Block diagonalization precoding and power allocation for clustering small-cell networks

Bulletin of Electrical Engineering and Informatics
Vol. 9, No. 6, December 2020, pp. 2364~2370
ISSN: 2302-9285, DOI: 10.11591/eei.v9i6.2580  2364
Journal homepage: http://beei.org
Block diagonalization precoding and power allocation for
clustering small-cell networks
Toha Ardi Nugraha1
, Indar Surahmat2
, Firdaus3
1,2
Department of Electrical Engineering, Universitas Muhammadiyah Yogyakarta, Indonesia
3
Department of Electrical Engineering, Universitas Islam Indonesia, Indonesia
Article Info ABSTRACT
Article history:
Received Dec 21, 2019
Revised Mar 15, 2020
Accepted Apr 9, 2020
The clustering network is a solution to improve data-rate transmission in
small-cells. In this case, clustering small-cells (CSCs) adopt a multiple
antennas concept. The multiple antennas are used to maximize the downlink
data-rate transmission at the users, but it requires precoding techniques to
minimize interference among CSC users. This paper proposes a block
diagonalization (BD) as a precoding technique for minimizing interference
among CSC users. The performance of the BD precoding implemented on
the clustering network under various numbers of small-cells. The CSC also
implements a water-filling power allocation (PA-CoopWF) to distribute
the available transmission power along with the CSCs antennas. To show
the performance, our paper simulates two types of precoding techniques;
those are the proposed BD and minimum mean square error (MMSE) in
CSCs. Based on the receiver user parts under the overlapping coordination
of CSCs, our method based on the BD precoding achieves considerably
higher data-rate transmission compared to the MMSE precoding, especially
on larger clusters. The simulation also shows that by implementing CSC with
the BD in short-range distances and higher numbers of antennas, it promotes
better data-rate performances compared to the MMSE precoding by 2.75 times
at distance 100m and 67% at 50 antennas.
Keywords:
Block diagonalization
Cellular network
Clustering network
Power allocation
Precoding
Small-cells
This is an open access article under the CC BY-SA license.
Corresponding Author:
Toha Ardi Nugraha,
Department of Electrical Engineering,
Universitas Muhammadiyah Yogyakarta,
Jl. Brawijaya, Tamantirto, Kasihan, Bantul, Yogyakarta 55183, Indonesia.
Email: toha@ft.umy.ac.id
1. INTRODUCTION
The implementation of small-cells is one of the effective solutions to improve data-rate in cellular
networks [1]. Small-cells are also a solution to extend cellular coverage. Small-cells are commonly installed
in urban or indoor building areas, so small-cells access-point is connected via cable backhaul to the gateway.
In [2], the authors propose an architecture of small-cells based resource allocation for wireless backhaul in
two-tier heterogeneous networks. The authors only focus on the backhaul transmission on the clustered
small-cells. Small-cells are also allowed to exchange their channel state information (CSI) over
the gateway [3, 4]. Therefore, the architecture of small-cells enables easy implementation of a clustering
network. There are some researchs in clustering focused on the small-cells network [5, 6]. The main concept
of clustering networks is that some cells in a network coordinates each other [7]. This method manages
coordination information for improving the performance of communication [8]. Clustered small-cells is one
of the solutions in order to improve the data-rate, particularly for the user in the cell edge, which has
interference effect from the neighbor small-cells [9, 10]. The coordination method is one of the key

Bulletin of Electr Eng & Inf ISSN: 2302-9285 
Block diagonalization precoding and power allocation for clustering… (Toha Ardi Nugraha)
2365
technologies to improve the data-rate of cell-edge users [11]. The interference problem is exploited or
mitigated by the coordination method between small-cells [12]. The coordination method improves
the efficiency of radio resources as well as satisfying the requirements of high data-rate, improve spectral
and energy efficiency [13-15].
One of the solutions to improve data-rate in a network is by employing multiple-input and output
(MIMO) concepts. MIMO concepts manage the frequency-time resources from transmitters to receivers [16].
On the other hand, interference problems appear in this multi-user MIMO concept. Therefore, a precoding
technique is a scheme to guarantee orthogonality across parallel channels and suppress interference before
the transmission signal. There are some techniques for employing precoding techniques, namely linear
and non-linear. A linear precoding is described by standalone matrix, for example, zero-forcing (ZF) [17, 18]
and minimum mean square error (MMSE) [19, 20]. The benefit of the linear precoding is the low complexity
in computations. In [21], the authors proposed a multi-user MIMO precoding technique in order to reduce
the negative impact of co-tier interference in the heterogeneous network. In [22], the authors investigated
a network of small-cells where the BSs were ready to form multiple clusters and coordinate to maximize
the overall sum-rate. The authors used a multi-user multiple antennas precoding based zero-forcing
beamforming (ZFBF) schemes. However, ZF and MMSE precodings are restricted only with one of
the receiver antennas. The antenna receiver cannot manage interference itself and only receive one spatial
channel. In this case, the transmitter must perform precodings in order to suppress the inter-user interference.
In [23], the authors proposed a regularized channel inversion (CI) precoding technique to enhance
the sum-rate assuming only single-antenna users are available in the system. In [24], the authors proposed
a novel of cooperative block diagonalization (BD) precoding to eliminate inter-user interference users under
the error model on the CSI. Therefore, the BD precoding is a great solution to be implemented in
the clustering and multi-user systems.
This paper proposes clustering small-cells (CSCs) using the BD precoding in order to manage
interference between the users in order to improve the data transmission rate of the networks. This paper also
investigates the impact of the additional number of antennas and the increment of distance between the CSCs
and the users on the performance. Moreover, the effect of changing the number of antennas is also analyzed.
This research assumes that CSCs use different channels with BS; therefore, there is no interference between
small-cells and BS users. In order to show the performance, our proposed algorithm is compared with other
linear precoding, MMSE techniques [25]. The rest of the paper is organized as follows: In section 2,
we describe the system model. Section 3 investigates our proposed method that is the interference mitigation
and the power allocation method. Section 4 explains the result and discussion of the simulations. Finally,
section 5 explains the conclusion of this paper.
2. SYSTEM MODEL
In this paper, we consider a various number of CSCs in a network as an example shown in Figure 1.
This paper investigates massive small-cells using transmit antennas and user equipments (UEs) with
the number of users , and receiver antennas having . In this case, each transmitter is equipped
with two antennas and each receiver is also equipped with two antennas, and also the number of CSCs
is with three small-cells. The users are randomly located at the cell edge zone and within the overlapping of
the neighbor cells. This system assumes that each small-cells has the same frequency. The rest of the main
simulation parameters are shown in Table 1
Table 1. Simulation parameters
Parameter Value
Carrier frequency 2 GHz
System bandwidth 5 MHz
Transmission Power 23 dBm
Noise Spectral density -174 dBm/Hz
No. of antenna each SC 2 antennas
No. of antenna each user 2 antennas
Pathloss model ITU indoor
Antenna pattern Omni directional
Figure 1. Clustering small-cells with coordination method

 ISSN: 2302-9285
Bulletin of Electr Eng & Inf, Vol. 9, No. 6, December 2020 : 2364 – 2370
2366
3. PROPOSED METHOD
This paper proposes CSC in order to improve the data-rate of the user in the cell edge. This scheme
mitigates the inter small-cells interference because the coordination in CSC facilitates a sharing of channel
feedback between the small-cells over a gateway. As illustrated in Figure 2, the proposed algorithm
is performed in three stages, each associated with exchanging the coordination request, coordination
response, the last stage is a sending the channel feedback and transmission of the data.
Figure 2. Stage of coordination methods of clustering small-cells, contain serving and neighbor small-cells
- Stage 1, this stage is a coordination REQUEST that user is monitored at the cell edge of serving small-
cells. The user uses the channel gain without considering the quality of the channels; therefore, there
is inter-cell interference between small-cells and neighboring small-cells. If the serving small-cells
increase the transmission power, the SNR of the cell edge user might be lost.
- Stage 2, in this stage, the method of CSCs coordinates their neighbors for making CSCs. First, we
calculate the number of CSCs antennas. The equation is formulated by ∑ where the number
of CSCs containing serving and neighbor small-cells is . Second, the total number of receiver antennas
is calculated by ∑ . Therefore, the channel matrix to receiver user is given by
[ ]. Third, the channel matrix of the multiple antennas for user given by
[ ] where superscript with is the conjugate transpose of a channel matrix. And
last, the channel matrix at the user is calculated by
∑ ∑ ∑ (1)
is the channel matrix from small-cells to user , ∑ represents the inter
small-cells interference experienced by user , is explained in the next section, and is complex
gaussian noise entries with zero-mean and variances . The interference between small-cells may lose
its diversity gain and the precoding technique manages inter small-cells interference nulling for CSCs.
Therefore, the objective of this clustering RESPONSE step is to ensure that the interference CSCs are
optimally managed. This step is used to find from the neighboring serving small-cells. is the
serving small-cell and is the number of neighbor small-cells. Neigbour small-cells are used for

2367
clustering if all off them can reach to the cell edge user. Then, the CSC is generated with . To
manage this step, CSI is informed to the gateway of small-cell networks. Therefore, all access-points
small-cells exchange information to each other and make DECISION.
- Stage 3, this stage is used to manage the data transmission rate of cell-edge users. The data transmission
rate of the user in the cell-edge is managed without reducing the quality of the CSCs. Inter user
interference management is performed by employing a BD precoding technique and it is described in the
next section.
3.1. Interference management
In this section, the proposed scheme implements the BD precoding in CSCs. Strengthening
the earlier statement, the BD precoding is used for mitigating inter-user interference in CSCs. The SNR for
the user with the BD precoding under perfect CSI is as follow:
1
j j j j j
C
i i i
u u u u u
i
y H w u n for all j n

  
 (2)
In order to obtain j
i
u
w , at the first, we must define
j
i
u
H from
       
*
1 1 1
... ...
j j j
H
H H
H H
u u u N
H H H H H
 
 

 
 
(3)
and singular value decomposition (SVD) to decompose the channel matrix into parallel non interference
spatial layers. The channel matrix is calculated by
* * * *(1) *(0)
,
[ ] 0
j j j j j
H
u u m u u u
SVD H U S
V S
   
    
(4)
*
, j
m u
V is a diagonal matrix with non-zero elements devote sub-channel’s gain.
*(1)
j
u
S and
*(0)
j
u
S are composed
of vectors that are corresponding to zero singular and non-zero singular values. Thus signals from other users
are not received.
3.2. Power allocation
In this paper, we use a power allocation (PA) using coordination water-filling (CoopWF) [26].
PA-CoopWF is a technique used to distribute the total available power along with the various antennas based
on the SNR distributions. The PA-CoopWA gains a better performance for the coordination channel
compared with the equal power for small-cells. The PA-CoopWF is calculated as follows:
2 2 2
1
1
j
j
N
u c
u
j j j
P P
Lu N Lu Lu
  


 
 
    
 
 
 
 (5)
c
P is coordination power CSCs and j
Lu is path-loss propagation for user . Finally, the formula to get the
data-rate j
u
R for the user using the PA-CoopWF is as follows:
*
2 2
1
log 1 j j
j
j
N
u u
u
u
P H
R B


 
 
 
 
 
 (6)
4. RESULTS AND DISCUSSION
This section describes the simulation results of the proposed methods and compared it to
the previous works. Figure 3 shows that the performance of proposed methods is slightly better almost
10 Mbps compared to MMSE investigated in single small-cells of each SNR target. The simulation also
investigated a number of CSCs in each SNR target. As an example, the CSCs with =4, 6, and 8 antennas,

 ISSN: 2302-9285
2368
our proposed scheme improves sum-rate about 10%, 21%, and 40% compared to MMSE with the same
number of antennas, respectively. Since the MMSE precoding technique works without removing the noise
of each channel, the channel interference cannot be mitigated perfectly at the receiver parts.
Figure 4 shows a comparison of the proposed method and MMSE in the same massive-antennas
deployment on CSCs scenarios. Based on the simulations, the graph informs that the average data-rate
improves gradually with the increase of the number of antennas and the performance gap of the proposed
precoding technique becomes larger in comparison to the MMSE methods. As an example, the simulations
investigate with 50 and 100 antennas; the proposed method improves the average-rate about 67% and 90%
compared to the MMSE precoding technique, respectively.
Figure 3. The impact of CSCs with difference level
of SNR receivers
Figure 4. BD and MMSE precoding technique with
various numbers of antennas
Finally, Figure 5 shows the average-rate when the CSCs and users are evaluated by the distances.
The proposed methods archive an average data-rate gain about 2.75 times compared to the MMSE precoding
at 100m. The graph shows that even though the average data-rate drops proportionally with the increment of
the distance, the performance gap of the proposed precoding technique in comparison to the MMSE methods
becomes larger. For the case that the distance of the receiver user fixed at 500m from the transmitter of CSC,
the proposed method provides a better transmission rate about 5 times compared to the MMSE precoding
technique. Therefore, our proposed precoding scheme is more efficient.
Figure 5. Downlink data-rate with difference distance from CSCs transmitter

2369
5. CONCLUSION
This paper investigates the clustering small-cells and precoding technique for improving data-rate in
the networks. The clustering small-cells methods employ the MIMO concept and implement a precoding
technique to minimize interference. This paper formulates clustering small-cells contains multiple antennas
for maximizing the downlink data-rate for the users. The BD precoding is proposed in clustering small-cells
to mitigate the interference channel between the users. This research also implements a water-filling power
allocation to improve the gain of each channel. Simulation results show that our proposed algorithms obtain
better performance of data rate compared to the MMSE precoding technique by 67% at 50 antennas and 2.75
times at distance 100m. For future research, our research will investigate the implementation of small-cells in
an indoor environment with channel error problems. Our future algorithm will also improve the precoding
technique to optimize the impact of imperfect channel state information.
ACKNOWLEDGEMENTS
This research is supported by the Indonesia Endowment Fund for Education (LPDP), Ministry of
Research, Technology, and Higher Education of Republic Indonesia, and Universitas Muhammadiyah
Yogyakarta.
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BIOGRAPHIES OF AUTHORS
Toha Ardi Nugraha received the B.Sc. degree in Telecommunication Engineering from Telkom
University, Indonesia, in 2011 and the M.Eng. degree in IT Convergence Engineering from
Kumoh National Institute of Technology, South Korea, in 2014. He worked at Research Centre,
PT. Telkom Indonesia for two years from 2000 to 2012, as a Research Assistant, and participated
in FP7 FREEDOM project founded by European Commission. Since 2016, He joined at
Department of Electrical Engineering, Universitas Muhammadiyah Yogyakarta, Indonesia, as a
lecturer. Currently, he is pursuing Ph.D. degree at the Department of Telecommunication
Engineering, Czech Technical University in Prague (CVUT), Czech Republic. His research
interest includes Wireless and Mobile Networks, Small-Cells, Device-to-Device
Communication, and Internet of Things.
Indar Surahmat obtained Bachelor Degree from Universitas Gadjah Mada in 2005 and Master
Degree from Institut Teknologi Bandung in 2011. Both are in Electrical Engineering. From
2005-2009, he worked at a telecommunication company as a Radio Frequency Network and
Planning Optimization Engineer. After graduated from Master Degree, he went back to work in
the same field until 2015. During work as a RF Engineer, he had handled thousands of BTS
deployments and optimized hundreds of site clusters. In 2015, he joined Universitas
Muhammadiyah Yogyakarta as a researcher and a lecturer. In 2017, he received a certification as
a professional engineer from The Institution of Engineers Indonesia. He is currently pursuing
PhD in Institute of High Frequency Technology, RWTH Aachen University. His research are in
fields of antennas for wireless communications, cellular networks, propagation models, and
traffic engineering.
Firdaus received the B.Eng degree in Electrical Engineering from Gadjah Mada University,
Yogyakarta in 2007 and M.Eng Degree in Telecommunication from Telkom University,
Bandung in 2010. He worked at Department of Electrical Engineering, Universitas Islam
Indonesia, Yogyakarta since 2010. He is currently pursuing his PhD in Razak Faculty of
Technology and Informatics, Universiti Teknologi Malaysia, Kuala Lumpur. He just passed the
thesis exam in November 2019. His research interest is in wireless communication, wireless
sensor network and indoor positioning.

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