Acceleration of a Broad Band Multi-input/multi- Output/multi-error, Filtered-x Lms Algorithm through Transform Domain Optimization

The Filtered-x LMS algorithm has been an essential component of many industrial active control systems. This algorithm can be used in mono-channel, as well as multi-channel systems. One of the drawbacks of the multi-channel Filtered-x LMS algorithm is that its convergence speed depends on the autocorrelation and intercorrelation of the different filtered reference signals and can be very slow. Paillard et al. (1993) presented a fast Filtered-X algorithm based on transform domain optimisation. This paper presents an extension of the Transform Domain Filtered-x LMS to the multi-channel case. From simulated results, the Transform Domain algorithm will be shown to give superior performance while retaining the structural simplicity of the standard Filtered-x LMS, allowing the algorithmic separation of the real time control process and the optimization process. This, in turn allows control at higher sampling rates. The increase in computational complexity caused by the transform, while not negligible, will be shown to be very reasonable.