CMA equalization with decision-directed phase correction

A modified version of the constant modulus algorithm (CMA) is presented: the phase-information modified CMA (PI-CMA), which adds a term to minimize the phase-alignment offset often produced by the CMA. The PI-CMA equalizer first acts as a standard CMA and once convergence within a defined region around a constant modulus value is achieved, a phase-alignment correction term is added to the algorithm, aligning (rotating) the constellation toward the orientation of the source constellation, a final phase ambiguity can be corrected by the use of coding or training. We show an application of the PI-CMA in a communication system which uses M-ary phase-shift keying (M-PSK) modulation.