Schur type algorithms for spatial LS estimation with highly pipelined architectures

A family of Schur-type spatial least-squares algorithms is presented for solving the spatial LS estimation problem, in which the correlation matrix is neither Toeplitz nor near-Toeplitz, by order recursion. Normalized spatial Levinson- and Schur-type algorithms are also derived. Highly pipelined architectures are designed to realize these recursions. The reflection coefficients are first computed using the spatial Schur type recursions. Then, the forward and backward filter parameters are calculated by the spatial Levinson-type recursions. A pyramid systolic array is demonstrated to calculate not only the filter parameters but also the LDU decomposition of the inverse cross-correlation matrix at every clock phase. This pyramid array can be mapped onto a two-dimensional systolic array which has a simpler structure. A square systolic array is developed to implement the Levinson- and Schur-type temporal recursive LS (RLS) algorithms. A highly concurrent architecture which exploits the parallelism of the spatial Schur-type recursions is illustrated to perform the LDU decomposition of the cross-correlation matrix