Determining Basis Vectors for Continuous Response Regions of a Uniform Rectangular Array with Applications to Two-Dimensional Nulling

摘要

We show that a two-dimensional (2D) region of the continuous response of an MxN rectangular array can be represented by a set of basis vectors characterizing the Kronecker product of two 1D-response quasimatrices. An optimal set of such basis vectors can be fast and efficiently extracted by exploiting that the Eigenvalue Decomposition (EVD) of the MNxMN Kronecker product of a matrix pair can be obtained by computing the EVDs of two matrices of sizes MxM and NxN. Further implementation savings can then be gained by choosing a separable set of 2D quiescent beamforming weights, W=w_uw_v^T, where M-element vector W_u operates on the array columns and N-element vector W_v operates on its rows. The overall approach is illustrated by applying it to the problem of modifying a given set of beamforming weights so as to insert discrete and extended nulls at pre-determined 2D spatial locations while optimally preserving the original “quiescent” beampattern.