Closed-Form Expressions of Upper Bound for Polarization-MDCSK System

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.