Statistical characteristics of a constrained adaptive array antenna (AAA) with a nonlinear function in the feedback loop that is tuned with the use of the discrete gradient algorithm are studied with consideration for fluctuations of the weighting vector. Statistical characteristics of this AAA are sought using the methods of perturbation theory. It is assumed that the vector of input signals and the weighting vector are related by a non-Gaussian statistical relationship. The problem is solved without specification of the particular form of the nonlinear function in the feedback loop. Expressions for the correlation function and the output-signal power, as well as the expression for the correlation matrix of fluctuations of the AAA weighting vector, are obtained in the first approximation.
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