Constrained least squares in adaptive, imperfect arrays

Two new constrained deterministic least-squares algorithms are presented which are capable of enabling a narrow-band zero-order generalized sidelobe canceller (SLC), in the presence of array imperfections, to null out jammers while preserving the friendly look-direction signal with minimal a priori knowledge of the signal environment. The algorithms are capable of solving deterministic least-squares optimization problems subject to an equality constraint in an iterative, adaptive manner by imposing a `soft´ constraint via the quadratic penalty function optimization method. The first algorithm is based on the matrix inversion lemma while the second is obtained by means of QR-decomposition using new three-dimensional Givens (1958) rotations and implemented with a systolic array architecture. These new constrained algorithms improve system performance when an artificial injection of a receiver noise vector is introduced