Abstract

New Tight Bounds for the Gaussian <i>Q</i>-Function and Applications

Highlights

  • The use of Gaussian Q-function (GQF) or its counterpart, the complementary error function erfc(·) in several scientific fields is of paramount importance

  • NUMERICAL RESULTS Tables 6, 7, and 8 summarize, for various modulation techniques under α − μ, κ − μ shadowed, and Málaga turbulence channels with pointing errors, respectively, a comparison between the exact average symbol error rate (ASER), computed numerically using (36), the upper bounds relied on the tightest proposed bound (i.e., U (4)(x)) given in (33) jointly with Jk,i outlined in Table 3 with K = 41, and on K3 [11, Eq (8)] with N = 8 and K4 [12, Eq (15)], evaluated numerically from (36)

  • The asymptotic upper bound is fitting for high SNR values for all considered fading models

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Summary

Introduction

The use of Gaussian Q-function (GQF) or its counterpart, the complementary error function erfc(·) in several scientific fields is of paramount importance. In [1], the GQF has been approximated by the ratio of an exponential function to a polynomial, while in [2] it was approximated by the sum of either three or four exponential functions via the Trapezoidal Rule. To this end, an approximate expression for GQF using an exponential function of degree-six polynomial was proposed in [3], based on tree-adjoining grammar guided genetic programming. A highly accurate approximation has been proposed for the GQF and its powers in [5], these expressions are lower

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