<title>Recent advances in reduced-rank adaptive filtering with application to high-speed wireless communications</title>

Abstract

The Wiener filter (WF) estimate of a desired signal from a vector observation is optimal in the x<SUB>0</SUB>[n] is optimal in the Minimum Mean Square Error (MMSE) sense, and is employed in many applications because it is easily implemented and only relies on second order statistics. If the observation vector is of high dimensionality, though, a reduced-rank approach is needed in order to reduce computational complexity and lessen sample support requirements. In the Principal Components (PC) method, the observation signal is transformed to lower dimensionality by a matrix composed of the principal eigenvectors of the autocorrelation matrix of the data. However, the PC method is suboptimum as it only relies on the autocorrelation matrix and does not factor in the cross-correlation vector between the desired signal and the data in choosing the basis vectors for the reduced dimension subspace. Goldstein, Reed, and Scharf recently developed the Multi-Stage Nested Wiener Filter (MSNWF) in which the reduced dimesion subspace is inherently the Krylov subspace generated by the autocorrelation matrix and the cross-correlation vector. The MSNWF provides better peformance than the PC method at a substantially reduced computational cost. We here provide an overview of the MSNWF and a number of recent results related to both our conceptual understanding of the MSNWF and efficient implementations of the MSNWF. An application of the MSNWF to space-time equalization for the CDMA Forward Link for Third Generation cellular communications is presented demonstrating its efficacy.