Estimation of the Modulation Index of CPM Signals Based on Laurent´s Decomposition

Based on Laurent´s representation of continuous-phase modulated (CPM) signals, a channel shaping prefiltering method is exploited to transform the overall channel impulse response (CIR) into one that approximates a two-path desired impulse response (DIR). By utilizing this property of the overall CIR, a differential algorithm for the estimation of the modulation index of partial-response CPM is derived as an approximation to a quasi-maximum likelihood estimator. In this algorithm, the tradeoff between the robustness to time-varying phase and performance can be controlled by a memory length parameter. Also, in this algorithm, an error compensation technique is proposed to reduce the estimation error resulting from the high-order components of Laurent´s decomposition. Simulation results show that this algorithm with an appropriate memory length has better performance at low signal-to-noise ratio (SNR) than other estimators applicable to partial-response CPM in the literature, and that the performance losses of this algorithm caused by residual carrier frequency offset (CFO) and timing offset are acceptable in practice. Owing to its high convergence rate, this algorithm is appropriate for short-packet applications.