An analytical expression for power spectra of M-ary L REC continuous phase modulation signals

Several different methods are available for computing the power spectral density (PSD) of a general continuous phase modulated (CPM) signal. For the case of rectangular frequency pulses with L=1 (that is, M-ary continuous phase frequency shift keying (CPFSK) or M -ary 1REC CPM), an analytical expression is known for the PSD when the data symbols are equally likely. An analytic expression is obtained for the PSD of an M-ary LREC CPM signal where L is an arbitrary positive integer and the data symbols are not necessarily equally likely. The technique employed does not require the tedious evaluation of integrals. Rather, the integrals are recognized as convolutions and the PSD is obtained using simple Fourier transform properties. Some numerical results and computational aspects of the method are discussed