Inc.