Adaptive algorithm for interference canceling in array processing

Abstract

In array processing, one technique for cancelling interference in the presence of colored noise is the ULLV decomposition of a pair of matrices. The factorization is stable and accurate, and is easy to update when a row is added to either one of the two matrices. In earlier work, we made the assumptions that both matrices must have at least as many rows as columns and that the matrix representing interference must have full column rank. In this paper, we relax the latter restriction and allow the interference matrix to be rank deficient. We present an algorithm for computing the decomposition and two techniques for updating it. The details on updating are quite different from those in the full rank case.

UTV Expansion Pack: Special-purpose rank-revealing algorithms

“…The remaining steps are identical to the algorithm from [18]. The single "1" in the bottom row of the third factor is chased to the left by interleaved swaps of neighbor columns and Givens rotations applied to the rows to annihilate the fill.…”

“…This led Luk and Qiao [18] to define an alternative decomposition, which we shall refer to as the ULLIV decomposition. Assume again that m ≥ n ≥ rank(A) while B has full row rank, i.e., rank(B) = p < n. Then the ULLIV decomposition takes the form…”

“…When a row b T is appended to B then we must distinguish whether the rank increases or stays the same, because of our assumption that B has full row rank. An updating algorithm for the former case is described in [18]; we found it convenient to augment the algorithm with an additional stage, which simplifies the rank-revealing step. This algorithm takes its basis in the formulation…”

“…An efficient algorithm for updating the ULLIV decomposition when a row a T is appended to A is described in [18]. The algorithm takes its basis in the formulation…”

Untitled

“…where L is now p × p; for more details about this version and its application in interference problems, see [30,39]. Other generalized UTV decompositions are discussed in [57] (matrix quotients of the form A −1 B) and [8] (a decomposition of the form…”