Fast Algorithm For Two-Dimensional Deterministic Nulling

In the past few years, we have developed techniques for inserting multiple discrete and wide continuous nulls for uniform linear array (ULA), and introduced for this purpose the use of quasi- and mixed- matrices and their factorizations. The techniques give an optimal solution, based on least squares criteria and a low-rank approximation to balance the null-depth and pattern distortion. The technique is extended to two-dimensional (2-D) uniform rectangular array (URA) in this paper. A fast algorithm is developed based on some efficient matrix properties of the Kronecker Product (KP). Essentially, we have converted a MN x MN matrix problem to M x M and N x N matrix problems to enable efficient implementation of 2-D deterministic nulling where M x N is the dimension of the URA.