LARGE-SCALE MULTI-USER MIMO APPROACH FOR WIRELESS BACKHAUL BASED HETNETS

Brajesh Kumar Kaushik et al. (Eds) : CCNET, CSIP, SCOM, DBDM - 2017
pp. 43– 52, 2017. © CS & IT-CSCP 2017 DOI : 10.5121/csit.2017.70505
LARGE-SCALE MULTI-USER MIMO
APPROACH FOR WIRELESS BACKHAUL
BASED HETNETS
Mostafa Hefnawi
Department of Electrical and Computer Engineering,
Royal Military College of Canada, Kingston, Canada
ABSTRACT
In this paper, we consider the optimization of wireless capacity-limited backhaul links in future
heterogeneous networks (HetNets). We assume that the HetNet is formed with one macro-cell
base station (MBS), which is associated with multiple small-cell base stations (SBSs). It is also
assumed both the MBS and the SBSs are equipped with massive arrays, while all mobiles users
(macro-cell and small-cell users) have single antenna. For the backhaul links, we propose to
use a capacity-aware beamforming scheme at the SBSs and MRC at the MBS. Using particle
swarm optimization (PSO), each SBS seeks the optimal transmit weight vectors that maximize
the backhaul uplink capacity and the access uplinks signal-to-interference plus noise ratio
(SINR). The performance evaluation in terms of the symbol error rate (SER) and the ergodic
system capacity shows that the proposed capacity-aware backhaul link scheme achieves similar
or better performance than traditional wireless backhaul links and requires considerably less
computational complexity.
KEYWORDS
HetNets, wireless backhaul, cognitive radio, Massive MIMO, multiuser MIMO, PSO.
1. INTRODUCTION
Recently, deploying small cell networks over existing macro-cellular networks, also known as
heterogeneous networks (HetNets), has emerged as a promising solution to deal with the
increasing wireless traffic demands in next generation 5G cellular networks [1]-[6]. The users in
these HetNets are offloaded from the congested macro-cell base stations (MBSs) to the small-cell
base stations (SBSs), which enhanced their quality of service (QoS) and increase the overall
system capacity. These HetNets are supported by Gigahertz bandwidth backhaul links that
connect MBSs and the associated SBSs. Such Gigahertz bandwidth can be achieved by
conventional optical fiber or millimeter-waves (mmWaves) based wireless backhauls. Optical
fiber backhauls wile reliable, they might be expensive and difficult to deploy in HetNets where
several small cells are unplanned and installed quite arbitrarily. Wireless backhauls, on the other
hand, are more attractive to overcome the restriction of deployment and installation and can
provide a cheap and scalable solution. However, to achieve high spectral efficiency in HetNets
with wireless backhauling, frequency reuse across the coexisting network tiers (backhaul and
access links) is essential and interference management is critical. Cognitive radio based HetNets
(CR-HetNets) has emerged as a promising solution that provides a more energy efficient and
dynamic way to use the spectrum by enabling small-cell to share licensed bands in opportunistic
manner [5]-[6]. In CR-HetNets, macro-cell users, which are considered as primary users (PUs)

44 Computer Science & Information Technology (CS & IT)
take the priority to access the channels, whereas small-cell users, which are considered as
secondary users (SUs), can access the channels as long as the corresponding PUs do not use them.
However, most of these proposed CR-HetNets have assumed opportunistic spectrum sharing
which may not be reliable and may limit the system capacity since it suffers from the
interruptions imposed by the primary network (PN) on the SUs who must leave the licensed
channel when PUs emerge. Also, with opportunistic spectrum sharing, SUs can still cause
interference to PUs due to their imperfect spectrum sensing. In cellular systems, one way to
overcome these limitations is to incorporate multiuser multi-input multi-output (MU-MIMO)
approach into cognitive radio networks (CRNs) to achieve higher spectral efficiency by
multiplexing multiple SUs on the same time-frequency resources and protecting PNs from SUs’
interferences. MU-MIMO techniques have been successfully deployed in 4G cellular systems for
traditional fixed spectrum assignment (FSA) approaches [7]-[15] and a vast number of multiuser
detection algorithms are presently being tailored towards solving the MU-MIMO processing in
cognitive networks ]16 [-] 22[, byimposingadditionalconstraints to protect licensed users’ QoS.
More specifically, capacity-aware MU-MIMO schemes have been proposed for both FSA [13]-
[15] and CR networks [16]-[17] using different multiuser detections schemes such as maximum
ratio combining (MRC) and minimum mean-squared error (MMSE), and have shown the
potential to exhibit better system capacity and provide better SER enhancement than traditional
singular value decomposition (SVD)-based MU-MIMO systems. On the other hand, it was shown
that the use of large-scale antenna arrays (also called massive MIMO) could achieve tremendous
boost of MU-MIMO systems system performance [23]-[26]. In this paper, therefore, we will be
applying the concept of MU massive MIMO and CR in HetNets. We assume that the MBSs and
SBSs are equipped with massive arrays, while all mobiles users have single antenna. We deploy
two MU-MIMO schemes, namely, MRC at the access link (SUs to SBSs) and capacity-
aware/MRC at the backhaul link (SBSs to MBS). Such a system can significantly improve the
system performance in terms of link reliability, spectral efficiency, and energy efficiency. It can
also achieve optimal performances with the simplest forms of user detection techniques, i.e.,
MRC [12]. On the other hand, most of the proposed capacity-aware MU-MIMO schemes require
the use of gradient search algorithms in order to solve the constrained optimization problem in
CRNs [16]-[17]. These techniques become very computationally expensive in large-scale MIMO
systems because of the vast amounts of baseband data that are generated and require the
constrained optimization problem to be differentiable. Thus, in our capacity-aware backhaul link
scheme we will be exploring free-derivative population-based training algorithms such as the
particle swarm optimization (PSO) that are well known by their simple/fast hardware
implementation. PSO was initially introduced by Kennedy and Eberhart in [27] and has received
a lot of attention in recent years. It is an evolutionary computation technique inspired by swarm
intelligence such as fish schooling and bird flocking looking for the best food spot (exploring the
optimal solution) in the search space where a quality measure, fitness, can be evaluated without
any a priori knowledge. The PSO algorithm in this paper will be used at the backhaul link to seek
iteratively the transmit beamforming weights of each SBS that maximize the uplink (UL) MIMO
backhaul channel capacity. Under the assumption of very large number of antennas at the SBSs
and the MBS, we derive semi-analytic expressions for the symbol error rate (SER) and the
ergodic channel capacity, which quantify the reliability and spectral efficiency of the MU-MIMO
based HetNet. The derived expressions are then used to evaluate the performance of the proposed
PSO-based capacity-aware (PSO-CA) backhaul link. The contribution of this paper includes the
extension of the cognitive capacity-aware massive MU-MIMO schemes to wireless backhaul
links and the development of semi-analytical model for the SER and channel capacity analyses in
HetNets.

Computer Science & Information Technology (CS & IT) 45
2. SYSTEM MODEL
We consider the UL access scenario shown in Fig. 1 of a HetNet with small cells and one
macro cell that share the same frequency band. Each small cell includes one SBS equipped with
massive N-element antenna array and single-antenna secondary users (SUs). Each SBS and its
users act as a cognitive networkthatcoexist, via concurrent spectrum access, with macro-cell
primary users (PUs) and their primary MBS, which is also equipped with massive M-element
antenna array. It is also assumed that both the SBS and the MBS detect independent OFDM data
streams from their mobile users simultaneously on the same time-frequency resources.
Figure 1. System Model: HetNet consisting of one macro-cell and K small-cells and their
corresponding users.
Let [ ] = , , ⋯ , and [ ] = , , ⋯ , denote, respectively, the set of
SUs signals and PUs signals transmitted on each subcarrier, , = 1, ⋯ , , where
denotes the number of subcarriers per OFDM symbol in the system.The analysis is done
separately on each subcarrier. For brevity therefore, we drop the frequency index .
2.1.Access link:
The N×1 received signal vector at the kth
SBS is given by
= ,!" + $ ,!%! + &'",!%! (1)
where ,!" ∈ ℂ*×
is the channel matrix between the kth
SBS and its users, ∈ ℂ ×
is
the transmittedsignal vector of users in the kth
small-cell, is the average power transmitted

by each user (Here we assume equal power allocation for all users) , $ ,!%! ∈ ℂ*×
is the
received AWGNvector at the SBS, and &'",!%! represents the interference introduced by macro-
cell users (PUs) at the SBS, and is given by
&'",!%! = ,'" , (2)
where ,'" ∈ ℂ*×
is the channel matrix between the kth
SBS and users, is the average
power transmitted by each PU, and ∈ ℂ ×
is the transmittedsignal vector of users in the
HetNet.
For the uplink access link, we consider MRC detection scheme at each SBS. The -./
SBS
processes its received signal by multiplying it by the N × receive beamforming weight
matrix12
as follows
3 = 12
= 12
,!" + 12
$ ,!%! + 12
&'",!%! (3)
The detection of user 4 by its -./
SBS can then be expressed as
5 ,6 = 7 ,6
2
= 7 ,6
2
,!" + 7 ,6
2
$ ,!%! + 7 ,6
2
&'",!%! (4)
where 5 ,6 is the 4 th
element of 3 and 7 ,6 is the 4 th
column of 1 .
2.2.Backhaul link:
For the backhaul link, the expression for the array output of the MBS in Fig. 1 can be written for
each subcarrier as
89:; = ∑ = ,>%!
?
@ A 3 + B>%! + &'",>%!, (5)
where 89:; is the C × 1 vector containing the outputs of the C −element array at the MBS,
= ,>%! is the C × frequency-domain channel matrix representing the transfer functions from
the −element antenna array of the kth
SBS to the C −element antenna array of the MBS,
A = EF , F … , FH I
J
is the × 1complex transmit weight vector of the -./
SBS, B>%!
is the receivedC × 1 complex additive white Gaussian noise vector at the MBS, and &'",>%![k]
represents the interference introduced by PUs to SUs at the MBS and is given by
&'",>%! = ='",>%! (6)
where ='",>%! is the C × L channel matrix from the PUs to the MBS’s C − element
antenna array.
The MBS detects the -./
SBS data by multiplying the output of the array 89:; with the C ×
1receiving weight vector, MN
2
as follows
O = MN
2
8PQR = ;N + ;S + SS + T (7)
where
;N = MN
2
= A 3 is the signal detected from the kth
SBS,

;UV
= MW
2
∑ =?
@ , X A 3 is the multiple-access interference (MAI) from the − 1 other SBSs,
SS = MN
2
='",>%! is the MAI from L PUs, and T = MN
2
B>%!is the noise signal at the
array output of the MBS,
For the backhaul link, it is assumed that each SBS is transmitting with a capacity-aware
beamforming scheme that will be discussed in section XX and that the MBS is detecting SBSs’
signals using MRC scheme.
3. SYMBOL ERROR RATE AND ERGODIC CHANNEL CAPACITY
The symbol error rate, YZ[ ,6 , associated with 4 ]
user of the -./
SBS can be expressed as
YZ[ ,6 = Z^_,`
Eabc 2bf ,6 gI, (8)
whereE [.] denotes the expectation operator, Q(.) denotes the Gaussian Q-function, f ,6 is the
signal-to-interference-plus-noise ratio (SINR) associated with the4 ./
user of the -./
SBS , and a
and b, are modulation-specific constants. For binary phase shift keying (BPSK), a = 1 and F =
1, for binary frequency shift keying (BFSK) with orthogonal signaling a = 1 and b = 0.5, while
for M-ary phase shift keying (M-PSK) a = 2 and b = sin (n/C).
Using (7), the signal detected from the4 ./
user of the -./
SBS can be expressed by (9) and the
signal detected by the MBS from the4 ]
user of the -]
SBS can be expressed by (10).
;N,6 = MN
2
= ,>%!A 5 ,6 = MN
2
= ,>%!A 7 ,6
2
= MN
2
= ,>%!A 7 ,6
2
,!" +MN
2
= ,>%!A 7 ,6
2
$ ,!%! + MN
r
= ,>%!A 7 ,6
2
&'",!%!
(9)
s ,6 = MN
2
8PQR = ;N,6 + ;S + SS + T (10)
The SINR at the MBS for user 4 of the kth
SBS can thus be depicted as
γ ,6 =
MN
2
= ,>%!A 7 ,6
2
,!" ,!"
2
7 ,6 A2
= ,>%!
2
u
MN
2: u
(11)
and the ergodic channel capacity, per subcarrier, for each SBS - is given by [13]
Cc= ,>%!, A g = Z w4xy z& + {
H
|:
}
~
•
= ,>%!A 7 ,6
2
,!"| €• (12)
whereE [.] denotes the expectation operator,: is the covariance matrix of the interference-plus-
noise, and is given by
: = :!%! + :'",>%! + :'",!%! + :‚, (13)
where
:RQR = ƒ = ,>%!
?
@ , X
A 3 32
A2
= ,>%!
2

:„…,PQR = =>%!,6 =>%!,6
†
:„…,RQR = = ,>%!A 7 ,6
2
,'" ,'"
2
7 ,6 A2
= ,>%!
2
:‡ = MN
2
MN + = ,>%!A 7 ,6
2
7 ,6 A2
= ,>%!
2
4. CAPACITY-AWARE BACKHAUL LINK
In the proposed capacity-aware backhaul link, the weight vector for the -./
SBS is updated at
each iteration n until it reaches the optimal beamforming vector, (A )ˆ , that maximizes the
ergodic backhaul channel capacity for each SBS-ofthe HetNet. This channel capacity can be
expressed, at each iteration n, by:
C(‰) = Z w4xy z& + {
H
|:
}
~
•
= ,>%!A (‰)7 ,6
2
,!"| €• (14)
To maximize the backhaul link capacity we propose to employ particle swarm optimization
algorithm where particles are mapped to the transmit beamforming and fly in the search space,
aiming to maximize the fitness function given by the channel capacity of (14). First, the PSO
generates Z random particles for each SBS (i.e., random weight vector AN
(Š)
, z = 1, . . . , Z of
length × 1 ) to form an initial population set S (swarm). The algorithm computes the channel
capacity according to (14) for all particles AN
(Š)
and then finds the particle that provides the global
optimal channel capacity for this iteration, denoted AN
(Š,‹Œ• )
. In addition, each particle z
memorizes the position of its previous best performance, denoted AN
(Š, Œ• )
. After finding these
two best values, PSO updates its velocity ŽN
(Š)
and its particle positions •N
(Š)
at each iteration n
using (15) and (16), respectively, where • and • are acceleration coefficients towards the
personal best position ( F‘’“) and/or global best position (gF‘’“), respectively, ” and ” are
two random positive numbers in the range of [0, 1], and • is the inertia weight which is
employed to control the exploration abilities of the swarm.
ŽN
(Š)
(‰ + 1) = –ŽN
(Š)
(‰) + u—˜— ™AN
(Š, Œ• )
(‰) − AN
(Š)
(‰)š + u›˜› ™AN
(Š,‹Œ• )
(‰) − AN
(Š)
(‰)š (15)
AN
(Š)
(‰ + 1) = AN
(Š)
(‰) + ŽN
(Š)
(‰ + 1) (16)
Large inertia weights will allow the algorithm to explore the design space globally. Similarly,
small inertia values will force the algorithms to concentrate in the nearby regions of the design
space. This procedure is repeated until convergence (i.e., channel capacity remains constant for a
several number of iterations or reaching maximum number of iterations). An optimum number of
iterations is tuned and refined iteratively by evaluating the average number of iterations required
for PSO convergence as a function of the target MSE for algorithm termination and as a function
of the population size. Since random initialization does not guarantee a fast convergence, in our
optimization procedure we consider that the initial value of AN
(Š)
(‰) at iteration index n = 0 is
given by the eigen-beamforming (EBF) weight, i.e., AN
(Š)
(0)= •žŸ 7 ,¡, where Ÿ¢£¤,¥V
denotes
the eigenvector corresponding to ¦¢£¤, , the maximum eigenvalue of = ,PQR
2
= ,PQR. This initial
guess enables the algorithm to reach a more refined solution iteratively by ensuring fast
convergence and allows to compute the initial value of the received beamforming vector at
iteration index n=0. In our case we assume MRC at the receiving MBS, i.e:

MN
2
(0) = (: )}—
= ,>%!A (0) (17)
5. SIMULATION RESULTS
In our simulation setups we consider a HetNet organized into K SBSs (K=20) and one macro-cell.
The number of antennas at the SBSs and at the MBS is the same, = C, and is varying from 25
to 100. Each SBS is serving = 10 users and the macro-cell is serving = 10 users, each
transmitting with a single antenna. We assume QPSK modulation. For the OFDM configurations,
we assume the 256-OFDM system (Nc = 256), which is widely deployed in broadband wireless
access services. For the backhaul link we assume an MU-MIMO system with capacity-aware
beamforming at each SBS and MRC detection at the MBS. For the access link we assume MRC
detection at each SBS. For the PSO parameters, the swarm size is 30, the maximum iteration
number is 25 and the acceleration coefficients are • = • = 2.The inertia weight• ranges from
0.9 to 0.4 and varies as the iteration goes on.
Fig. 2 shows the system capacity of the proposed PSO-CA and the traditional eigen-beamforming
schemes for M = = 25, a‰© 100. It is observed that for both cases PSO-CA is outperforming
eigen-beamforming. It is also noted that as we increase the number of antennas the performance
gap between the two schemes is reduced. This means that when the number of base station
antennas becomes large, PSO-CA is able to achieve the same level or better performance than
eigen-beamforming with less computational complexity. Fig. 3,on the other hand, compares the
SER performance of both schemes for the same scenario as in Fig. 2. It is observed PSO-CA is
outperforming eigen-beamforming in both cases.
Figure 2. Ergodic channel capacityof HetNet using PSO-CA and eigen-beamforming schemes for K=20
SBSs and M=N=25 and 100 antennas.

Figure 3. SER performance of HetNet using PSO-CA and eigen-beamforming schemes for K=20 SBSs and
M=N=25 and 100 antennas.
6. CONCLUSION
This paper proposes a capacity-aware wireless backhaul link where cognitive small cells
communicate with a MBS using a PSO-based large-scale multiple-input multiple-output (LS-
MIMO) beamforming scheme. The proposed algorithm iteratively seeks the optimal transmit
weight vectors that maximize the channel capacity of each SBS in the HetNet. It was shown that
the proposed system is able to achieve a low computational complexity (without requiring an
inverse of the covariance matrix) with the same level or better performance than the convectional
eigen-beamforming.
ACKNOWLEDGEMENTS
The author would like to thank the Canadian MicroelectronicsCorporation (CMC) for providing
the Heterogeneous Parallel Platform to run the computationally-intensive Monte-Carlo
Simulations
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AUTHORS
Dr. Hefnawi is currently a professor and the Chair of Graduate Studies Committee in
the Department of Electrical and Computer Engineering at the Royal Military College
of Canada. Dr. Hefnawi is a licensed professional engineer in the province of Ontario.
He is a contributing author of a number of refereed journal, book chapters, and
proceeding papers in the areas of wireless communications. His research interest
includes cognitive radio, wireless sensor network, massive MIMO, cooperative
MIMO, multiuser MIMO, and smart grid communications.

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