CONJUGATE-GRADIENT TECHNIQUES FOR ADAPTIVE FILTERING

Recent advances in hardware technology have made possible the implementation of sophisticated algorithms for adaptive filtering. The least mean squares (LMS) method, which has found widespread use owing to its simplicity, has poor convergence properties. The recursive least squares (RLS) method possesses superior convergence properties, but it is computationally intensive and has high storage requirements for matrix manipulations. Modifications of the RLS technique to reduce complexity have resulted in "fast" RLS methods, many of which unfortunately tend to be numerically unstable. In this paper the technique of conjugate gradients is applied for the adaptive filtering problem. The choice of the gradient average window in the algorithm provides one with a trade-off between computational complexity and convergence performance. The method is capable of providing convergence comparable to RLS schemes at a computational complexity that is intermediate between the LMS and the RLS methods and does not suffer from any known instability problems.