A Generalized Lower Bound on the Bit Error Rate of DCSK Systems Over Multi-Path Rayleigh Fading Channels

This brief presents a generalized closed-form expression of the lower bound on the bit error rate (BER) of differential chaos-shift-keying (DCSK) systems. The analytical expressions are derived for multi-path Rayleigh fading channels. Unlike already existing research work, where numerical integration is the only way forward to derive the average BER for DCSK systems, this brief provides a generalized analytical expression of the lower bound on the BER. In this vein, the bounds of Q-function are used to solve complex integrals of the average BER expressions. Furthermore, a theoretical framework is also provided to generalize the derived analytical expression for the multi-carrier DCSK and the quadrature chaos shift keying systems. For validation of these results, a detailed comparative study with already existing numerical simulations is also provided. In this brief, the analytically derived bound matches the simulation results with a very narrow gap. Therefore, the bound allows the prediction of the actual BER of any chaos-based transmit reference modulation system and its derivatives, with negligible gap.