Limits for CPM signals representation by walsh functions

TLDR: This paper explores the feasible limits for complexity reduction of a very simple front-end block for the calculus of phase transition metrics on a continuous phase modulation (CPM) receiver and enables the reductiou of the matched filters or correlators to just two integrators, regardless of the CPM scheme.

Abstract: This paper explores the feasible limits for complexity reduction of a very simple front-end block for the calculus of phase transition metrics on a continuous phase modulation (CPM) receiver. A quasi-optimum receiver of very low complexity is attained by splitting the function of the optimum receiver bank filters in two blocks: calculus of projections coefficients on a low dimensional space of Walsh functions followed by simple matrix calculus. A sequence detection algorithm follows this block The presented approach enables the reductiou of the matched filters or correlators to just two integrators, regardless of the CPM scheme. Research ou the reduction limits of the space dimension is conducted using catastrophic Wary CPM schemes, taking advantage of their very low number of phase states. Performance of lREC h=1/2 16-ary scheme is for the fist time presented. A rule is defined concerning the number of Walsh functions that must be used. That outcome proves to be valid for two CPM schemes of high power gain. The receiver is tested under additive white gaussian noise (AWGN).