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Cyclic spectral analysis of continuous-phase modulated signals

Continuous-phase modulated (CPM) signals play a prominent role in modern communication systems due to their desirable constant-modulus property and the ability to control their power and bandwidth efficiencies. Popular CPM signals include the classical minimum-shift keyed (MSK) signal, the LREC family of signals also known as continuous-phase frequency-shift-keyed (CPFSK) signals, and Gaussian MSK, which is used in state-of-the-art GSM and PCS mobile communication systems. CPM signals, like virtually all man-made communication signals, are known to exhibit cyclostationarity, which implies that their probabilistic parameters, such as mean, second moment, and higher order cumulants, are almost-periodic functions of time. A novel representation of CPM signals as a sum of PAM signals is presented for both integer and noninteger modulation index cases. Then, the Nth-order cyclostationarity properties of binary CPM signals are derived in terms of Nth-order temporal and spectral moment and cumulant functions. Moreover, the case of M-ary CPM signals is briefly addressed. The results are illustrated with simulations involving MSK, LREC, and GMSK signals.