Coherent LMS algorithms

Pilot symbol-assisted adaptive algorithms provide coherent detection for communication systems when the filtering coefficients, such as beamforming weights or equalizer coefficients, are converged. This property can be exploited to speed up the convergence of adaptive algorithms used. In this letter, two new adaptive algorithms, coherent least mean square (C-LMS) and coherent normalized LMS (CN-LMS), are proposed by constraining the desired signal component of the filtering output to be always coherent in phase with the reference signal at each iteration. For same adaption step size, these new algorithms provide faster convergence, while yield same steady-state excess mean-square error as compared with their standard LMS counterparts.