Optimum Coherent Phase and Frequency Demodulation of a Class of Modulating Spectra

The optimum phase-locked loop demodulator is obtained for a carrier, phase modulated by a stationary Gaussian modulating process whose spectrum is proportional to 1/1 + (f/B)2n where n is any positive integer. Results are obtained also when the carrier is frequency modulated by the process for the limiting cases n = 1 and as n approaches infinity. It is shown that for phase modulation the output SNR as a function of the channel SNR in the bandwidth B varies from linear to exponential behavior as n increases from 1 to ∞. For the limiting cases the performance of frequency modulation is slightly inferior to that for phase modulation.