Adaptive linear-phase complex filtering algorithms

The paper discusses the problem about complex adaptive filtering with linear-phase. By deriving the real version of Wiener equation subject to the linear-phase constraint, the problem of complex filters can be treated in real ways instead of complex one. The real modified LMS, RLS, Kalman-type algorithms and steered LMS algorithm are introduced to solve the Wiener equation (the last algorithm is for a steered problem in which the beam-steering vector is determined from signal power spectrum). It is noted that the number of real-time multiplications required by the presented algorithms are about half of those required by conventional complex ones when implementing an adaptive filter.