Exact Spectral Analysis of Single-h and Multi-h CPM Signals through PAM decomposition and Matrix Series Evaluation

TL;DR

This paper presents a novel closed-form spectral analysis of single-h and multi-h CPM signals using PAM decomposition and matrix series evaluation, providing exact PSD expressions and new insights into CPM structure.

Contribution

It introduces a new method for closed-form spectral evaluation of CPM signals, leveraging Markov chain reinterpretation, which was not previously available in the literature.

Findings

Derived true closed-form PSD for CPM signals.

Revealed new insights into CPM signal structure.

Established a Markov chain framework for spectral analysis.

Abstract

In this paper we address the problem of closed-form spectral evaluation of CPM. We show that the multi-h CPM signal can be conveniently generated by a PTI SM. The output is governed by a Markov chain with the unusual peculiarity of being cyclostationary and reducible; this holds also in the single-h context. Judicious reinterpretation of the result leads to a formalization through a stationary and irreducible Markov chain, whose spectral evaluation is known in closed-form from the literature. Two are the major outcomes of this paper. First, unlike the literature, we obtain a PSD in true closed-form. Second, we give novel insights into the CPM format.