An adaptive IIR channel equaliser: A Kalman filter approach

Using discrete time Wiener filtering theory a closed form for the optimum mean-square error (MSE) infinite impulse response (IIR) linear equaliser is derived. The minimum phase spectral factorisation, which is an integral part of the derivation of the IIR equaliser, may be circumvented through the use of a Kalman equaliser such as that originally proposed by Lawrence and Kaufman. The structure is made adaptive by using a system identification algorithm operating in parallel with a Kalman equaliser. In common with Luvison & Pirani, a least mean squares (LMS) algorithm was chosen for the system identification because the input to the channel is white. A new technique is introduced which both estimates the variance of channel noise and compensates the Kalman filter for errors in the estimate of the channel impulse response.