False lock performance of quadriphase receivers

Quadriphase receivers, like biphase receivers, have the ability to false lock on a sideband on the data modulation. The theory associated with this phenomenon for receivers of binary phase-shift-keying (BPSK), using Costas loop demodulation, has recently been documented in the literature. This paper considers the corresponding theory for receivers of balanced quadriphase-shift-keying (QPSK) employing a quadriphase Costas loop (or equivalent fourth-power loop) for demodulation. Specific closed form expressions for false lock performance are developed and numerically evaluated for the particular case of single pole arm filters and an NRZ data format for each of the two statistically independent quadrature modulations.