Degradation of FSK Detection Performance Due to Tone Phase Jitter

Abstract

The paper develops some new results for the degradation in SNR, due to unwanted phase jitter, for a FSK receiver system. The unwanted phase modulation is assumed to be present equally on either FSK tone and is modeled as a sample function of a Gaussian random process. Results are derived based on a standard type FSK system employing bandpass filters, square law envelope detectors, a subtractor, and a post detection lowpass data filter. The degradation was found to depend on the mark-space filter bandwidths, the doppler frequency of the received tones, the nominal SNR and the post detection filter bandwidths. The degradation is minimal for small doppler shifts; however, once the tones, in the predetection filters were displaced to within the post detection filter bandwidth of the predetection filter band edge, the degradation increased dramatically. This was due to the fact that the filtering of the phase noise caused the envelope detectors to produce self noise. In fact, at high SNR's the degradation is primarily due to self noise or envelope distortion due to filtering of the phase jitter spectrum. It is important to point out that the degradation found here is due only to phase noise effects and not sin χ/χ losses. The results derived here are accurate for phase jitter variances ≲0.1. In addition, it is assumed that the lowpass equivalent filter impulse response of the bandpass filter be real, that is, the lowpass equivalent transfer function must be hermetian symetric.