On the Average Achievable Rate of QPSK and DQPSK OFDM Over Rapidly Fading Channels

Motivated by recent experimental observations, where differentially coherent detection outperforms coherent detection on certain underwater acoustic channels, we revisit the performance of these two methods with respect to the achievable rate in orthogonal frequency-division multiplexing systems. Our comparison is based on a class of time-varying channels, where coherent quadrature phase shift keying (QPSK) detection requires channel estimation through a set of designated pilot symbols, while differentially coherent QPSK (DQPSK) enjoys an almost pilot-free detection. We show that given the cost of pilot overhead and channel estimation errors, the average rate achievable with DQPSK can be higher than that of QPSK. We use analytical results to identify channels for which this is the case, and expand the results to larger constellation sizes such as 8PSK, 16PSK, and 16QAM. In addition to acoustic channels, wireless radio channels with unusually long delay spread or high Doppler spread, such as those found in unmanned aerial systems and high-speed trains, may also benefit from using differentially coherent detection. In general, differentially coherent detection is favored in rapidly time-varying channels which require large pilot overhead and/or whose bit error rate performance is dominated by channel estimation errors. Our analysis includes the results for array receivers and soft detectors, showing that the favorable parameter range for differentially coherent detection expands significantly in both cases.