An Analytically Tractable Approximation for the Gaussian Q-Function

• Published in: IEEE communications letters Vol. 12; no. 9; pp. 669 - 671
• Main Authors: Isukapalli, Yogananda, Rao, Bhaskar D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Blocking; Closed-form solution; Computational modeling; Derivation; Error probability; Exact sciences and technology; Exact solutions; Fading; Gaussian; Gaussian approximation; Mathematical analysis; Measurement; Nakagami distribution; Nakagami-m fading; Performance analysis; Q-function; Quadrature phase shift keying; Rayleigh channels; Symbols; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Performance evaluation; Gaussian Q-function; Bit error rate; Gaussian approximation; Quadrature phase shift keying; Nakagami fading; Gaussian process; Simulation; Nakagami-m fading; Telecommunication system; Metric; Differential method; Symbol error rate
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2008.080815

In this letter we propose an approximation for the Gaussian Q-function that enables simpler evaluation of important communication system performance metrics. The approximation enables derivation of closed-form expressions for metrics such as average symbol, bit and block error probabilities which are known to be analytically involved as they require computation of the expectation of Q-function and its integer powers, for any m of Nakagami-m fading. The tightness of the approximation is verified by simulations. The usefulness of the approximation is demonstrated by obtaining a simple closed form expression for the average symbol error probability of differentially encoded QPSK in Nakagami-m fading.