Optimum phase-only adaptive nulling

Optimum weighting of adaptive antenna arrays is accomplished by computing the weight vector that maximizes the signal-to-interference-plus-noise ratio (SINR). The optimal weight vector is in general complex with each weight having different magnitudes and phases. However, the design of some antenna arrays facilitates phase-only weighting or phase-only adjustments, whereupon it is desirable to compute the constrained optimal weight vector whose components have fixed magnitudes but variable phases. This constrained optimization problem may be posed as the problem of maximizing the SINR on the space of phase-only vectors. This paper addresses the problem of computing optimal phase-only adaptive weight vectors by exploiting several properties of phasor and matrix algebra. Two new algorithms (the phase-only conjugate gradient and phase-only Newton's method) are introduced. The convergence properties. SINR performance, sidelobe level performance, and nulling performance of these algorithms are demonstrated using simulations and experimental data.