New Accurate Approximation for Average Error Probability Under $\kappa-\mu$ Shadowed Fading Channel

TL;DR

This paper introduces new accurate approximations for average error probability in communication systems over $$-shadowed fading channels, improving the precision of error analysis for various modulation schemes.

Contribution

It develops novel approximations for error probabilities of $M$-PSK and DQPSK modulations over $$-shadowed fading, using trapezoidal integral and bounds on Marcum Q-function.

Findings

The approximations closely match exact error probabilities.

The proposed methods outperform existing bounds in accuracy.

Numerical results validate the effectiveness of the new approximations.

Abstract

This paper proposes new accurate approximations for average error probability (AEP) of a communication system employing either $M$-phase-shift keying (PSK) or differential quaternary PSK with Gray coding (GC-DQPSK) modulation schemes over $\kappa-\mu$ shadowed fading channel. Firstly, new accurate approximations of error probability (EP) of both modulation schemes are derived over additive white Gaussian noise (AWGN) channel. Leveraging the trapezoidal integral method, a tight approximate expression of symbol error probability for $M$-PSK modulation is presented, while new upper and lower bounds for Marcum $Q$-function of the first order (MQF), and subsequently those for bit error probability (BER) under DQPSK scheme, are proposed. Next, these bounds are linearly combined to propose a highly refined and accurate BER's approximation. The key idea manifested in the decrease property of modified Bessel function $I_{v}$, strongly related to MQF, with its argument $v$. Finally, theses approximations are used to tackle AEP's approximation under $\kappa-\mu$ shadowed fading. Numerical results show the accuracy of the presented approximations compared to the exact ones.