Statistical characteristics of adaptive antenna arrays with constraints

The statistical characteristics of constrained adaptive antenna arrays (AAA) are determined; these are the mean value and the covariance matrix of the weights, the total power of the output signal, and the output SNR. It is shown that the dispersion of the component fluctuations of the weight coefficient vector is less than that of unconstrained AAAs in accordance with the number of superimposed linearly independent constraints, providing the required frequency characteristic in the specified direction. It is also shown that fluctuations of weight coefficients lead to a disruption of the constraints. As an example, a two-element AAA with a single linear constraint is considered.