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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 schemesover $\kappa-\mu$ shadowed fading channel. Firstly, new accurate approximationsof error probability (EP) of both modulation schemes are derived over additivewhite Gaussian noise (AWGN) channel. Leveraging the trapezoidal integralmethod, a tight approximate expression of symbol error probability for $M$-PSKmodulation is presented, while new upper and lower bounds for Marcum$Q$-function of the first order (MQF), and subsequently those for bit errorprobability (BER) under DQPSK scheme, are proposed. Next, these bounds arelinearly 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, thesesapproximations are used to tackle AEP's approximation under $\kappa-\mu$shadowed fading. Numerical results show the accuracy of the presentedapproximations compared to the exact ones.

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