The Influence of Weight-Vector Fluctuations on Statistical Properties of an Adaptive Antenna Array with a Fast Recurrent Tuning Algorithm

Abstract

We present the results of statistical analysis of an adaptive antenna array tuned in accordance with the fast recurrent algorithm of inversion of a sample estimate of the correlation matrix with allowance for weight-vector fluctuations. Using the perturbation-theory methods in the first (Born) approximation, we obtain the spectral-correlation characteristics of the output signal of an antenna array. Fluctuations are shown to result in signal distortions at the output of an adaptive antenna array. Comparing the obtained expressions with the corresponding formulas for the antenna array with a gradient tuning algorithm, we see that for equal convergence rates of the above algorithms, the output-signal distortions are more pronounced for the fast recurrent algorithm. It is also shown that the weight-vector fluctuations are anisotropic for the fast algorithm, i.e., they are absent in the restriction direction, minimal in the interference direction, and maximal in all other directions. The weight-vector fluctuations in an adaptive antenna array with a gradient tuning algorithm are isotropic in the restriction subspace, i.e., they are the same in all directions and are equal in magnitude to fluctuations in the interference direction for the fast algorithm. The weight-vector fluctuations are also absent in the restriction direction for the gradient tuning algorithm.