A Novel Unambiguous Acquisition Algorithm Based on Decomposition and Reconstruction of Sub-correlation Functions for Semi-integer CPM Signals

Abstract

Continuous phase modulation (CPM) is a nonlinear modulation scheme known for its excellent frequency and power efficiency. CPM with a semi-integer modulation index greater than 1 not only has spectral splitting characteristics like binary offset carrier modulation but also exhibits superior tracking performance and compatibility. However, the multiple side peaks in the autocorrelation function (ACF) of the semi-integer CPM signals introduce ambiguity threats in signal acquisition, and most existing ambiguity cancellation methods are not suitable for CPM signals due to the nonlinear nature of CPM signals. Therefore, a novel unambiguous acquisition algorithm based on decomposition and reconstruction of sub-correlation functions (DRSCF) is proposed for semi-integer CPM signals. The algorithm further decomposes the first pulse amplitude modulation waveform after Laurent decomposition to obtain sub-signal waveforms suitable for CPM signals and reconstructs the unambiguous correlation function by a nonlinear combination of sub-correlation functions. Subsequently, energy loss compensation is performed using ACF. Theoretical analysis and simulation results show that the proposed technique effectively eliminates the ambiguity threat in the acquisition process of semi-integer CPM signals at the expense of some detection performance loss while maintaining the narrow correlation peak characteristics of semi-integer CPM signals.