Reduced-rank equalization for EDGE via conjugate gradient implementation of multi-stage nested Wiener filter

The Wiener filter solves the Wiener-Hopf equation and may be approximated by the Multi-Stage Nested Wiener Filter (MSNWF) which lies in the Krylov subspace of the covariance matrix of the observation and the crosscorrelation vector between the observation and the desired signal. Moreover, since the covariance matrix is Hermitian, the Lanczos algorithm can be used to compute the Krylov subspace basis. The Conjugate Gradient (CG) method is another approach in order to solve a system of linear equations. In this paper, we derive the relationship between the CG method and the Lanczos based MSNWF and finally transform the formulas of the MSNWF into those of the CG algorithm. Consequently, we present a CG based MSNWF where the filter weights and the Mean Square Error (MSE) are updated at each iteration step. The obtained algorithm is used to linearily equalize the received signal in an Enhanced Data rates for GSM Evolution (EDGE) system. Simulation results demonstrate the ability of the MSNWF to reduce receiver complexity while maintaining the same level of system performance. Keywords—Adaptive Filtering, Conjugate Gradients, EDGE, Multipath Propagation, Reduced-Rank Equalization, Space-Time Processing, Wireless Communications.