The Wideband Nulling Problem, Architectures and Algorithms

Charles M. Rader
Lincoln Laboratory
Massachusetts Institute of Technology

A wideband nulling architecture uses an array of N antennas and with each antenna, a tapped delay lines with K taps. An output takes the form of a weighted sum of the signals present at all the taps, N*K weights in all. The problems of nulling are first to find the suitable weights and then, second, to apply them to the data. Finding the suitable weights will usually require us to solve N*K linear equations for N*K unknowns. The normal cost of solving N*K equations for N*K unknowns would increase with N like N^3 and increase with K like K^3, but because of structure in the linear equations, there are algorithms whose cost is proportional to only (K^2)*(N^3). (By comparison, finding suitable weights based on dividing the problem up into independent narrow band pieces, an approximation, should be even faster.) In this paper, we will consider the non-approximate methods, exploiting the fact that the matrix of constant coefficients is block-Toeplitz. We will explain how one such method works, using hyperbolic rotations, and then we will connect it to an order-recursive nulling architecture.