An adaptive Kalman equalizer: Structure and performance

The development of an adaptive infinite impulse response (IIR) linear equalizer is described. Using discrete time Wiener filtering theory, a closed form for the optimum mean-square error IIR filter is derived. A performance comparison using both minimum and non-minimum phase channels indicates the complexity/performance advantages inherent in the IIR system compared to an optimum finite impulse response (FIR) solution. The minimum phase spectral factorization, which is an integral part of the derivation of the IIR equalizer, may be circumvented through the use of a Kalman equalizer 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 equalizer. In common with Luvison and Pirani, a least mean squares (LMS) algorithm was chosen for the system identification because the input to the channel is white and hence the LMS algorithm will produce consistent predictable results with little added complexity. 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. Computer simulation results show that the convergence performance of this new adaptive IIR filter is roughly equivalent to an FIR equalizer which is trained using a recursive least squares algorithm. However, the order of the new filter is always lower than the FIR filter.