A threshold criterion for phase-lock demodulation

An analytical threshold criterion has been developed for the general phase-lock receiver utilizing Booton´s quasi-linearization technique. This criterion is established for arbitrary information and noise spectral densities. The information is assumed phase- or frequency-encoded on the received signal. Explicit results are centered around the case of additive white Gaussian noise. The principal nonlinearity is assumed to be the phase detector which is represented as a product device. Threshold curves are derived for three types of signals: 1) Bandlimited phase-encoded white Gaussian signals, optimal receiver; 2) Bandlimited phase-encoded white Gaussian signals, second-order receiver; 3) Frequency-encoded white signals, optimal receiver. The phase-encoded white Gaussian signal threshold is then compared with Shannon´s results. It was found that the optimal receiver threshold occurs 10 log10(e) or 4.34 db above Shannon´s limit. The second-order receiver was found to threshold 2 to 3 db above the optimal receiver in the region of normally encountered output signal-to-noise power ratios. Frequency-encoded white signals represent the character of residual noise in a communication link oscillator system. Residual frequency noise is induced by the ever present thermal noise in oscillator circuits. This particular thermal-induced noise cannot be removed entirely. For this fundamental noise process maximum receiver sensitivities are derived. An interesting result of quasi-linearization is that, for the signals considered, previous solutions of the Wiener-Hopf equation may be applied with only slight modifications.