IET Signal Processing
Research Article
Performance analysis of cooperative small
cell systems under correlated Rician/Gamma
fading channels
ISSN 1751-9675
Received on 15th February 2017
Revised 14th July 2017
Accepted on 1st August 2017
doi: 10.1049/iet-spr.2017.0078
www.ietdl.org
Xingwang Li
1,2
, Jingjing Li
1
, Lihua Li
2
, Liutong Du
2
, Jin Jin
3
, Di Zhang
4
1
School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 45400, People's Republic of China
2
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, People's
Republic of China
3
School of Information and Engineering, Zhengzhou University, Zhengzhou 450001, People's Republic of China
4
GITS/GITI, Waseda University, Tokyo 169-0072, Japan
E-mail: lilihua@bupt.edu.cn
Abstract: Small cell networks (SCNs) have emerged as promising technologies to meet the data traffic demands for the future
wireless communications. However, the benefits of SCNs are limited to their hard handovers between base stations (BSs). In
addition, the interference is another challenging issue. To solve this problem, this study employs a cooperative transmission
mechanism focusing on correlated Rician/Gamma fading channels with zero-forcing receivers. The analytical expressions for
the achievable sum rate, symbol error rate and outage probability are derived, which are applicable to arbitrary Rician factors,
correlation coefficients, the number of antennas, and remain tight across entire signal-to-noise ratios (SNRs). Asymptotic
analyses at the high and low SNR regimes are carried out in order to further reveal the insights of the model parameters on the
system performance. Monte-Carlo simulation results validate the correctness of their derivations. Numerical results indicate that
the theoretical expressions provide sufficiently accurate approximation to simulated results.
1 Introduction
With the proliferation of data-hungry devices and services (high-
definition video, online gaming, Internet of things etc.), the cellular
service providers are facing great challenges for the unprecedented
data traffic. Small cell networks (SCNs) were proposed to meet the
demands and improve the capacity performance in the fifth
generation (5G) mobile communication [1–3]. SCNs can achieve a
multitude of benefits, such as user terminal (UT) experiences and
spatial reuses of the time–frequency resources [4], which arise
from the deployment of a large number of self-organising, low-
cost, low-power base stations (BSs) in fixed areas [5, 6].
In spite of the useful features of SCNs, it is difficult to attain the
tractable analyses (e.g. [4–7]). Besides, the propagation wave tends
to be unpredictable in the case of SCNs. Yet by prior studies, the
channels between users and the BS are characterised by the
deterministic or line-of-sight (LoS) components due to the smaller
cell size and lower antenna heights, for instance the study in [8].
Another challenging tickler posed by SCNs is the hard handovers,
which occur frequently amongst SCNs under the high and medium
mobile environments [9]. Finally, contrary to traditional macrocell,
interference amongst SCNs results in obvious performance
degradation of wireless networks [10].
In light of those above, a general cooperative SCNs model is
considered to tackle the above challenges, where small fading,
large-scale fading, and correlation are taken into account. With this
model, all BSs are connected to the central service (CS) via delay
and error-free backhaul links (e.g. optical fiber or high-speed
cable). In SCNs, due to the even shorter access distances between
transmitters and receivers, the propagation channels are
characterised by deterministic or LoS components [9]. On this
basis, the Rician multipath model is well suited to characterise the
fading fluctuation of LoS wireless environment [7, 9, 11]. Yet the
shadowing fading effect is not taken into account within Rician
model, whereas by prior study, the Lognormal (LN) shadowing
model is a prevalent model to capture this [8]. For this reason,
Rician/Lognormal (RCLN) model is proposed to characterise the
SCNs fading environment [12, 13]. The main drawback of RCLN
model is that the composite probability density function (PDF) of
the signal-to-noise ratio (SNR) at the receivers is not in closed-
form, which incurs the ponderous performance evaluation. To
solve this problem, the LN shadowing is approximated by the
mathematical friendlier Gamma shadowing, which is revealed to
have a good fit to the experimental data [14, 15]. Unfortunately,
most of the existing studies only consider small-scale fading [7, 9,
10] or simply assume that large-scale fading (shadowing fading
and path loss) is a priori constant [11, 16]. Besides, the effect of
correlation is not considered either. As pointed out in [14], large-
scale fading coefficients are different due to different access
distances and shadowing fading effects, which cannot be
eliminated after pre-processing method [17, 18]. Therefore, how to
tame the large-scale fading effect is of significant importance in the
performance evaluation, which will be done by this study.
In this paper, we pursue a detailed performance analysis of
SCNs over correlated Rician/Gamma (RG) fading channels with
zero-forcing (ZF) receivers. To the best of authors’ knowledge, the
relevant studies have been published in [9, 11, 19, 20]. In [19], the
lower bound on the achievable sum rate of multi-cell cooperative
MIMO systems over Rayleigh/Lognormal fading channels was
investigated, while its validity is challenged in the LoS propagation
environment and the promising SCNs are not considered yet. On
similar grounds, Mirhosseini and Tadaion [20] studied the
performance of dense SCNs with multi-antenna BS employing the
spatial Poisson point process model but does not consider the
Rician composite channel, correlation and shadowing fading. In
[11], the queuing performance of cooperative SCNs was analysed
based on the finite-state Markov model. With the aid of random
matrix theory, Hoydis et al. [9] presented an approximate
expression for outage probability (OP) of cooperative SCNs over
Rician fading channels. Unfortunately, the common characteristics
of [9, 11, 20] are the lack of consideration of the shadowing fading,
correlation, as well as the ZF receivers.
Motivated by the above discussion, we henceforth study the
performance of cooperative SCNs over composite RG fading
channels with ZF receivers, where the Rician channel matrix has
arbitrary-rank deterministic component, and the correlation at the
transmitters is also involved. The analysis includes three key
metrics, i.e. achievable sum rate (ASR), symbol error ratio (SER)
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