Affine-Projection Least-Mean-Magnitude-Phase Algorithms Using a Posteriori Updates

The least-mean-magnitude-phase (LMMP) algorithm is useful for complex-valued signal processing applications where precise control of magnitude and/or phase error information can provide improved estimation performance. Because it is a gradient procedure, however, the convergence speed of the algorithm can be limited for correlated input signals. In this paper, we derive affine-projection least-mean-magnitude-phase (AP-LMMP) algorithms based on an a posteriori update relation that have improved convergence performance over that of the LMMP algorithm without significant increases in complexity. We employ different nonlinear lookahead approaches depending on the projection order to compute the magnitudes of the a posteriori output signals and use these to implement the coefficient updates. Simulations indicate that AP-LMMP algorithms can outperform other algorithms in situations where their use is appropriate.