Digital Phase Lock for Optimum Demodulation

This paper considers the discrete-time demodulation of random angle modulated signals embedded in Gaussian noise. It is first shown, with the aid of the discrete Karhunen-Loeve expansion, that under suitable conditions, a particular nonuniform sampling digital phase lock loop (DPLL) is the approximately optimum digital al demodulator in the maximum a posterior (MAP) sense. significance is the fact that the phase detector of this digital loop consists merely of a sampler; a digital multiplier is not required at the loop input. Next, an approximate nonlinear analysis is carried out for the condition in which random phase modulation is present at the input of a first order loop of the above class. These results are confirmed by simulation. Finally, the optimum demodulators for phase and frequency modulation are derived via Kalman filtering techniques and their performances presented.