Power spectral density of digital continuous phase modulation with correlated data symbols. Part 1: Autocorrelation function method

A general method for computing the power spectral density (PSD) of an encoded, continuous phase modulated (CPM) signal with correlated data symbols is presented in the paper. The encoder is a finite-state sequential machine which introduces correlation between symbols transmitted in different time slots. The method used is the so-called autocorrelation function method, in which the autocorrelation functon is first computed and then numerically Fourier-transformed to obtain the PSD. A key result is that the autocorrelation function is obtained via a recursive equation that is in keeping with the assumed Markov property of the data source. The computational complexity of the present method is linear in the length of the baseband pulse, and this enables one to calculate the PSD of CPM signals with a long pulse length. Our primary goal is to specifically consider the PSD of convolutionally encoded CPM signals. However, our algorithm is presented in a general format and numerical results are included for a wide class of digital CPM signals.