New Accurate Approximation for Average Error Probability

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 generalized 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 (MQF) of the first order, and subsequently those for bit error probability (BEP) under DQPSK scheme, are proposed. Next, these bounds are linearly combined to propose a highly refined and accurate BE P's approximation. The key idea manifested in the decrease property of modified Bessel function Iv, strongly related to MQF, with its argument v. As an application, these approximations are used to tackle AEP's approximation under κ - μ shadowed fading. Numerical results show the accuracy of the presented approximations compared to the exact ones.

Keywords

• Bit error probability
• bounds refinement
• DQPSK modulation
• M-PSK modulation%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">M</italic>-PSK modulation
• Q-function%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> Marcum <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">Q</italic>-function
• symbol error rate