Abstract
In this letter, we derive a closed-form bit error rate (BER) of $M$ -ary differential chaos shift keying ( $M$ -DCSK) systems over multipath Rayleigh fading channels via approximating Gaussian $Q$ -function by polynomials. The approximation is made piecewisely using polynomials of different degrees and Remez algorithm is applied to achieve the minimax approximation. Our method can be extended into the existing non-coherent transmit-reference chaos-based modulation systems, e.g., short-reference DCSK and multi-carrier DCSK systems. The derived closed-form BERs are compared with the simulated ones in order to verify the efficiency of proposed approximation scheme.
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