# New Accurate Approximation for Average Symbol Error Probability Under κ-μ Shadowed Fading Channel

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Yassine Mouchtak, Faissal El Bouanani

## Abstract

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

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