A Modulation Index Estimation Algorithm of CPM Signal Based on Time-frequency Domain Characteristics

‍ ‍At present， under non-cooperative condition， the modulation index estimation algorithm of continuous phase modulation （CPM） signal in narrowband system depends on the prior information of constraint length. To avoid dependence on the constraint length， this paper creatively proposes a modulation index estimation algorithm based on time-frequency domain characteristics. CPM signals can be divided into continuous phase frequency shift keying （CPFSK） signals and non-CPFSK signals according to the characteristics of phase pulse. Firstly， determine the signal type according to the characteristics of phase pulse. Secondly， based on the cyclic property of CPM signals， the power spectrum of the transformed signal is used to estimate the frequency offset and integer multiples of the denominator of the modulation index. Third， complete signal carrier synchronization， timing synchronization and smooth processing； Then， based on the difference of the phase distribution of signals under different parameter conditions， aiming at the signal whose modulation index is adjusted to integer， calculate the Euclidean distance between the quantile function curve of the signal and the template curve under the corresponding constraint length in each sign period， and the modulation index of the template curve corresponding to the minimum Euclidean distance is chosen as the integral multiple of the modulation index molecule of the pre-adjustment signal. Finally， the modulation index value is determined by the results of the denominator and the numerator estimation. The simulation results show that for CPM signals with partial response of arbitrary frequency pulses， if the signal modulation index h is less than 1， the average recognition accuracy is more than 81% when the signal-to-noise ratio is greater than 16 dB. If the signal modulation index h is greater than 1， the average recognition accuracy is greater than 82.2% when the signal-to-noise ratio is greater than 18 dB. The simulation experiment proves that the proposed algorithm does not require the constraint length prior information， and is applicable to partial response CPM signals with arbitrary modulation index. Moreover， it can distinguish signals with similar modulation index values to a certain extent. The validity of the proposed algorithm is proved by the experiment of parameter estimation of real signal.