Fast RLS algorithm using dichotomous coordinate descent iterations

The recursive least squares (RLS) adaptive filtering problem is expressed in terms of auxiliary normal equations with respect to increments of the filter weights. By applying this approach to the exponentially weighted case, a new structure of the RLS algorithm is derived. For solving the auxiliary equations, dichotomous coordinate descent (DCD) iterations with no explicit division and multiplication are used. This results in a transversal RLS adaptive filter with as low complexity as 3N multiplications per sample (N being the filter length), which is only slightly higher than the complexity of the Least Mean Squares (LMS) algorithm (2 AT multiplications). Simulations are used to compare the performance of the proposed algorithm against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is discussed and results of such implementation are presented.