1Robust Detection of Binary CPMs with Unknown Modulation Index

Abstract—We consider soft-output detection of a binary con-tinuous phase modulation (CPM) generated through a low-cost transmitter, thus characterized by a significant modulation index uncertainty, and sent over a channel affected by phase noise. The proposed detector is designed by adopting a simplified representation of a binary CPM signal with the principal com-ponent of its Laurent decomposition and is obtained by using the framework based on factor graphs and the sum-product algorithm. It does not require an explicit estimation of the modulation index nor of the channel phase and is very robust to large uncertainties of the nominal value of the modulation index. Being soft-output in nature, this detector can be employed for iterative detection/decoding of practical coded schemes based on a serial concatenation, possibly through a pseudo-random interleaver, of an outer encoder and a CPM modulation format. Keywords—Continuous phase modulation, modulation index mis-match, phase noise, factor graph, sum product, iterative detection and decoding. I