The Kalman Filter for the Equalization of a Digital Communications Channel

Abstract

Consideration is given to the use of the discrete Kalman filter as an equalizer for digital binary transmission in the presence of noise and intersymbol interference. When the channel is modeled as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -tap transversal filter, the Kalman filter assumes a similar form with "feed forward and feedback." It is shown how the Kalman filter can be used to estimate both the tap weights and the binary signal. Computer results on a fixed 6-tap channel show that use of the 6-tap Kalman filter yields a considerably smaller error probability than when a conventional transversal equalizer with 15 taps is used. Limited computer studies on the same channel, assumed to be initially unknown, suggest that the Kalman filter is capable of converging rapidly in the adaptive mode. Though these results are very encouraging, much work remains in the study and optimization of performance in the adaptive mode.