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This study introduces approximate closed-form expressions for polarization M-ary differential chaos shift keying (P-MDCSK) error probability. The new method simplifies performance analysis, showing minimal deviation from simulations.

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Area of Science:

  • Electrical Engineering
  • Information Theory
  • Wireless Communications

Background:

  • Performance analysis of polarization M-ary differential chaos shift keying (P-MDCSK) often relies on tight upper bounds involving the Q-function.
  • Direct evaluation of the Q-function lacks a closed-form expression, hindering simplified analysis of P-MDCSK performance bounds.

Purpose of the Study:

  • To derive approximate closed-form expressions for the error probability of P-MDCSK.
  • To overcome the limitations of non-closed Q-function expressions in performance analysis.
  • To provide a computationally tractable method for evaluating P-MDCSK error bounds.

Main Methods:

  • Utilizing a polynomial approximation of the Q-function to derive the closed-form expressions.
  • Conducting simulations under additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels for verification.
  • Comparing the derived approximate expressions against simulation results.

Main Results:

  • The derived approximate closed-form expressions for P-MDCSK error probability show a negligible gap compared to simulation results.
  • A marginal deviation of approximately 0.4 dB was observed between theoretical expressions and simulations at a bit error rate (BER) of 10-4.
  • The proposed method validates the accuracy of the approximate closed-form expressions.

Conclusions:

  • The developed approximate closed-form expressions offer an effective and simplified approach for analyzing P-MDCSK performance.
  • This method provides a valuable tool for communication schemes where exact bit error rate (BER) closed-form formulas are unattainable.
  • The study demonstrates the utility of Q-function approximation for simplifying complex communication performance analyses.