Performance of optimum phase-only adaptive nulling algorithms

Optimal weighting of adaptive antenna arrays is accomplished by computing the weight vector w that maximizes the signal-to-interference-plus-noise ratio. The optimal weight vector w=R ^-1v (R=covariance, v=steering 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, e.g., a phase-only adaptive weight vector of the form w=(e ^jφ1, e^jφ2, …, e^jφn) ^T. This constrained optimization problem may be posed as the problem of maximizing the SINR on the space of phase-only vectors, which can be solved via, conjugate gradient and Newton methods. This paper describes the convergence and nulling performance of these algorithms