Title: Evaluation of symbol error probability using a new tight Gaussian Q approximation

Authors: Tanmay Mukherjee; Gangadhar Nayak; Dilip Senapati

Addresses: Department of Computer Science, Ravenshaw University, Cuttack, Odisha, India ' Department of Mathematics, Ravenshaw University, Cuttack, Odisha, India ' Department of Computer Science, Ravenshaw University, Cuttack, Odisha, India

Abstract: In wireless communication systems, various performance metrics requires an evaluation of the Gaussian Q function. However, it is challenging to obtain a closed approximation to the Gaussian Q function in vicinity of small arguments. In this context, this paper portrays a tight approximation to the Gaussian Q function using the Gauss-Legendre numerical integration technique. This can be effectively used towards the computation of symbol error probability (SEP) integrals of different modulation techniques over fading channels. The framework provides an excellent agreement in contrast to the existing methods for SEP computation in Nakagami-m fading channels for all possible values of fading parameter. The model operates well for both higher and lower input arguments of the signal to noise ratios (SNRs). Furthermore, for performance evaluation in Nakagami-m fading channel, this approximation is used to derive the analytical solution for the SEP integrals in general rectangular and non-rectangular quadrature amplitude modulation (QAM).

Keywords: Gauss-Legendre quadrature formula; symbol error probability; SEP; Gaussian Q function; Nakagami-m fading; quadrature amplitude modulation; QAM; additive white Gaussian noise; AWGN.

DOI: 10.1504/IJSCC.2021.113241

International Journal of Systems, Control and Communications, 2021 Vol.12 No.1, pp.60 - 71

Accepted: 10 Feb 2020
Published online: 25 Feb 2021 *

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