This work proposes an optimum receiver for signals corrupted by AWGN using a 3-stage process: replacement of the bank of filters by projection on Walsh functions; derivation of metrics from 1/4 of them by using a symmetry-based algorithm; and sequence detection with the M-algorithm. In this paper, the receiver is tested over AWGN and frequency-flat Rayleigh fading (FFRF) with and without phase compensation. It is found that the geometric algorithm used to derive the metrics introduces robustness to phase synchronism errors. The research on the reduction limits of the space dimension is conducted using catastrophic M-ary CPM schemes, taking advantage of their small number of phase states. Performance of 1REC h=1/2 16-ary under Rayleigh fading is for the first time presented. All the outcomes prove to be valid for two proposed high power gain CPM schemes. Two optimum CPM schemes and their respective sub-optimum receivers for mobile communications are presented. The receiver remains quasi-optimum over the tested multipath channel. The common minimum shift keying (MSK) is a particular case of this research.