Joint Target-Message Reception of Constant-Envelope CPM for Joint Radar and Communications

This paper presents a likelihood-consistent joint target-message receiver for a strictly constant-envelope continuous phase modulation (CPM) waveform in pulsed phased-array joint radar–communication (JRC). Station A performs monostatic detection with the transmitted message, while Station B performs bistatic detection and communication with an available, degraded, or absent target-independent reference path. The target-scattered message is included only under the target-present hypothesis. A log-domain 16-state recursion evaluates the exact finite-alphabet CPM message marginal over the complete 46+2-symbol, 92-bit frame and is verified against direct enumeration on a six-bit unit frame to floating-point precision. At a 10 dB reference-path SNR, marginalization increases detection probability relative to single-path max-log reconstruction by 4.67 percentage points (95% paired interval 1.33–8.00) and 8.33 percentage points (4.33–12.33) at target-path SNRs of 10 and 14 dB, respectively; the corresponding joint-success differences are zero. Across 2048 ordered error events, the directed conditional distance has a Spearman correlation of −0.970 with empirical pairwise error probability. The CPM parameterization guarantees a constant active-pulse envelope at every array element, whereas constrained common-phase selection provides only a secondary adjustment of message-dependent ambiguity sidelobes. System-level experiments in a coastal setting use independent 92-bit messages and matched transmission resources for the proposed CPM waveform and RRC-QPSK. Both waveforms recover all evaluated direct-path payloads, showing that the proposed constant-envelope waveform preserves communication reliability at the tested operating point. The same records demonstrate geometry-consistent monostatic and bistatic target recovery, while finite-scatterer tests define the boundary of the single-scattering-center model.