RLS Algorithm with Variable Fogetting Factor for Decision Feedback Equalizer over Time-Variant Fading Channels

In a high-rate indoor wireless personal communication system, the delay spread due to multipath propagation results in intersymbol interference (ISI) which can significantly increase the transmission bit error rate (BER). Decision feedback equalizer (DFE) is an efficient approach to combating the ISI. Recursive least squares (RLS) algorithm with a constant forgetting factor is often used to update the tap-coefficient vector of the DFE for ISI-free transmission. However, using a constant forgetting factor may not yield the optimal performance in a nonstationary environment. In this paper, an adaptive algorithm is developed to obtain a time-varying forgetting factor. The forgetting factor is used with the RLS algorithm in a DFE for calculating the tap-coefficient vector in order to minimize the squared equalization error due to input noise and due to channel dynamics. The algorithm is derived based on the argument that, for optimal filtering, the equalization errors should be uncorrelated. The adaptive forgetting factor can be obtained based on on-line equalization error measurements. Computer simulation results demonstrate that better transmission performance can be achieved by using the RLS algorithm with the adaptive forgetting factor than that with a constant forgetting factor previously proposed for optimal steady-state performance or a variable forgetting factor for a near deterministic system.