Performance analysis of least squares-based multichannel decision feedback equalization of time-varying channels

Most of the techniques developed for mitigating the problems caused by multipath and Doppler effects in wireless communication channels rely on equalization. The Decision Feedback Equalizer (DFE) is a widely used equalization method which is particularly robust for underwater acoustic channels. However, in this and many other applications, the characteristics of the communications channel are unknown and time-varying so the DFE must adapt its filter coefficients based upon observations of the received signal. This paper presents a theoretical characterization of the performance of the multi-channel DFE equalizer when the number of symbols that can be received in the time period over which the channel can be considered time-invariant is limited. The derived result highlights that the optimal equalizer design is a trade-off between the MMSE requirement for longer constituent filters and the insight that the limit on the number of stationary observations also limits the number of filter coefficients that can be effectively adapted. The derived characterization and its interpretation are validated via simulations and processing of experimental data.