A tight approximate analytical framework for performance analysis of equal gain combining receiver over independent Weibull fading channels

EURASIP Journal on Wireless Communications and Networking, Jan 2017

In this paper, a method for approximating the probability distribution of sum of independent and identical Weibull random variables is adopted to analyze the performance of equal gain combiner (EGC) receiver over non-identical Weibull fading channel (WFC). Our main result is to derive a generalized expression of the probability density function (PDF) of the signal-to-noise ratio (SNR) at the EGC output in the case of non-identical WFC. Based on this PDF, accurate approximation of significant performance criteria, such as outage probability (OP), the amount of fading (AoF), and average symbol/bit error probability (ASEP/ABEP), are derived. In addition, we derived the analytical expressions for channel capacities under various adaptation policies such as optimal rate adaptation (ORA), optimal simultaneous power and rate adaptation (OPRA), channel inversion with fixed rate (CIFR), and truncated channel inversion with fixed rate (TCIFR). The proposed mathematical analysis is complemented by several numerical results and validated using Monte Carlo simulation method.

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A tight approximate analytical framework for performance analysis of equal gain combining receiver over independent Weibull fading channels

Bessate and El Bouanani EURASIP Journal on Wireless Communications and Networking A tight approximate analytical framework for performance analysis of equal gain combining receiver over independent Weibull fading channels Abdelmajid Bessate 0 Faissal El Bouanani 0 0 ENSIAS Mohammed V University In Rabat , Rabat , Morocco In this paper, a method for approximating the probability distribution of sum of independent and identical Weibull random variables is adopted to analyze the performance of equal gain combiner (EGC) receiver over non-identical Weibull fading channel (WFC). Our main result is to derive a generalized expression of the probability density function (PDF) of the signal-to-noise ratio (SNR) at the EGC output in the case of non-identical WFC. Based on this PDF, accurate approximation of significant performance criteria, such as outage probability (OP), the amount of fading (AoF), and average symbol/bit error probability (ASEP/ABEP), are derived. In addition, we derived the analytical expressions for channel capacities under various adaptation policies such as optimal rate adaptation (ORA), optimal simultaneous power and rate adaptation (OPRA), channel inversion with fixed rate (CIFR), and truncated channel inversion with fixed rate (TCIFR). The proposed mathematical analysis is complemented by several numerical results and validated using Monte Carlo simulation method. Equal gain combining (EGC); Cumulative distribution function (CDF); Probability density function (PDF); Moment generating function (MGF); Average symbol/bit error probability (ASEP/ABEP); Adaptation policies; Fox H-function; Meijer G-function 1 Introduction Antenna diversity is one of the most practical, effective, and widely employed technique in wireless communication receivers to reduce the effects of fading and to provide increased signal strength at the receiver. Different techniques are known to combine the signals received from multiple diversity branches. The most popular diversity techniques are equal-gain combining (EGC), maximalratio combining (MRC), selection combining (SC), and a combination of MRC and SC, called generalized-selection combining (GSC). The SC receiver chooses the branch with the strongest instantaneous signal-to-noise ratio (SNR), while MRC provides optimal performance, at the expense of implementation complexity, since it requires knowledge of all channel parameters. In EGC receiver, the signals in all branches are weighted with the same factor, irrespective of the signal amplitude. Moreover, cophasing of all input signals is needed to avoid output signal cancellation. The performance of EGC and MRC diversity receivers has been extensively conducted in many previous works for several well-known fading statistical models, such as Rayleigh, Rice, and Nakagami—assuming independent or correlative fading [1–6]. The Weibull distribution is a well-known model for describing multipath fading channels in both indoor and outdoor radio propagation environments. In [7], novel analytical expressions for the joint probability density function (PDF), moment generating function (MGF), and cumulative distribution function (CDF) are derived for the multivariate Weibull distribution. The presented theoretical results are applied to analyze the performance of several diversity receivers such as SC, EGC, and MRC techniques operating under correlated Weibull fading channels (WFC). For these diversity receivers, several useful performance criteria such as moments of output SNR, including the amount of © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. fading (AoF), and outage probability (OP) are analytically derived. Moreover, the average symbol error probability (ASEP) for several coherent and noncoherent modulation schemes is studied using moment generating function (MGF) approach. In [8], capitalizing on the general α-μ fading model simple and precise closed-form approximations to the PDF and CDF of the sum of independent and identically distributed (i.i.d) Weibull variates are derived. These approximations find applicability in several wireless communications issues such as signal detection and combining, linear equalizers, intersymbol interference, and phase jitter [8]. Considering related works, C. Sagias et al. [9, 10], have presented a moments-based approach to analyzing the performance of dual-branch EGC and MRC receivers, operating under either independent or correlated, but not necessary identically distributed WFC. In this respect, significant performance criteria, such as average output SNR, AoF, and spectral efficiency at low power re (...truncated)


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Abdelmajid Bessate, Faissal El Bouanani. A tight approximate analytical framework for performance analysis of equal gain combining receiver over independent Weibull fading channels, EURASIP Journal on Wireless Communications and Networking, 2017, pp. 3, Volume 2017, Issue 1, DOI: 10.1186/s13638-016-0790-2