Statistical Design and Performance of High-Sensitivity Frequency-Feedback Receivers

Current interest in high-sensitivity receivers for frequency modulation is centered around two implementations of the device: phase-lock and frequency-feedback. Enloe and later Cahn presented linearized frequency-feedback receiver design theory based on a twin threshold concept. This paper presents the derivation of a quasi-linear model for the frequency-feedback receiver for the situation of Gaussian signals and noise. A statistical optimization is then performed giving the loop transfer function and threshold performance for a maximum sensitivity receiver. The design theory is based on a single threshold concept deviating from previous twin threshold approach. It is shown that in an optimum design the modulation error is less than 1 rad. This allows the use of a narrow-band IF filter and obviates the need to consider threshold characteristics of the discriminator within the loop. A significant result of this analysis is that although the quasi-linear receiver models differ in detail, threshold for a maximum sensitivity FM feedback and for a phase-lock receiver is identical. It was found that in FM feedback, as previously determined by Develet for the phase-lock receiver, threshold occurs at 10 log10(e)= 4.34 db above the ultimate limit determined by information theory arguments. This 4.34-db degradation is independent of modulation index. It is anticipated that the results in this paper will free the design engineer from concern about which device is theoretically better and allow his choice to be influenced solely by hardware considerations.