Closed-Form BER Expressions of M-Ary DCSK Systems Over Multipath Rayleigh Fading Channels

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.

在这封信中，我们通过多项式逼近高斯Q函数，推导出了多径瑞利衰落信道上M元差分混沌键控（M - DCSK）系统的闭式误码率（BER）。这种逼近是使用不同次数的多项式分段进行的，并且应用了雷米兹算法来实现极小极大逼近。我们的方法可以扩展到现有的基于非相干发射参考混沌的调制系统中，例如短参考DCSK和多载波DCSK系统。为了验证所提出的逼近方案的有效性，我们将推导出的闭式误码率与模拟得到的误码率进行了比较。