Two-channel constrained least squares problems: solutions using power methods and connections with canonical coordinates

Authors:
A. Pezeshki;L.L. Scharf;M.R. Azimi-Sadjadi;Yingbo Hua
Affiliations:
Dept. of Electr. & Comput. Eng., Colorado State Univ., Fort Collins, CO, USA;-;-;-
Venue:
IEEE Transactions on Signal Processing
Year:
2005

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Abstract

The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered, and a general set of solutions is derived. For each set of constraints, the solution is determined by a coupled (asymmetric) generalized eigenvalue problem. This eigenvalue problem establishes a connection between two-channel CLS filtering and transform methods for resolving channel measurements into canonical or half-canonical coordinates. Based on this connection, a unified framework for reduced-rank Wiener filtering is presented. Then, various representations of reduced-rank Wiener filters in canonical and half-canonical coordinates are introduced. An alternating power method is proposed to recursively compute the canonical coordinate and half-canonical coordinate mappings. A deflation process is introduced to extract the mappings associated with the dominant coordinates. The correctness of the alternating power method is demonstrated on a synthesized data set, and conclusions are drawn.