Carrier-Tracking Loop Performance for Quaternary and Binary PSK Signals

By expressing the open-loop response voltage as a Fourier series in terms of the phase-tracking error and then utilizing a very useful mean-value expression, we assess the performance of loops suited to recovering the carrier of four-phase (quaternary) and two-phase (binary) phase-shift-keyed (QPSK and BPSK) signals. At high signal to noise ratios (SNRs) they perform comparably, but at low SNRs the former´s performance deteriorates much more rapidly. The loop´s ability to maintain the carrier frequency despite the noise accompanying the PSK signal is measured by the mean and the variance of the oscillator´s control voltage. In particular, Spilker´s loop for QPSK and the Costas loop for BPSK signals are discussed.