<title>Recursive reduced-rank adaptive equalization for wireless communications</title>

Abstract

The Multi-Stage Nested Wiener Filter (MSNWF) and the Conjugate Gradient (CG) method yield the solution of the Wiener-Hopf equation in the Krylov subspace of the covariance matrix of the observation and the crosscorrelation vector between the observation and the desired signal. Using the Lanczos algorithm instead of the Arnoldi algorithm for the MSNWF simplifies the computation of the Krylov subspace basis. In this paper, we show the relationship between the CG method and the Lanczos based MSNWF and finally derive that the MSNWF may be mathematically transformed into the CG algorithm. Consequently, we present a new implementation of the MSNWF where the weight vector and the Mean Square Error (MSE) is directly updated as each new stage is added. The new algorithm is applied to an Enhanced Data rates for GSM Evolution (EDGE) system where it linearily equalizes the received signal. Simulation results demonstrate the ability of the MSNWF to reduce the receiver complexity while maintaining the same level of system performance.