A new approach to least-squares adaptive filtering

A new adaptive algorithm, which is different from the gradient based algorithms and the recursive least-squares algorithms, from the point of view of the mathematical basis that it depends on, to be used for least-squares adaptive filtering is proposed. The algorithm is based on iterative solution methods which are used for the solution of linear equations. It is shown that the new algorithm provides an unbiased estimator for optimum Wiener solution. The proposed method is compared to the least mean square (LMS) algorithm and the recursive least squares (RLS) algorithm, considering computational complexity and rate of convergence criteria. It has been observed that the new algorithm has the convergence rate advantage over the LMS and computational complexity advantage over RLS algorithm. On the other hand, the new method combines the desirable convergence characteristics of the RLS when the eigenvalue spread of the correlation matrix of the input signal is not large. It has been shown that the new method of madpr (multiplication and division per recursion) is always much smaller than that of the RLS and smaller than that of the FRLS algorithm, for M⩽7, where M is the number of the adjustable weights in the algorithm (order of the system)