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
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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)