Odd symmetry of weights vector in linearly-constrained adaptive arrays with desired signal

Abstract

The paper discusses the conditions of an odd symmetry in linearly-constrained least squares criterion adaptive array. It is shown, that the vectors, which optimal weight vector of such adaptive array consists of, and the optimal vector itself, have an odd symmetry, i.e. pairs of symmetrical elements of the vectors are complex-conjugated. To ensure this property, the vector of constrains (radiation pattern values in directions of interest) has to be specified as a real-valued ones. The odd symmetry allows to calculate the weights of the adaptive array in real-valued arithmetic at the cost of two or four times less number of arithmetic operations, comparing with similar calculations, based on complex-valued arithmetics. Adaptive algorithms, based on real-valued arithmetics, provide a 1.5 … 2 times shorter transient response and a 2 … 3 dB deeper notches in the steady-state radiation pattern towards interference sources comparing with complex-valued algorithms.