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Imperfect carrier synchronization causes a performance loss for coherent phase-shift-keyed (PSK) communications. This detection loss is greater for quaternary signaling (QPSK) than for the binary case (BPSK). The use of an offset form of QPSK, also known as double-biphase modulation, is shown to yield a probability of bit error in detection that is equal to the average of the detection performances for BPSK and conventional QPSK. Because of frequency instabilities in communications systems, it is sometimes difficult to obtain carrier synchronization with sufficiently low jitter to preclude significant detection losses. The use of offset QPSK in lieu of conventional QPSK modulation is shown to lower by almost 3 dB the required SNR of the synchronizer phase reference for satisfying a specified value of allowable detection loss.