Widely linear (WL) adaptive filters have been receiving much attention recently, since they take advantage of the full second-order statistics of improper signals. While this approach provides estimation gains if compared to their strictly linear (SL) counterparts,WL algorithms generally present higher computational complexity. In order to reduce the computational cost, we presented in a previous paper a reduced-complexity (RC) version of the WL-RLS algorithm – the RC-WL-RLS algorithm – which was shown to be 4 times less expensive than the WLRLS, but still keeps the O(N2) complexity (where N is the length of the regressor vector). In this paper, we modify the RCWL- RLS, applying the dichotomous coordinate descent (DCD) algorithm to iteratively solve the normal equations. With this approach, we reduce the number of multiplications per iteration and obtain a numerically stable widely-linear RLS algorithm with computational complexity linear on N. Simulations are presented to support our approach.

### Low-complexity widely linear RLS filter using DCD iterations

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