Simplified approximations to the average of some useful forms of Gaussian Q functions with MRC diversity reception over Nakagami- q and Rician fading channels and their applications

Simple and accurate SEP approximation of hexagonal‐QAM in AWGN channel and its application in parametric , , fading, and log‐normal shadowing

“…In addition, for more complex log‐normal shadowing, accurate GH (64 terms) approximation is proposed, which is also expressed in terms of simple exponentials. The proposed approach can be extended to maximal‐ratio combining diversity reception, like in [35].…”

On the average of the product of two Gaussian Q functions over η − μ and κ − μ fading channels using MRC diversity reception

“…It can be clearly seen that for κ − μ shadowed fading channel also, the exact and approximated curves are in excellent agreement with each other. (8) and (9) For large γ¯, i.e. γ¯→ ∞, the values of ϕ ≃ 0, ξ ≃ 0, ϱ ≃ 0 and χ ≃ 0.…”

“…respectively. As per the authors' knowledge, (8) and (9) are novel and include simple exponential and power functions. These can be easily computed using the commercial mathematical softwares packages like MATLAB, unlike F D (n) [7], which requires complex numerical integrations.…”

“…However, this is achieved after sacrificing the accuracy of the integral, specially at lower signal-to-noise ratios (SNRs). Recently, Sadhwani and Yadav [9] simplified the required integral over Nakagami-q and Rician fading channels, employing maximal ratio combining (MRC) diversity reception. This enabled an easy calculation of the SEP of various coherent digital modulation techniques like square-QAM (SQAM), rectangular-QAM, cross-QAM, triangular-QAM (TQAM) and hexagonal-QAM (HQAM).…”

“…This is achieved by using a more accurate approximation of the Gaussian Q function [24]. The proposed approximated integrals are accurate for the complete SNR range, unlike [9], and are valid for each unique value of the fading parameters unlike [3,4]. In addition, the need of complex computations of F D (n) [7] is also eliminated by expressing the proposed approximated integrals in terms of simple exponential and power functions.…”