DIFFERENTIAL DETECTION IN QUADRATURE QUADRATURE PHASE-SHIFT KEYING (Q2PSK) SYSTEMS

A generalized Q2PSK signaling format is considered for differential encoding and differential detection. Performance in the presence of additive white Gaussian noise (AWGN) is analyzed. Symbol error rate is found to be approximately twice the symbol error rate in a quaternary DPSK system operating at the same E(b)/N0. However, the bandwidth efficiency of differential Q2PSK is substantially higher than that of quaternary DPSK. In differential detection, it is quite reasonable to suspect that errors tend to occur in pairs. It is shown that when the error is due to AWGN, the ratio of double error rate to single error rate can be very high, and the ratio may approach zero at high signal-to-noise ratio. In an attempt to improve the error rate performance, differential detection through maximum-likelihood decoding based on multiple or N symbol observations is considered. It is shown that if N is large, then at high signal-to-noise ratio, this maximum-likelihood decoding gives a 3 dB advantage in the error rate performance over the conventional (N = 2) differential detection. Thus the energy loss in conventional (N = 2) differential detection, as compared to coherent detection, can be fully recovered if the observation is extended to a large number of symbol durations and maximum-likelihood decoding is employed.