Detection of Digital FSK and PSK Using a First-Order Phase-Locked Loop

A classical problem in digital frequency-shifted keyed (FSK) demodulation is the evaluation of the bit error probability performance when an estimator-correlator that incorporates a phaselocked loop (PLL) is employed. Although some attention has been devoted to this problem in the past, an accurate account of the mechanism which produces decision errors has not yet been advanced. This paper examines a special case, viz., a first-order PLL preceded by a wideband IF filter, of the above problem using a new approach which is based upon the renewal Markov process theory and the Meyr distribution. In particular, the ad hoc approach of invoking the Gaussian assumption on the decision variable and patching it with a correction term based on Rice´s click theory is not used. Rather, the effective noise is properly characterized by unfolding the renewal Markov process associated with the loop phase error. As a slight extension of the results, the performance of the above PLL detector operating on low data rate PSK is given and demonstrated to be approximately 3 dB superior to that of FSK reception. The theory and analysis presented herein apply to the special case where the bandwidth of the IF filter preceding the first-order PLL is required to be several times the data rate because of frequency uncertainties due to channel Doppler and oscillator instabilities, but the frequency deviation to data rate ratio may be chosen small (if desired) to optimize system error probability performance. In addition to presenting results for the case where the oscillator instabilities are assumed absent and channel Doppler is prefectly tuned out at the receiver oscillator, the effects of small residual Doppler on bit error probability performance is considered. In all cases tested, excellent agreement was obtained between theory and computer simulation results.