Capacity of the non-coherent DCSK system over Rayleigh fading channel

Capacity bounds are calculated for the differential chaos shift keying (DCSK) system with non-coherent detectors, including differentially coherent detector and energy detector, over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Through theoretical analysis and numerical simulations, it is found that the capacity characteristics of the non-coherent DCSK system are significantly different from those of the coherent case. It is shown that there are different capacity bounds corresponding to different spreading factor values. Optimal code rates are found, which minimise the required bit signal-to-noise ratio for a reliable communication system, and they are increasing with the increase of the spreading factor value over an AWGN channel while decreasing over a Rayleigh fading channel. As compared with the AWGN channel, the performance over a Rayleigh fading channel is much more sensitive to the code rate. The new results are useful as benchmark for designing capacity-approaching codes for the non-coherent DCSK system.