On prefilter computation for reduced-state equalization

In advanced time-division multiple-access (TDMA) mobile communications systems, reduced-state equalization algorithms have to be employed because high-level modulation is used in order to improve spectral efficiency. Reduced-state equalizers yield only high performance, if the overall discrete-time system to be equalized is minimum-phase. Therefore, in general, a discrete-time prefilter has to be inserted in front of equalization. For prefilter computation, several approaches are investigated in this paper. For the finite impulse response (FIR) prefilter case, which seems to be more relevant for practical applications than the in finite impulse response case, we discuss a method based on minimum mean-squared error decision-feedback equalization and a novel approach based on linear prediction (LP). The LP method seems to be very robust and requires an only moderate amount of computational complexity. Here, the prefilter consists of the cascade of a channel-matched filter and a prediction-error filter, which may be viewed as a finite-length approximation to the noise whitening part of the ideal prefilter transfer function. A key observation of the paper is that the proposed cascaded structure enables a very efficient prefilter computation because a prediction-error filter can be calculated via the Levinson-Durbin algorithm. Simulation results are given, which demonstrate that the performance of reduced-state equalization with proper FIR prefiltering is close to that of equalization combined with ideal all-pass prefiltering. Furthermore, it is shown that high performance can be obtained for TDMA mobile communications systems, if the LP scheme is employed for prefiltering.