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Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI
Journal Pre-proof Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI Tasher Ali Sheikh, Joyatri Bora, Md Anwar Hussain PII:
S2352-8648(19)30034-3
DOI:
https://doi.org/10.1016/j.dcan.2019.08.002
Reference:
DCAN 173
To appear in:
Digital Communications and Networks
Received Date: 26 January 2019 Revised Date:
19 June 2019
Accepted Date: 29 August 2019
Please cite this article as: T.A. Sheikh, J. Bora, M.A. Hussain, Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI, Digital Communications and Networks (2019), doi: https://doi.org/10.1016/j.dcan.2019.08.002. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Chongqing University of Posts and Telecommunications. Production and hosting by Elsevier B.V. All rights reserved.
Graphical Table of Contents Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Tasher Ali Sheikh*, Joyatri Bora, Md. Anwar Hussain Brief abstract: — The capacity of a massive MIMO cellular network depends on user and antenna selection algorithms, and also on the acquisition of perfect channel state information (CSI). Low computational cost algorithms for user and antenna selection significantly may enhance the system capacity, as it would consume a smaller bandwidth out of the total bandwidth for downlink transmission. The objective of this paper is to maximize the system sum-rate capacity with efficient user and antenna selection algorithms and linear precoding. We consider in this paper, a slowly fading Rayleigh channel with perfect acquisition of CSI to explore the system sum-rate capacity of a massive MIMO network. For user selection, we apply three algorithms, namely Semi-orthogonal user selection (SUS), descending order-based user scheduling (DOSUS), and Random user selection (RUS) algorithm. In all the user selection algorithms, the selection of base station (BS) antenna is based on maximum signal-to-noise ratio (SNR) to the selected users. Hence users are characterized by having both small scale fading (SSF) due to slowly fading Rayleigh channel and large-scale fading (LSF) due to distances from the base station.
Further, we use
linear precoding techniques such as zero forcing (ZF), minimum mean square error (MMSE), and maximum ratio transmission (MRT) to reduce interferences thereby improving average system sum-rate capacity. Results using SUS, DOSUS, and RUS user selection algorithms with ZF, MMSE, and MRT precoding techniques are
compared. We also analyzed and compared the computational complexity of all the three user selection algorithms. The computational complexities of the three algorithms that we achieved in this paper are O(1) for RUS and DOSUS, and O(M2N) for SUS which are less than the other conventional user selection methods.
Figure-2: Massive MIMO System with joint user and antenna selection scheme
2
Tasher Ali Sheikh, et al.
Digital Communication and Networks (DCN)
Available online at www.sciencedirect.com
Science Direct Journalhomepage:www.keaipublishing.com/en/journals/digital-communications-and-networks ISSN:2352-8648
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Tasher Ali Sheikh∗a, Joyatri Borab, Md. Anwar Hussainc a,b,c
Department of Electronics and Communication Engineering, North Eastern Regional Institute of Science and Technology, Nirjuli,
Arunachal Pradesh,791109, India.
Abstract The capacity of a massive MIMO cellular network depends on user and antenna selection algorithms, and also on the acquisition of perfect channel state information (CSI). Low computational cost algorithms for user and antenna selection significantly may enhance the system capacity, as it would consume a smaller bandwidth out of the total bandwidth for downlink transmission. The objective of this paper is to maximize the system sum-rate capacity with efficient user and antenna selection algorithms and linear precoding. We consider in this paper, a slowly fading Rayleigh channel with perfect acquisition of CSI to explore the system sum-rate capacity of a massive MIMO network. For user selection, we apply three algorithms, namely Semi-orthogonal user selection (SUS), descending order-based user scheduling (DOSUS), and Random user selection (RUS) algorithm. In all the user selection algorithms, the selection of base station (BS) antenna is based on maximum signal-to-noise ratio (SNR) to the selected users. Hence users are characterized by having both small scale fading (SSF) due to slowly fading Rayleigh channel and large-scale fading (LSF) due to distances from the base station.
Further, we use linear precoding techniques such as zero forcing (ZF), minimum mean
square error (MMSE), and maximum ratio transmission (MRT) to reduce interferences thereby improving average system sum-rate capacity. Results using SUS, DOSUS, and RUS user selection algorithms with ZF, MMSE, and MRT precoding techniques are compared. We also analyzed and compared the computational complexity of all the three user selection algorithms. The computational complexities of the three algorithms that we achieved in this paper are O(1) for RUS and DOSUS, and O(M2N) for SUS which are less than the other conventional user selection methods. KEYWORDS: Massive MIMO; User Selection; Antenna Selection; Complexity; DOSUS and Antenna Selection; 5G.
∗
Tasher Ali Sheikh (Corresponding author) PhD Scholar department of ECE, NERIST, Nirjuli, Arunachal Pradesh, 791109, India
(email:[email protected]). b
Joyatri Bora, Assistant Professor department of ECE, NERIST, Nirjuli, Arunachal Pradesh,791109,Inida (email: [email protected]). Md. Anwar Hussain, Professor of ECE department NERIST, Nirjuli, Arunachal Pradesh,791109,India (email: [email protected]).
c
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
the users’ terminal in a massive MIMO network. In
1. Introduction
addition, these two user selection algorithms are mostly
The demands for wireless services are rising
used in the practical cellular networks because of it low
extensively because of endlessly growing the number of
system computational cost. As user selection is required
users
communications.
in small-scale MIMO system, it is also necessary for
High-resolution multimedia communication requiring
large-scale MIMO system, which is a new challenging
user capacity above 100Mbps is challenging from the
task for researchers [10-12]. It is observed that the
existing mobile services networks. Recently highly
numbers of BS antennas are very less than the number of
focused research interests in the future 5G wireless
users in conventional multiuser MIMO cellular networks,
communications are obviously with an objective of
whereas due to very huge numbers of BS antennas, the
providing very high user and system capacity. T. L.
usual theoretical treatment does not work in massive
Marzetta has recently proposed in [1] a technique called
MIMO system. For large-scale MIMO system with M
Massive Multiple Input Multiple Output (MIMO), and
number of base station antennas and N number of users,
others such as [2-3] as a candidate technology for 5G. In
each equipped with single antenna, the ergodic
massive MIMO system, tens or hundreds of base station
computational cost for SUS scheme might be very high
(BS) antennas are used for transmission to hundreds or
which is approximately O(M3N).
with
multimedia
thousands of users, each equipped with a single antenna or multiple antennas. The technology is seen to scale-up the data rate by instantaneously transferring the data within a limited bandwidth [4]. The technology is characterized with important features such as huge degrees of freedom, lower consumption of transmission power, higher spectral efficiency, and reliability.
For conventional small-scale MIMO networks, many research works are published that suggested many antenna selection criterion and algorithms [13] like specific antenna selection for practical receiver, an error-rate
oriented
antenna
selection
principle,
capacity-oriented antenna selection, norm like greedy search antenna selection, and dominant-submatrix search
Further, designing efficient scheduling schemes for
and convex optimization. In recent years, some of them
user and antenna selections enhances system capacity
have been implemented in massive MIMO network for
and quality of service [5-6]. Mitigation of inter-user
improving the average system capacity [14-18], [20]. To
interferences requires designing of appropriate precoding
improve the systems performance and to lower the
schemes, and orthogonality among the users. For
computational complexity, an opportunistic hybrid
efficient use of MIMO, joint antenna selection and user
beamforming-based algorithm were proposed in [31] for
scheduling, is mostly preferred. For that reason,
uplink
algorithms such as Exhaustive search algorithm (ESA),
multiuser detection with large number of users. For
Frobenius norm based user selection, Secrecy rate based
small-scale MIMO, an exhaustive search algorithm is
user selection (SRS), Greedy user scheduling algorithm
most favourable and widely used, but it is not useful in
(GSA), branch and bound (BAB) algorithm are found in
massive MIMO network because of a large number of
the literature. The difficulties with the cited algorithms
BS antennas. So an efficient antenna selection algorithm
are that they involve huge system computational cost for
is required for massive MIMO network for enhancing
execution. Authors in [7-8] suggested a user selection
ergodic system sum-rate capacity, as well as it also
technique such as SUS based on instantaneous CSI of
important to minimize the computational cost of the
users, and in [9] the authors proposed a greedy user
executing the algorithms.
selection method. The computational complexity in conventional user selection schemes are reported to be high,
and
hence
low
computational
complexity
algorithms are important for future generation wireless networks.
User
selection
schemes
such
as
the
round-robin algorithm (RRA) and random user selection (RUS) [23] are stated to offer equivalent services among
millimetre-wave
(mm-wave)
systems
for
To resolve the above-mentioned difficulties in massive MIMO, an appropriate joint user and antenna selection algorithm is required. In recent years, researchers have suggested some joint antenna selection and user scheduling (JASUS) algorithms to alleviate difficulties of massive MIMO. Authors in [19] have
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
proposed a downlink BAB-JASUS algorithm for
system capacity is derived with random user selection
decreased computational cost and enhanced ergodic
(RUS) and maximum SNR based antenna selection
capacity for massive MIMO. To lower the feedback
(RUS-AS) criterion.
overhead, authors in [27] proposed an antenna group selection algorithm. To achieve maximum system sum-rate capacity and to reduce the computational cost in broadcast channel and distributed massive MIMO cellular network, and with a limited backhaul authors in [24] and [28] proposed joint antenna selection and user scheduling algorithms. It is a very challenging job, due to variation of channel condition and limited radio frequency channel
in large-scale
MIMO
cellular
networks, to obtain maximum capacity with lower computational cost algorithms. In [29], authors have reported a model of a joint antenna selection and user-scheduling algorithms for massive MIMO networks. The huge numbers of antenna of the users are usually distributed
randomly
in
massive
MIMO
cellular
Our contribution in this paper: We enhance and maximize the system sum-rate capacity of a massive MIMO cellular system considering the channel between the BS and the users having both LSF and SSF natures. We propose a simple and low complexity SUS-AS algorithm where the near-orthogonal users are selected based on SSF and the user rates are calculated based on SSF and LSF. In our proposed DOSUS-AS algorithm, users are selected based on LSF and the user rates are calculated using both SSF and LSF. In the proposed RUS-AS algorithm, users are randomly selected and the user rates are calculated using both SSF and LSF. We propose to select BS antennas in all three algorithms based on maximum SNR to a selected user.
networks and hence consume higher power. Hence, to
The remaining part of the paper organizes as below.
reduce the power consumption in massive MIMO
In section-2, the system model is described. The
cellular networks, authors in [30] proposed a joint user
algorithms are briefly presented in Section-3. The
scheduling and transmit beam-selecting algorithm for
computational complexity calculation is analyzed in
efficient utilization of power. Cooperative multiuser
Section-4. The simulation results and discussion is
beamforming
described in Section-5. The conclusion is presented in
strategy,
which
can
save
power
consumption in mm-wave distributed antenna system, is reported in [29]. In this paper, we explore three algorithms for the joint user and antenna selection in massive MIMO cellular networks. We consider a time division duplex (TDD) system and channel has characteristics both the SSF owing to slowly fading Rayleigh channel and LSF for distance between the users and the antennas. Users are assume as randomly and uniformly distributed in the
section-6. Notation: The symbols are denoted as- the
Hermitian of a matrix or a vector is . Γ , Frobenius-norm of a vector is‖. ‖ an absolute value of
a scalar is|. |and
represents
0,
. The upper
bold and lower bold letter denoted as a vector and matrix respectively. 2. System Model
specified circular geographical area. The user distances
We assume a downlink TDD based massive MIMO
from the base station hence, the large-scale fading is
cellular network, which is shown in Figure-1 and
representing the LSF. We apply linear precoding
Figure-2. The channel is assumed slowly fading and be
schemes such as zeros forcing (ZF), minimum mean
in same over the block lengths of the information bearing
square error (MMSE), and maximum ratio transmission
signals in downlink massive MIMO network, where the
(MRT) for reduction of inter-user interferences. In
M-antennas in the BS serve N-single antenna users. The
algorithm-1, the average system capacity is derived with
magnitude of M is very large in massive MIMO cellular
the criterion of semi-orthogonal user selection (SUS) and
network. For simultaneous data transmission in TDD
maximum SNR based antenna selection (SUS-AS). In
mode in each coherence time slot, we suppose λs (λs<
algorithm-2, average system capacity is calculated with
are the sets of the number of users selected from N users,
descending order of distances of the specified number of
using SUS, DOSUS, and RUS algorithm. Based on the
users to be scheduled and maximum SNR based antenna
maximum channel gains an equal number of BS antennas
selection (DOSUS-AS) method. In algorithm-3, average
are selected from M antennas for simultaneous data
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
transmission with selected and scheduled users. As we consider the model to be a practical scenario, the channels are characterized by both SSF and LSF. The κth user’s downlink received signal is given by =
+
where k=1, 2,…, N,
∈ℂ
……… 1 ×
is the channel gain
matrix from M-BS antenna to transmitted
signal
where # is the factor, )
= ∑& '( "# $ % active user’s transmit power scaling vector
is
Figure-2: Massive MIMO System with joint user and antenna selection scheme
is the weighted column vector of the
beam-forming, % ∈ ℂ*×
and
user, the downlink
With linear precoding, the ᴋth user received signal
is the information bearing symbols is the additive white Gaussian noise
(AWGN) having identical and independent distribution with zero mean and unit covariance.
is rewritten in Eq. (3). = "#
) %
+ "#
is the received
signal vector by user k.
7
∈<= ,'>
8/9 :;
)' %'
+ ? ……… 3
Two vectors S, and T are said to be orthogonal or
where c is LSF factor, d is distance from kth user to BS
semi-orthogonal to each other if the angle between them
antenna, and ℓ is path loss exponent. The respective
|12 3| ≤ 5……… 2 ‖1‖‖3‖
weighted column vectors of the beam-forming codes are
∅ ≈ 90. and /0%∅ = 0 as shown in Eq. (2) below [23].
shown below in Eq. (5). )AB =
)EE1F =
Where the value of θ is positive and that defined in [23]. So in this paper, we assumed θ =0.1 for simulation. We
C
C
)EK3 =
N⁄
C
C :
……… 4
+ѱ H C
:I
……… 6
……… 5
linear precoding schemes like ZF, MMSE and MRT are
where M = ?
employed in downlink massive MIMO system to reduce
column. For equal distribution of power among the
inter-user-interference (IUI) and inter-signal-interference
selected users, total transmitted power satisfies Eq. (7).
assume the channel has a known perfect CSI. The simple
# denotes the ratio of total noise to
transmit power, P ∈ ℂ
#Q
(ISI).
R;
×
is the identity matrix of κth
≥ 7 #T; … … … 7 T;∈<=
th
The κ user received signal simplifies as shown below. ,VW
,
= "# X )
Z[
, \]
,VW %
+ "#
8/9 :; X )',VW %'
7
∈<= ,'>
+ ? ……… 8
= "# X )
,
+ "#
Z[ %
7
∈<= ,'>
8/9 :; X )',
Z[ %'
+ ? ……… 9
= "# X )
, \] %
+ "#
7
∈<= ,'>
8/9 :; X )',
\] %'
+ ? … … … 10
Figure-1: Block diagram of downlink massive MIMO
where Pᴋ,ZF, Pᴋ,MMSE, and Pᴋ,MRT are the κth column matrix
network with N-single antenna users and M-BS antennas.
of the respective precoding matrix. Optimal distributions of total transmit power amongst the users; using water-filling algorithm [33] is shown below.
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI where ` = 1
#<= = ^ − `
⁄|X2
|N
)
, and
… … … 11
is the
and δ is water level measured by the equation below. #Q
R;
0,
= 7 7 #<= … … … 12 a∈
∈*
An equal number of BS antennas are selected based on maximum channel gain between an antenna and a scheduled user, for simultaneous data transmission. For the
selected
user
and
BS
antenna
pair,
signal-to-interference plus noise ratio, b is expressed as shown below in Eq. (13). b =
# |X ) |N … … … 13 ? N + # ∑'> , ∈<= /9 :; |X )' |N
The Eq.13 is further simplified as shown below. b =
M + ∑'>
|X ) |N , ∈<= /9
:;
|X )'
|N
… … … 14
where M = ? ⁄# and Pk is the κth column vector of N
the precoding matrix for the respective precoding schemes. The ergodic capacity C of the TDD based downlink
5.
For each k in o do
6.
wXy x Xxz{ w
‖X| ‖‖Xxz{ ‖
8.
end
9.
}f~; = tj
11.
=
N
12. End
+1
13. ℧ZƒZ = ℧„…
14. For each user in ℧ZƒZ
Steps of Antenna Selection Algorithm 15. Channel vectors of selected user sets X<=
16. Number of BS antenna M 17. ← 1; ⋀ ← p1, … , … , ‡r; ℧<=,<= ← ∅ ≤ λ‰
18. While
19.
Šf~; = tj
‹∈⋀ •X‹,<= •
N
20. ℧„…,„… ← ℧„…,„… ∪ Œ‰•Ž ; ⋀ ← ⋀\℧„…,„… ; X•,„… = X‰•Ž,„… ←
21.
22. End
<=
∈u •X ,u •
10. ℧<= ← ℧<= ∪ }f~; ; • ← •\℧<= ; X = X<=
(15).
|X ) |N ef h 7 i0jN k1 + l … … … 15 g M + ∑'> , ∈<= /9 :; |X )' |N
≤5
7.
massive MIMO system is finally expressed as in Eq. c = d1 −
< ef
While
3
+1
23. ℧„…,„… = ℧„… ,•‘•
(
Algorithm-2: Random User Scheduling (RUS) and 3. Proposed Algorithms
antenna selection (RUS-AS).
We consider a massive MIMO system, as explained in
Stages
section 2 with user channels attenuating with LSF and
Algorithm
fading gains with SSF in slowly varying Rayleigh
1.
channel model. The objective here is to study the
3.
enhance
linear
4.
precoding for mitigating the effect of inter-user
5.
interference. We apply three user scheduling and antenna
6.
section algorithms and to explain the results for the
7.
end
problems in hand, we elaborate the same here.
8.
end
using
9. Algorithm-1: Semi-orthogonal User Scheduling and antenna selection (SUS-AS). Stages of Semi-orthogonal user Scheduling (SUS) Algorithm 1. 2. 3. 4.
To select first user,℧ = tj tj ℧<= ← ℧<= − ℧ ;
While
< λ‰
Randomly select users ’“”• –t0 o
℧<= ← ℧<= ∪ ’“”• ; ω ← ω\℧„… ; X = X<= =
+1
℧„… ← ℧˜‘•
Steps of Antenna Selection Algorithm
10. For each user in ℧˜‘•
11. Channel vectors of selected users set X„…
12. Number of BS antenna M 13. ← 1; ⋀ ← p1, … , … , ‡r; ℧„…,„… ← ∅
Input: Number of BS antenna M Number of User terminals N; ← 1; o ← p1, … . , … qr; ℧<= ← ∅
Scheduling
Number of Users N;
joint user and antenna selection, as explained earlier, for capacity
user
← 1; o ← p1, … … qr; ℧<= ← ∅
2.
sum-rate
Random
Input: Number of BS antenna M;
performance of three user scheduling algorithms with ergodic
of
14. While ∈u ‖X
‖N
≤ λ‰
15. Šf~; = tj
‹∈⋀ •X‹,<= •
N
(RUS)
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
16. ℧„…,„… ← ℧<=,<= ∪ Šf~; ; ⋀ ← ⋀\℧„…,„… ; X‹,<= = Xf~;,<=
computation is computed by summing real addition,
17.
subtraction, multiplication and division associated with
←
+1
18. End
each step of the algorithm. A flop is equivalent to a real
19. ℧„…,„… = ℧„… ,˜‘•
floating-point operation, a complex addition is equivalent to two flops, and one complex multiplication is
Algorithm 3: Descending Order of SNR based User Scheduling
(DOSUS)
and
antenna
selection
Stages of Descending Order of SNR based User Scheduling (DOSUS) Algorithm Input: Number of BS antenna M;
Number of Users N; 2. ← 1; o ← p1, … . , … qr; ℧<= ← ∅
3.
5.
from iteration n=1 to N. In each iteration, a newly
Descending order SNR based User Selection i.e.
selected semi-orthogonal user is added to the set
‖N
’f~; = tj 9™%/™ š ∈u ‖X ℧„… ← ℧„… ∪ ’“”• ; ω ← ω\℧›œ ; X = X<=
6.
=
7. 8.
end
9.
end
containing earlier chosen users. In each iteration, new users which are semi orthogonal to the users in the set
+1
are found and from which the one with the largest channel vector norm is kept and added to the set, with (nN)2M flops. The algorithm terminates when the
10. ℧<= = ℧•žZƒZ
specified number of semi-orthogonal users are selected. The final expression of φ is as shown below.
Steps of Antenna Selection Algorithm
11. For each user in ℧Ÿ
•‘•
12. Channel vectors of selected user sets X<=
¦
¡ = 4NM − N + 7¤N + pM 16n − 12 − 2n + 2r
13. Number of BS antenna M 14. ← 1; ⋀ ← p1, … , … , ‡r; ℧„…,„… ← ∅ ≤ λ‰
15. While
16. Šf~; = tj
‹∈⋀ •X‹,<= •
•(
+ p 12M + 1 N − 1 + Nr§
N
¡ = 4q‡ − q + MN +
17. ℧„…,„… ← ℧„…,„… ∪ Šf~; ; ⋀ ← ⋀\℧„…,„… ; X‹,<= = Xf~;,<=
18.
←
19. end
i.e. 1 ≤ ef ≤ q.
The calculation of flops in SUS algorithm starts
For each k in o do
4.
users are very much less than the number of total users,
A. The Complexity of SUS algorithm
< ef
While
flops slightly differs from the actual complexity computation. In this paper, the number of scheduled
(DOSUS-AS).
1.
equivalent to six flops [25]. The actual calculation of
+1
−
20. ℧„…,„… = ℧<=,•žZƒZ
16‡N ‡ + 1 − 12‡N 2
2‡ ‡ + 1 + 2‡ 2
+ 12‡N + ‡ q − 1 + q‡
4. Analysis of Computational complexity Of Proposed Algorithms
¡ = 7q‡ − q + 8‡¨ − 17‡N + 12q‡N ¡ = O q‡N
In this section, we quantify the computational complexity of the three algorithms, particularly the SUS
Hence complexity of our modified SUS algorithm is
algorithm, we use here. Moreover, we compare the
O(NM2).
computational
complexity
of
our
modified
SUS
algorithm with SUS other algorithms that are shown in table-1. Generally, computational complexity of an algorithm is quantified in terms of flop counts as expressed as φ. A flop count for a given matrix
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Table-1: Complexity Comparison of SUS algorithm
maximum
ratio
transmission
(MRT)
to
3 reduce
interference thereby improving average system sum-rate capacity. We also assume that the cellular network is a Reference
Computational Complexity
Reference [28]
Reference [26]
« - ¨ ¬ q h ≈ ªd « 3 ≈ª q
¨
circular geographical area with outer radius taR® = 300
and inner radius ta'‹ = 45 .
We assume coherence time τ=256, wireless path-loss exponent ℓ=2, and LSF factor c=10-3.. Users are randomly and uniformly distributed in the cell and to schedule λs=8 number of users and select equal number of BS antennas. We consider the noise power level is, wk2=-174dBm , and the bandwidth is 3.5GHz throughout this paper for cellular service operations in 5G, for
Proposed Algorithm-1
≈ ª q‡N
downlink transmit power in the range of 5-20 dBm.
irrespective of their locations and channels with the base station. The same is true for DOSUS, as the specified numbers of users are selected based on closeness to the
210
190 180 5
of users are picked at one go. Hence the complexity of RUS and DOSUS is O(1) as because the algorithms require only one iteration, and
205 200
SUS-AS DOSUS-AS RUS-AS
195 190 185 180 5
20
10 15 SNR (dBm)
20
(d)
190
185
185
SUS-AS DOSUS-AS RUS-AS
180 175 170 5
the flop count is 1. 4. Simulation Results and Discussion
10 15 SNR (dBm)
210
(c) Average sum-rate (bits/Hz/s)
order of distances and the first block of specified number
SUS-AS DOSUS-AS RUS-AS
200
base station and distances of users from the BS are assume to be known. The users are arranged in ascending
(b) Average sum-rate (bits/Hz/s)
specified number of users randomly at one go
220
Average sum-rate (bits/Hz/s)
In the RUS algorithm, the algorithm selects the
Average sum-rate (bits/Hz/s)
(a)
A. The Complexity of RUS and DOSUS algorithms:
10 15 SNR (dBm)
20
180 175
SUS-AS DOSUS-AS RUS-AS
170 165 5
10 15 SNR (dBm)
20
Figure-3: Average system sum-rate with linear precoding: (a) ZF, (b) MMSE, (c) MRT, and (d) no precoding, for
As explained earlier, the objective of this paper is to
SUS-AS, DOSUS-AS, RUS-AS algorithms, and M=32,
maximize the system sum-rate capacity with efficient
N=64.
user and antenna scheduling algorithms and linear precoding. We consider a slowly fading Rayleigh
The simulation results showing average system
channel with perfect acquisition of CSI to explore the
sum-rate versus downlink transmit power is shown in Fig.
system sum-rate capacity of a massive MIMO network.
3, with total number of BS antennas M=32 and users
The users are characterized by having both small scale
N=64, from where we select and schedule λs=8 users and
fading (SSF) due to slowly fading Rayleigh channel and
antennas. Fig. 3(a) shows results using ZF, Fig. 3(b)
large-scale fading (LSF) due to distance dependent
using MMSE, Fig. 3(c) using MRT, with applications of
large-scale path loss from the base station to users.
the scheduling algorithms SUS-AS, RUS-AS and
Further, we use linear precoding techniques such as zero
DOSUS-AS. The results with no precoding and for all
forcing (ZF), minimum mean square error (MMSE), and
the three scheduling algorithms are also shown in Fig.
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
3(d). It is observed from Fig. 3(a), that the average
and (c) RUS-AS algorithm, with ZF, MMSE, MRT and
system rates using ZF, the performances of SUS-AS and
no precoding, for M=32, N=64.
DOSUS-AS are almost same with significant increasing trend and RUS-AS differ in around 2 bits in the higher
The average system sum-rates vs. number of BS
SNR regime only. The similar results with MMSE for
antennas, using the scheduling algorithms are shown in
SUS-AS and DOSUS-AS are observed from Fig. 3(b),
Fig. 5(a) for ZF, Fig. 5(b) for MMSE, Fig. 5(c) for MRT
but here the RUS-AS differ in around 5 bits throughout
and Fig. 5(d) for no precoding case, downlink transmit
the SNR range. The results using MRT, as observed from
power being 15 dB. As is known that increasing the BS
Fig. 3(c) the performances of all the three scheduling
antenna increases diversity gain, the average system
algorithms remain static in the whole SNR range, the
sum-rate shows increasing trend in all the cases.
RUS-AS performing least keeping around 15 bits lower from the other two. Similar trend as in Fig. 3(c) is also
The SUS-AS algorithm show highest results and
seen in Fig. 3(d) for the case of no precoding but with
RUS-AS the lowest. Use of MMSE for M=65 to 150,
average system sum-rate even lowers than the RUS-AS.
DOSUS-AS result is almost the average of RUS-AS and SUS-AS, with significant sum-rate difference between
To compare the performances of ZF, MMSE, MRT,
SUS-AS and DOSUS-AS, between DOSUS-AS and
and no precoding in a particular scheduling case, we plot
RUS-AS. Similar trend is for ZF in Fig. 5(a). More or
the average system sum-rate versus downlink transmit
less similar trends are seen for MRT and no precoding
power in Fig. 4(a) for DOSUS-AS, Fig. 4(b) for SUS-AS,
case as observed in Fig. 5(c) and Fig. 5(d), but here the
and Fig. 4(c) for the RUS-AS algorithm. It is observed
RUS-AS perform much less compared to SUS-AS and
from Fig. 4(a) and Fig. 4(b), that all the cases of
DOSUS-AS.
precoding show similar performances, ZF and MMSE show significant increasing sum-rate, and MRT and no
210 200
220 210 200
210
ZF MMSE MRT Without Precoding
200
190
180 5
Average sum-rate (bits/Hz/s)
ZF MMSE MRT Without Precoding
(b)
190
180
10 15 SNR (dBm)
20
5
10 15 SNR (dBm)
20
(c) ZF MMSE MRT Without Precoding
200 190 SUS-AS DOSUS-AS RUS-AS
180 170
(c)
190
160
200 190 180
SUS-AS DOSUS-AS RUS-AS
170
(d) 195 190 185
SUS-AS DOSUS-AS RUS-AS
180
180 170
210
40 60 80 100 120 140 160 160 40 60 80 100 120 140 160 M Number of BS Antennas M Number of BS Antennas
175
SUS-AS DOSUS-AS RUS-AS
40 60 80 100 120 140 160 M Number of BS Antennas
190
170 165 40 60 80 100 120 140 160 M Number of BS Antennas
Figure-5: Average system sum-rate versus number of BS
180
antennas, for downlink transmit SNR=15dBm, N=64,
170
using (a) ZF, (b) MMSE, (c) MRT, and (d) no precoding,
160 5
200
210
Average sum-rate (bits/Hz/s)
220
220
Average sum-rate (bits/Hz/s)
Average sum-rate (bits/Hz/s)
(a)
(b) 220
Average sum-rate (bits/Hz/s)
attains much higher performance.
Average sum-rate (bits/Hz/s)
cases and in all the scheduling algorithms, ZF precoding
(a) 220
Average sum-rate (bits/Hz/s)
precoding showing static results. Out of all the precoding
10 15 SNR (dBm)
20
for SUS-AS, DOSUS-AS, RUS-AS algorithms.
Figure-4: Average system sum-rate versus downlink
The average system sum-rates vs. number of BS
transmit power, applying (a) DOSUS-AS, (b) SUS-AS
antennas, using the ZF, MMSE, MRT and no precoding
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI are shown in Fig. 6(a) for DOSUS-AS, Fig. 6(b) for
sum-rate shows increasing trend in all the cases. In the cases of SUS-AS and RUS-AS, ZF and MMSE perform similarly, whereas MRT and no precoding show similar
210 200 SUS-AS DOSUS-AS RUS-AS
190 180
trend. The same may be remarked for DOSUS-AS, with
40
considerable difference between ZF and MMSE at the of
the
number
of
210 200 190 180 170
ZF MMSE MRT Without Precoding
40 60 80 100 120 140 160 M Number of BS Antennas
antennas. (b)
Average sum-rate (bits/Hz/s)
Average sum-rate (bits/Hz/s)
(a)
BS
220 210 200 190 180 170
ZF MMSE MRT Without Precoding
40 60 80 100 120 140 160 M Number of BS Antennas
Average sum-rate (bits/Hz/s)
(c) 210 200
ZF MMSE MRT Without Precoding
210 200 190 SUS-AS DOSUS-AS RUS-AS
180 170
60 80 100 120 140 N Number of Users
40 60 80 100 120 140 N Number of Users
(c) Average sum-rate (bits/Hz/s)
mid-range
Average sum-rate (bits/Hz/s)
antenna increases diversity gain, the average system
(b)
200 190 SUS-AS DOSUS-AS
180
RUS-AS
170
160 40
60 80 100 120 140 N Number of Users
(d) Average sum-rate (bits/Hz/s)
being 15 dBm. As is known that increasing the BS
(a) 220
Average sum-rate (bits/Hz/s)
SUS-AS, Fig. 6(c) for RUS-As, downlink transmit power
3
200 190 SUS-AS DOSUS-AS
180
RUS-AS
170 160 40 60 80 100 120 140 N Number of Users
Figure-7: Average system sum-rate versus no. of users, for different scheduling algorithms and using precoding (a) ZF, (b) MMSE, (c) MRT, and (d) no precoding for M=32, and downlink transmit SNR=15dBm.
190 180
To explore the effect of variation of the number of
170
users on the average system sum-rate for M=32, transmit
160
downlink SNR=15 dBm, and λs=8. We observe 40 60 80 100 120 140 160 M Number of BS Antennas
simulation results in Fig. 7 using the three scheduling algorithms, Fig. 7(a) using ZF, Fig. 7(b) using MMSE,
Figure-6: Average system sum-rate versus number of BS
Fig. 7(c) using MRT, and Fig. 7(d) without precoding.
antennas with downlink transmit SNR=15dBm and N=64,
The increase in the total number of users is observed to
for (a) DOSUS-AS, (b) SUS-AS, and (c) RUS-AS
increase the receive diversity gain resulting in increased
algorithm, with ZF, MMSE, MRT and no precoding
average system sum-rates. It is seen that SUS-AS shows
cases.
highest performance and RUS-AS the lowest irrespective of precoding types. Except in the case of MMSE precoding, SUS-AS and DOSUA-AS perform similarly with around 2-5 bits difference. In MMSE the average system sum-rate between SUS-AS and DOSUS-AS widens to around 10 bits from N=60 onward. The variation of the average system sum-rate versus the no. of users are shown in Fig. 8 for three scheduling algorithms with ZF, MMSE, MRT and no precoding case. Fig. 8(a) shows the result with DOSUS-AS, Fig. 8(b) with SUS-AS, and Fig. 8(c) with RUS-AS, with all the four precoding cases. It is observed that average system sum-rate increases with the increase of number of users, SUS-AS performing better than the other two.
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI algorithm-3 is O(1), and of algorithm-1 is
200 190 ZF MMSE MRT Without Precoding
180 170
Average sum-rate (bits/Hz/s)
Average sum-rate (bits/Hz/s)
210
220
Average sum-rate (bits/Hz/s)
200
number of antennas for simultaneous data transmission
ZF MMSE
using TDD mode. The antennas are selected based on
MRT Without Precoding
210
maximum SNR to scheduled users. The three algorithms
200
are considered of low complexity. We observe that the 190
SUS-AS user scheduling with maximum SNR based antenna selection technique enhances the average system
180
40 60 80 100 120 140 N Number of Users (c) 210
where λs is the number of users scheduled with an equal
(b)
(a)
3
ª¯q<= ‡
40 60 80 100 120 140 N Number of Users
sum-rate to the highest extent when ZF precoding scheme is used. We also observe that for given value of
ZF MMSE MRT Without Precoding
N, the increase of M increases the system sum-rate in all the three scheduling algorithms and with any precoding
190
scheme. The same is observed when M is fixed and N is
180
increased. This shows that increase in M or N increases 170
the diversity gain thereby enhancing the system
160
sum-rate.
40 60 80 100 120 140 N Number of Users
Figure-8: Average system sum-rate versus no. of users
Acknowledgements
for (a) DOSUS-AS, (b) SUS-AS, and (c) RUS-AS algorithm, with ZF, MMSE, MRT and no precoding
The authors hereby acknowledge the financial support of
cases, for M=32, downlink transmit SNR=15dBm.
the Ministry of Electronics and Information Technology (Meity) Govt. of India, in this research work (Grant PhD-MLA-4(96)/2015-2016).
5. Conclusion In this paper, we explored how the average system
References
sum-rate of a massive MIMO cellular mobile service depends on the user selection and antenna scheduling
[1] T. L. Marzetta, “Noncooperative Cellular Wireless with Unlimited
algorithms with different precoding schemes.
Numbers of Base Station Antennas,” IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp. 3590-3600, Nov. 2010.
The main objective is to reduce inter-user
[2] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O.
interference by adopting appropriate user selection and
Edfors, and F. Tufvesson, “Scaling Up MIMO: Opportunities and
antenna scheduling algorithms to enhance the average
Challenges with Very Large Arrays,” IEEE Signal Processing
system sum-rate. We consider a slowly fading Rayleigh
Magazine, vol.30, no.1, pp.40-60, 2013.
channel with perfect acquisition of CSI to explore the
[3] E. G. Larsson, O. Edfors, F. Tufvesson and T. L. Marzetta,
system sum-rate capacity of a massive MIMO network.
“Massive MIMO for next generation wireless system,” IEEE
The users are characterized by having both small scale
Communications Magazine, vol. 52, no. 2, pp. 186-195, Feb. 2014.
fading (SSF) due to slowly fading Rayleigh channel and
[4] T. A. Sheikh, J. Bora and M. A. Hussain, “A Survey of Antenna
distance dependent large-scale path loss (LSF). We
and User Scheduling Techniques for Massive MIMO-5G Wireless
studied the system sum-rate variation with variation in
System,” 2017 International Conference on Current Trends in
the downlink transmit power, number of BS antenna, and
Computer, Electrical, Electronics and Communication (CTCEEC),
the number of users.
Mysore, 2017, pp. 578-583, 2017. [5] O. Bai, H. Gao, T. Lv, and C. Yuen, “Low-complexity user
We applied linear precoding schemes such as ZF,
scheduling in the downlink massive MU-MIMO system with linear
MMSE, and MRT and user scheduling algorithms such
precoding," IEEE Int. Conference on Communication, China (ICCC),
as
SUS-AS,
computational
DOSUS-AS, complexity
and of
RUS-AS.
The
pp. 380-384, Oct. 2014.
algorithm-2
and
[6] T. A. Sheikh, J. Bora and M. A. Hussain, “Combined User and
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI st
3
Antenna Selection in Massive MIMO Using Precoding Technique”,
with Imperfect Channel Estimation,” IEEE
International Journal of Sensors, Wireless Communications and
Technology Conference (VTC Spring), Glasgow, Scotland, pp.1-6, Mar.
Control, vol.9, no.1, pp.1-10, 2019.
2015.
[7] G. Lee and Y. Sung, “Asymptotically optimal simple user
[19] Y. Dong, Y. Tang, and K. Zhang, “Improved Joint Antenna
scheduling for massive MIMO downlink with two-stage beamforming,”
Selection and User Scheduling for Massive MIMO System,” 16th IEEE
IEEE 15th International Workshop on Signal Processing Advances in
International Conference on Computer and Information Science
Wireless Communications (SPAWC), Toronto, Canada, pp. 60-64, Jun.
(IEEE/ICIS), Wuhan, China,pp.69-74, May, 2017.
2014.
[20] Y. Gao, W. Jiang, and T. Kaiser, “Bidirectional Branch and Bound
[8] T. A. Sheikh, J. Bora and M. A. Hussain, “Sum-rate Performance of
Based Antenna Selection in Massive MIMO System.” IEEE 26th
Massive MIMO Systems in Highly Scattering Channel with
Annual International Symposium on Personal, Indoor, and Mobile
Semi-orthogonal and Random User selections”, Radioelectronics and
Radio Communications, Hong Kong, China, pp. 563 -568, Sept. 2015.
Communications Systems, Vol. 61, No. 12, pp. 547-555, 2018.
[21] H. Huh, “Large system analysis of multi-cell MIMO Downlink:
[9] Y. Xu, G. Yue, and S. Mao, “User grouping for massive MIMO in
Fairness scheduling and inter-cell cooperation,” Ph.D. dissertation,
FDD system: New design methods and analysis,” IEEE Journals and
Univ. Southern California, Los Angeles, CA, USA, 2012.
Magazines, vol. 2, pp. 947–959, Aug. 2014.
[22] H. Yang and T. Marzetta, “Performance of conjugate and
[10] E. Bjornson, L. Sanguinetti, J. Hoydis and M. Debbah, “Optimal
zero-forcing beamforming in large-scale antenna system,” IEEE
Design of Energy-Efficient Multi-User MIMO System: Is Massive
Journal of Selected Areas of Communication, vol. 31, no. 2, pp.
MIMO the Answer?,” IEEE Transactions on Wireless Communications,
172-179, Feb. 2013.
vol. 14, no. 6, pp. 3059-3075, June 2015.
[23] T. Yoo and A. Goldsmith, “On the optimality of multiantenna
[11] J. Nam, A. Adhikary, J. Y. Ahn, and G. Caire, “Joint spatial
broadcast scheduling using zero-forcing beamforming,” IEEE Journal
division and multiplexing: Opportunistic beamforming, user grouping
on Selected Areas in Communication, vol. 24, no. 3, pp. 528–541, Mar
and simplified downlink scheduling,” IEEE J. Sel. Topics Signal
2006.
Process., vol. 8, no. 5, pp. 876–890, Oct. 2014.
[24] M. Benmimoune, E. Driouch, W. Ajib, and D. Massicotte, “Joint
[12] H. Liu, H. Gao, S. Yang, T. Lv, “Low-complexity downlink user
transmit antenna selection and user scheduling for massive MIMO
selection for massive MIMO system,” IEEE System Journal, vol.11,
system,” 2015 IEEE Wireless Communication and Networking
no.2, pp.1072-1083, Jun 2017.
Conference (WCNC 2015), New Orleans, LA, pp. 381-386, 2015.
[13] Y. Gao, H. Vinck and T. Kaiser, “Massive MIMO Antenna
[25] G. H. Golub and C. F. Van Loan, “Matrix Computations,” 3rd Ed.
Selection: Switching Architectures, Capacity Bounds, and Optimal
Baltimore, MD: The John Hopkins Univ. Press, 1996.
Antenna Selection Algorithms,” IEEE Transactions on Signal
[26] L. Jin, X. Gu, Z. Hu, “Low-Complexity Scheduling Strategy for
Processing, vol. 66, no. 5, pp. 1346-1360, Mar, 2018.
Wireless Multiuser Multiple-Input Multiple-Output Downlink System”
[14] X. Gao, O. Edfors, F. Tufvesson, and E. G. Larsson, “Massive
IET Communications, vol. 5, no.7, pp. 990-995, May, 2011.
MIMO in Real Propagation Environments: Do All Antennas Contribute
[27] B. Lee, L. Ngo and B. Shim, “Antenna group selection based user
Equally?”, IEEE Trans. Commun., vol. 63, no.11, pp. 3917-3928, Nov.
scheduling
2015.
Communications Conference, Austin, TX, 2014, pp. 3302-3307, 2014.
[15] B. Fang, Z.P. Qian, W.S., and W. Zhong, “RAISE: A New Fast
[28] G. Xu, A. Liu, W. Jiang, H. Xiang and W. Luo, “Joint user
Transmit Antenna Selection Algorithm for Massive MIMO System,”
scheduling and antenna selection in distributed massive MIMO systems
Wireless Personal Commun., vol. 80, no. 3, pp. 1147-1157, Feb. 2015.
with limited backhaul capacity,” China Communications, vol. 11, no. 5,
[16] K. Dong, N. Prasad, X.D. Wang, and S.H. Zhu, “Adaptive antenna
pp. 17-30,May 2014.
selection and Tx/Rx beamforming for large-scale MIMO system in 60
[29] X. Liu and X. Wang, “Efficient Antenna Selection and User
GHz channels,” EUSIP Journal Wireless Commun. and Network., vol.
Scheduling in 5G Massive MIMO-NOMA System,” IEEE 83rd
2011, no. 59, pp.1-14., 2011.
Vehicular Technology Conference (VTC Spring), Nanjing, pp.1-5,
[17] Gkizeli M. and Karystinos G.N., “Maximum-SNR Antenna
2016.
Selection Among a Large Number of Transmit Antennas,” IEEE J. Sel.
[30] J. Yan,D. Li, Z. Shi, Y. Guo,W. Wu, “Energy efficient joint user
Topics Signal Process., vol. 8, no. 5, pp. 891-901, Oct. 2014.
scheduling and transmit beamforming in downlink DAS”, Wireless
[18] D. Mi, M. Dianati, S. Muhaidat, and Y. Chen, “A Novel Antenna
Networks, pp-1-15, 2018.
Selection Scheme for Spatially Correlated Massive MIMO Uplinks
[31] Q. Yu, C. Han, L. Bai, J. Choi and X. Shen, “Low-Complexity
for
massive
MIMO
systems,”
81
IEEE
Vehicular
Global
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Multiuser
Detection
in
Millimeter-Wave
Systems
Based
on
Opportunistic Hybrid Beamforming,” IEEE Transactions on Vehicular Technology, vol.67, no.10, pp. 10129-10133, 2018, [32] L. Bai, T. Li, Q. Yu, J. Choi, and W. Zhang, “Cooperative Multiuser Beamforming in mm-Wave Distributed Antenna Systems,’ IEEE Transactions on Vehicular Technology, vol.67, no.12, pp. 12394-12397, 2018, [33] B. M. Lee, J. Choi, J. Bang, and B. C. Kang, “An energy efficient antenna selection for large scale green MIMO systems,” IEEE Int. Symp. On Circuits and Systems (ISCAS), pp. 950-953, May 2013.
3
Conflict of Interest The authors has no conflict of interest regarding the paper entitle: Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI.
S2352-8648(19)30034-3
DOI:
https://doi.org/10.1016/j.dcan.2019.08.002
Reference:
DCAN 173
To appear in:
Digital Communications and Networks
Received Date: 26 January 2019 Revised Date:
19 June 2019
Accepted Date: 29 August 2019
Please cite this article as: T.A. Sheikh, J. Bora, M.A. Hussain, Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI, Digital Communications and Networks (2019), doi: https://doi.org/10.1016/j.dcan.2019.08.002. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Chongqing University of Posts and Telecommunications. Production and hosting by Elsevier B.V. All rights reserved.
Graphical Table of Contents Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Tasher Ali Sheikh*, Joyatri Bora, Md. Anwar Hussain Brief abstract: — The capacity of a massive MIMO cellular network depends on user and antenna selection algorithms, and also on the acquisition of perfect channel state information (CSI). Low computational cost algorithms for user and antenna selection significantly may enhance the system capacity, as it would consume a smaller bandwidth out of the total bandwidth for downlink transmission. The objective of this paper is to maximize the system sum-rate capacity with efficient user and antenna selection algorithms and linear precoding. We consider in this paper, a slowly fading Rayleigh channel with perfect acquisition of CSI to explore the system sum-rate capacity of a massive MIMO network. For user selection, we apply three algorithms, namely Semi-orthogonal user selection (SUS), descending order-based user scheduling (DOSUS), and Random user selection (RUS) algorithm. In all the user selection algorithms, the selection of base station (BS) antenna is based on maximum signal-to-noise ratio (SNR) to the selected users. Hence users are characterized by having both small scale fading (SSF) due to slowly fading Rayleigh channel and large-scale fading (LSF) due to distances from the base station.
Further, we use
linear precoding techniques such as zero forcing (ZF), minimum mean square error (MMSE), and maximum ratio transmission (MRT) to reduce interferences thereby improving average system sum-rate capacity. Results using SUS, DOSUS, and RUS user selection algorithms with ZF, MMSE, and MRT precoding techniques are
compared. We also analyzed and compared the computational complexity of all the three user selection algorithms. The computational complexities of the three algorithms that we achieved in this paper are O(1) for RUS and DOSUS, and O(M2N) for SUS which are less than the other conventional user selection methods.
Figure-2: Massive MIMO System with joint user and antenna selection scheme
2
Tasher Ali Sheikh, et al.
Digital Communication and Networks (DCN)
Available online at www.sciencedirect.com
Science Direct Journalhomepage:www.keaipublishing.com/en/journals/digital-communications-and-networks ISSN:2352-8648
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Tasher Ali Sheikh∗a, Joyatri Borab, Md. Anwar Hussainc a,b,c
Department of Electronics and Communication Engineering, North Eastern Regional Institute of Science and Technology, Nirjuli,
Arunachal Pradesh,791109, India.
Abstract The capacity of a massive MIMO cellular network depends on user and antenna selection algorithms, and also on the acquisition of perfect channel state information (CSI). Low computational cost algorithms for user and antenna selection significantly may enhance the system capacity, as it would consume a smaller bandwidth out of the total bandwidth for downlink transmission. The objective of this paper is to maximize the system sum-rate capacity with efficient user and antenna selection algorithms and linear precoding. We consider in this paper, a slowly fading Rayleigh channel with perfect acquisition of CSI to explore the system sum-rate capacity of a massive MIMO network. For user selection, we apply three algorithms, namely Semi-orthogonal user selection (SUS), descending order-based user scheduling (DOSUS), and Random user selection (RUS) algorithm. In all the user selection algorithms, the selection of base station (BS) antenna is based on maximum signal-to-noise ratio (SNR) to the selected users. Hence users are characterized by having both small scale fading (SSF) due to slowly fading Rayleigh channel and large-scale fading (LSF) due to distances from the base station.
Further, we use linear precoding techniques such as zero forcing (ZF), minimum mean
square error (MMSE), and maximum ratio transmission (MRT) to reduce interferences thereby improving average system sum-rate capacity. Results using SUS, DOSUS, and RUS user selection algorithms with ZF, MMSE, and MRT precoding techniques are compared. We also analyzed and compared the computational complexity of all the three user selection algorithms. The computational complexities of the three algorithms that we achieved in this paper are O(1) for RUS and DOSUS, and O(M2N) for SUS which are less than the other conventional user selection methods. KEYWORDS: Massive MIMO; User Selection; Antenna Selection; Complexity; DOSUS and Antenna Selection; 5G.
∗
Tasher Ali Sheikh (Corresponding author) PhD Scholar department of ECE, NERIST, Nirjuli, Arunachal Pradesh, 791109, India
(email:[email protected]). b
Joyatri Bora, Assistant Professor department of ECE, NERIST, Nirjuli, Arunachal Pradesh,791109,Inida (email: [email protected]). Md. Anwar Hussain, Professor of ECE department NERIST, Nirjuli, Arunachal Pradesh,791109,India (email: [email protected]).
c
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
the users’ terminal in a massive MIMO network. In
1. Introduction
addition, these two user selection algorithms are mostly
The demands for wireless services are rising
used in the practical cellular networks because of it low
extensively because of endlessly growing the number of
system computational cost. As user selection is required
users
communications.
in small-scale MIMO system, it is also necessary for
High-resolution multimedia communication requiring
large-scale MIMO system, which is a new challenging
user capacity above 100Mbps is challenging from the
task for researchers [10-12]. It is observed that the
existing mobile services networks. Recently highly
numbers of BS antennas are very less than the number of
focused research interests in the future 5G wireless
users in conventional multiuser MIMO cellular networks,
communications are obviously with an objective of
whereas due to very huge numbers of BS antennas, the
providing very high user and system capacity. T. L.
usual theoretical treatment does not work in massive
Marzetta has recently proposed in [1] a technique called
MIMO system. For large-scale MIMO system with M
Massive Multiple Input Multiple Output (MIMO), and
number of base station antennas and N number of users,
others such as [2-3] as a candidate technology for 5G. In
each equipped with single antenna, the ergodic
massive MIMO system, tens or hundreds of base station
computational cost for SUS scheme might be very high
(BS) antennas are used for transmission to hundreds or
which is approximately O(M3N).
with
multimedia
thousands of users, each equipped with a single antenna or multiple antennas. The technology is seen to scale-up the data rate by instantaneously transferring the data within a limited bandwidth [4]. The technology is characterized with important features such as huge degrees of freedom, lower consumption of transmission power, higher spectral efficiency, and reliability.
For conventional small-scale MIMO networks, many research works are published that suggested many antenna selection criterion and algorithms [13] like specific antenna selection for practical receiver, an error-rate
oriented
antenna
selection
principle,
capacity-oriented antenna selection, norm like greedy search antenna selection, and dominant-submatrix search
Further, designing efficient scheduling schemes for
and convex optimization. In recent years, some of them
user and antenna selections enhances system capacity
have been implemented in massive MIMO network for
and quality of service [5-6]. Mitigation of inter-user
improving the average system capacity [14-18], [20]. To
interferences requires designing of appropriate precoding
improve the systems performance and to lower the
schemes, and orthogonality among the users. For
computational complexity, an opportunistic hybrid
efficient use of MIMO, joint antenna selection and user
beamforming-based algorithm were proposed in [31] for
scheduling, is mostly preferred. For that reason,
uplink
algorithms such as Exhaustive search algorithm (ESA),
multiuser detection with large number of users. For
Frobenius norm based user selection, Secrecy rate based
small-scale MIMO, an exhaustive search algorithm is
user selection (SRS), Greedy user scheduling algorithm
most favourable and widely used, but it is not useful in
(GSA), branch and bound (BAB) algorithm are found in
massive MIMO network because of a large number of
the literature. The difficulties with the cited algorithms
BS antennas. So an efficient antenna selection algorithm
are that they involve huge system computational cost for
is required for massive MIMO network for enhancing
execution. Authors in [7-8] suggested a user selection
ergodic system sum-rate capacity, as well as it also
technique such as SUS based on instantaneous CSI of
important to minimize the computational cost of the
users, and in [9] the authors proposed a greedy user
executing the algorithms.
selection method. The computational complexity in conventional user selection schemes are reported to be high,
and
hence
low
computational
complexity
algorithms are important for future generation wireless networks.
User
selection
schemes
such
as
the
round-robin algorithm (RRA) and random user selection (RUS) [23] are stated to offer equivalent services among
millimetre-wave
(mm-wave)
systems
for
To resolve the above-mentioned difficulties in massive MIMO, an appropriate joint user and antenna selection algorithm is required. In recent years, researchers have suggested some joint antenna selection and user scheduling (JASUS) algorithms to alleviate difficulties of massive MIMO. Authors in [19] have
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
proposed a downlink BAB-JASUS algorithm for
system capacity is derived with random user selection
decreased computational cost and enhanced ergodic
(RUS) and maximum SNR based antenna selection
capacity for massive MIMO. To lower the feedback
(RUS-AS) criterion.
overhead, authors in [27] proposed an antenna group selection algorithm. To achieve maximum system sum-rate capacity and to reduce the computational cost in broadcast channel and distributed massive MIMO cellular network, and with a limited backhaul authors in [24] and [28] proposed joint antenna selection and user scheduling algorithms. It is a very challenging job, due to variation of channel condition and limited radio frequency channel
in large-scale
MIMO
cellular
networks, to obtain maximum capacity with lower computational cost algorithms. In [29], authors have reported a model of a joint antenna selection and user-scheduling algorithms for massive MIMO networks. The huge numbers of antenna of the users are usually distributed
randomly
in
massive
MIMO
cellular
Our contribution in this paper: We enhance and maximize the system sum-rate capacity of a massive MIMO cellular system considering the channel between the BS and the users having both LSF and SSF natures. We propose a simple and low complexity SUS-AS algorithm where the near-orthogonal users are selected based on SSF and the user rates are calculated based on SSF and LSF. In our proposed DOSUS-AS algorithm, users are selected based on LSF and the user rates are calculated using both SSF and LSF. In the proposed RUS-AS algorithm, users are randomly selected and the user rates are calculated using both SSF and LSF. We propose to select BS antennas in all three algorithms based on maximum SNR to a selected user.
networks and hence consume higher power. Hence, to
The remaining part of the paper organizes as below.
reduce the power consumption in massive MIMO
In section-2, the system model is described. The
cellular networks, authors in [30] proposed a joint user
algorithms are briefly presented in Section-3. The
scheduling and transmit beam-selecting algorithm for
computational complexity calculation is analyzed in
efficient utilization of power. Cooperative multiuser
Section-4. The simulation results and discussion is
beamforming
described in Section-5. The conclusion is presented in
strategy,
which
can
save
power
consumption in mm-wave distributed antenna system, is reported in [29]. In this paper, we explore three algorithms for the joint user and antenna selection in massive MIMO cellular networks. We consider a time division duplex (TDD) system and channel has characteristics both the SSF owing to slowly fading Rayleigh channel and LSF for distance between the users and the antennas. Users are assume as randomly and uniformly distributed in the
section-6. Notation: The symbols are denoted as- the
Hermitian of a matrix or a vector is . Γ , Frobenius-norm of a vector is‖. ‖ an absolute value of
a scalar is|. |and
represents
0,
. The upper
bold and lower bold letter denoted as a vector and matrix respectively. 2. System Model
specified circular geographical area. The user distances
We assume a downlink TDD based massive MIMO
from the base station hence, the large-scale fading is
cellular network, which is shown in Figure-1 and
representing the LSF. We apply linear precoding
Figure-2. The channel is assumed slowly fading and be
schemes such as zeros forcing (ZF), minimum mean
in same over the block lengths of the information bearing
square error (MMSE), and maximum ratio transmission
signals in downlink massive MIMO network, where the
(MRT) for reduction of inter-user interferences. In
M-antennas in the BS serve N-single antenna users. The
algorithm-1, the average system capacity is derived with
magnitude of M is very large in massive MIMO cellular
the criterion of semi-orthogonal user selection (SUS) and
network. For simultaneous data transmission in TDD
maximum SNR based antenna selection (SUS-AS). In
mode in each coherence time slot, we suppose λs (λs<
algorithm-2, average system capacity is calculated with
are the sets of the number of users selected from N users,
descending order of distances of the specified number of
using SUS, DOSUS, and RUS algorithm. Based on the
users to be scheduled and maximum SNR based antenna
maximum channel gains an equal number of BS antennas
selection (DOSUS-AS) method. In algorithm-3, average
are selected from M antennas for simultaneous data
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
transmission with selected and scheduled users. As we consider the model to be a practical scenario, the channels are characterized by both SSF and LSF. The κth user’s downlink received signal is given by =
+
where k=1, 2,…, N,
∈ℂ
……… 1 ×
is the channel gain
matrix from M-BS antenna to transmitted
signal
where # is the factor, )
= ∑& '( "# $ % active user’s transmit power scaling vector
is
Figure-2: Massive MIMO System with joint user and antenna selection scheme
is the weighted column vector of the
beam-forming, % ∈ ℂ*×
and
user, the downlink
With linear precoding, the ᴋth user received signal
is the information bearing symbols is the additive white Gaussian noise
(AWGN) having identical and independent distribution with zero mean and unit covariance.
is rewritten in Eq. (3). = "#
) %
+ "#
is the received
signal vector by user k.
7
∈<= ,'>
8/9 :;
)' %'
+ ? ……… 3
Two vectors S, and T are said to be orthogonal or
where c is LSF factor, d is distance from kth user to BS
semi-orthogonal to each other if the angle between them
antenna, and ℓ is path loss exponent. The respective
|12 3| ≤ 5……… 2 ‖1‖‖3‖
weighted column vectors of the beam-forming codes are
∅ ≈ 90. and /0%∅ = 0 as shown in Eq. (2) below [23].
shown below in Eq. (5). )AB =
)EE1F =
Where the value of θ is positive and that defined in [23]. So in this paper, we assumed θ =0.1 for simulation. We
C
C
)EK3 =
N⁄
C
C :
……… 4
+ѱ H C
:I
……… 6
……… 5
linear precoding schemes like ZF, MMSE and MRT are
where M = ?
employed in downlink massive MIMO system to reduce
column. For equal distribution of power among the
inter-user-interference (IUI) and inter-signal-interference
selected users, total transmitted power satisfies Eq. (7).
assume the channel has a known perfect CSI. The simple
# denotes the ratio of total noise to
transmit power, P ∈ ℂ
#Q
(ISI).
R;
×
is the identity matrix of κth
≥ 7 #T; … … … 7 T;∈<=
th
The κ user received signal simplifies as shown below. ,VW
,
= "# X )
Z[
, \]
,VW %
+ "#
8/9 :; X )',VW %'
7
∈<= ,'>
+ ? ……… 8
= "# X )
,
+ "#
Z[ %
7
∈<= ,'>
8/9 :; X )',
Z[ %'
+ ? ……… 9
= "# X )
, \] %
+ "#
7
∈<= ,'>
8/9 :; X )',
\] %'
+ ? … … … 10
Figure-1: Block diagram of downlink massive MIMO
where Pᴋ,ZF, Pᴋ,MMSE, and Pᴋ,MRT are the κth column matrix
network with N-single antenna users and M-BS antennas.
of the respective precoding matrix. Optimal distributions of total transmit power amongst the users; using water-filling algorithm [33] is shown below.
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI where ` = 1
#<= = ^ − `
⁄|X2
|N
)
, and
… … … 11
is the
and δ is water level measured by the equation below. #Q
R;
0,
= 7 7 #<= … … … 12 a∈
∈*
An equal number of BS antennas are selected based on maximum channel gain between an antenna and a scheduled user, for simultaneous data transmission. For the
selected
user
and
BS
antenna
pair,
signal-to-interference plus noise ratio, b is expressed as shown below in Eq. (13). b =
# |X ) |N … … … 13 ? N + # ∑'> , ∈<= /9 :; |X )' |N
The Eq.13 is further simplified as shown below. b =
M + ∑'>
|X ) |N , ∈<= /9
:;
|X )'
|N
… … … 14
where M = ? ⁄# and Pk is the κth column vector of N
the precoding matrix for the respective precoding schemes. The ergodic capacity C of the TDD based downlink
5.
For each k in o do
6.
wXy x Xxz{ w
‖X| ‖‖Xxz{ ‖
8.
end
9.
}f~; = tj
11.
=
N
12. End
+1
13. ℧ZƒZ = ℧„…
14. For each user in ℧ZƒZ
Steps of Antenna Selection Algorithm 15. Channel vectors of selected user sets X<=
16. Number of BS antenna M 17. ← 1; ⋀ ← p1, … , … , ‡r; ℧<=,<= ← ∅ ≤ λ‰
18. While
19.
Šf~; = tj
‹∈⋀ •X‹,<= •
N
20. ℧„…,„… ← ℧„…,„… ∪ Œ‰•Ž ; ⋀ ← ⋀\℧„…,„… ; X•,„… = X‰•Ž,„… ←
21.
22. End
<=
∈u •X ,u •
10. ℧<= ← ℧<= ∪ }f~; ; • ← •\℧<= ; X = X<=
(15).
|X ) |N ef h 7 i0jN k1 + l … … … 15 g M + ∑'> , ∈<= /9 :; |X )' |N
≤5
7.
massive MIMO system is finally expressed as in Eq. c = d1 −
< ef
While
3
+1
23. ℧„…,„… = ℧„… ,•‘•
(
Algorithm-2: Random User Scheduling (RUS) and 3. Proposed Algorithms
antenna selection (RUS-AS).
We consider a massive MIMO system, as explained in
Stages
section 2 with user channels attenuating with LSF and
Algorithm
fading gains with SSF in slowly varying Rayleigh
1.
channel model. The objective here is to study the
3.
enhance
linear
4.
precoding for mitigating the effect of inter-user
5.
interference. We apply three user scheduling and antenna
6.
section algorithms and to explain the results for the
7.
end
problems in hand, we elaborate the same here.
8.
end
using
9. Algorithm-1: Semi-orthogonal User Scheduling and antenna selection (SUS-AS). Stages of Semi-orthogonal user Scheduling (SUS) Algorithm 1. 2. 3. 4.
To select first user,℧ = tj tj ℧<= ← ℧<= − ℧ ;
While
< λ‰
Randomly select users ’“”• –t0 o
℧<= ← ℧<= ∪ ’“”• ; ω ← ω\℧„… ; X = X<= =
+1
℧„… ← ℧˜‘•
Steps of Antenna Selection Algorithm
10. For each user in ℧˜‘•
11. Channel vectors of selected users set X„…
12. Number of BS antenna M 13. ← 1; ⋀ ← p1, … , … , ‡r; ℧„…,„… ← ∅
Input: Number of BS antenna M Number of User terminals N; ← 1; o ← p1, … . , … qr; ℧<= ← ∅
Scheduling
Number of Users N;
joint user and antenna selection, as explained earlier, for capacity
user
← 1; o ← p1, … … qr; ℧<= ← ∅
2.
sum-rate
Random
Input: Number of BS antenna M;
performance of three user scheduling algorithms with ergodic
of
14. While ∈u ‖X
‖N
≤ λ‰
15. Šf~; = tj
‹∈⋀ •X‹,<= •
N
(RUS)
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
16. ℧„…,„… ← ℧<=,<= ∪ Šf~; ; ⋀ ← ⋀\℧„…,„… ; X‹,<= = Xf~;,<=
computation is computed by summing real addition,
17.
subtraction, multiplication and division associated with
←
+1
18. End
each step of the algorithm. A flop is equivalent to a real
19. ℧„…,„… = ℧„… ,˜‘•
floating-point operation, a complex addition is equivalent to two flops, and one complex multiplication is
Algorithm 3: Descending Order of SNR based User Scheduling
(DOSUS)
and
antenna
selection
Stages of Descending Order of SNR based User Scheduling (DOSUS) Algorithm Input: Number of BS antenna M;
Number of Users N; 2. ← 1; o ← p1, … . , … qr; ℧<= ← ∅
3.
5.
from iteration n=1 to N. In each iteration, a newly
Descending order SNR based User Selection i.e.
selected semi-orthogonal user is added to the set
‖N
’f~; = tj 9™%/™ š ∈u ‖X ℧„… ← ℧„… ∪ ’“”• ; ω ← ω\℧›œ ; X = X<=
6.
=
7. 8.
end
9.
end
containing earlier chosen users. In each iteration, new users which are semi orthogonal to the users in the set
+1
are found and from which the one with the largest channel vector norm is kept and added to the set, with (nN)2M flops. The algorithm terminates when the
10. ℧<= = ℧•žZƒZ
specified number of semi-orthogonal users are selected. The final expression of φ is as shown below.
Steps of Antenna Selection Algorithm
11. For each user in ℧Ÿ
•‘•
12. Channel vectors of selected user sets X<=
¦
¡ = 4NM − N + 7¤N + pM 16n − 12 − 2n + 2r
13. Number of BS antenna M 14. ← 1; ⋀ ← p1, … , … , ‡r; ℧„…,„… ← ∅ ≤ λ‰
15. While
16. Šf~; = tj
‹∈⋀ •X‹,<= •
•(
+ p 12M + 1 N − 1 + Nr§
N
¡ = 4q‡ − q + MN +
17. ℧„…,„… ← ℧„…,„… ∪ Šf~; ; ⋀ ← ⋀\℧„…,„… ; X‹,<= = Xf~;,<=
18.
←
19. end
i.e. 1 ≤ ef ≤ q.
The calculation of flops in SUS algorithm starts
For each k in o do
4.
users are very much less than the number of total users,
A. The Complexity of SUS algorithm
< ef
While
flops slightly differs from the actual complexity computation. In this paper, the number of scheduled
(DOSUS-AS).
1.
equivalent to six flops [25]. The actual calculation of
+1
−
20. ℧„…,„… = ℧<=,•žZƒZ
16‡N ‡ + 1 − 12‡N 2
2‡ ‡ + 1 + 2‡ 2
+ 12‡N + ‡ q − 1 + q‡
4. Analysis of Computational complexity Of Proposed Algorithms
¡ = 7q‡ − q + 8‡¨ − 17‡N + 12q‡N ¡ = O q‡N
In this section, we quantify the computational complexity of the three algorithms, particularly the SUS
Hence complexity of our modified SUS algorithm is
algorithm, we use here. Moreover, we compare the
O(NM2).
computational
complexity
of
our
modified
SUS
algorithm with SUS other algorithms that are shown in table-1. Generally, computational complexity of an algorithm is quantified in terms of flop counts as expressed as φ. A flop count for a given matrix
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Table-1: Complexity Comparison of SUS algorithm
maximum
ratio
transmission
(MRT)
to
3 reduce
interference thereby improving average system sum-rate capacity. We also assume that the cellular network is a Reference
Computational Complexity
Reference [28]
Reference [26]
« - ¨ ¬ q h ≈ ªd « 3 ≈ª q
¨
circular geographical area with outer radius taR® = 300
and inner radius ta'‹ = 45 .
We assume coherence time τ=256, wireless path-loss exponent ℓ=2, and LSF factor c=10-3.. Users are randomly and uniformly distributed in the cell and to schedule λs=8 number of users and select equal number of BS antennas. We consider the noise power level is, wk2=-174dBm , and the bandwidth is 3.5GHz throughout this paper for cellular service operations in 5G, for
Proposed Algorithm-1
≈ ª q‡N
downlink transmit power in the range of 5-20 dBm.
irrespective of their locations and channels with the base station. The same is true for DOSUS, as the specified numbers of users are selected based on closeness to the
210
190 180 5
of users are picked at one go. Hence the complexity of RUS and DOSUS is O(1) as because the algorithms require only one iteration, and
205 200
SUS-AS DOSUS-AS RUS-AS
195 190 185 180 5
20
10 15 SNR (dBm)
20
(d)
190
185
185
SUS-AS DOSUS-AS RUS-AS
180 175 170 5
the flop count is 1. 4. Simulation Results and Discussion
10 15 SNR (dBm)
210
(c) Average sum-rate (bits/Hz/s)
order of distances and the first block of specified number
SUS-AS DOSUS-AS RUS-AS
200
base station and distances of users from the BS are assume to be known. The users are arranged in ascending
(b) Average sum-rate (bits/Hz/s)
specified number of users randomly at one go
220
Average sum-rate (bits/Hz/s)
In the RUS algorithm, the algorithm selects the
Average sum-rate (bits/Hz/s)
(a)
A. The Complexity of RUS and DOSUS algorithms:
10 15 SNR (dBm)
20
180 175
SUS-AS DOSUS-AS RUS-AS
170 165 5
10 15 SNR (dBm)
20
Figure-3: Average system sum-rate with linear precoding: (a) ZF, (b) MMSE, (c) MRT, and (d) no precoding, for
As explained earlier, the objective of this paper is to
SUS-AS, DOSUS-AS, RUS-AS algorithms, and M=32,
maximize the system sum-rate capacity with efficient
N=64.
user and antenna scheduling algorithms and linear precoding. We consider a slowly fading Rayleigh
The simulation results showing average system
channel with perfect acquisition of CSI to explore the
sum-rate versus downlink transmit power is shown in Fig.
system sum-rate capacity of a massive MIMO network.
3, with total number of BS antennas M=32 and users
The users are characterized by having both small scale
N=64, from where we select and schedule λs=8 users and
fading (SSF) due to slowly fading Rayleigh channel and
antennas. Fig. 3(a) shows results using ZF, Fig. 3(b)
large-scale fading (LSF) due to distance dependent
using MMSE, Fig. 3(c) using MRT, with applications of
large-scale path loss from the base station to users.
the scheduling algorithms SUS-AS, RUS-AS and
Further, we use linear precoding techniques such as zero
DOSUS-AS. The results with no precoding and for all
forcing (ZF), minimum mean square error (MMSE), and
the three scheduling algorithms are also shown in Fig.
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI
3
3(d). It is observed from Fig. 3(a), that the average
and (c) RUS-AS algorithm, with ZF, MMSE, MRT and
system rates using ZF, the performances of SUS-AS and
no precoding, for M=32, N=64.
DOSUS-AS are almost same with significant increasing trend and RUS-AS differ in around 2 bits in the higher
The average system sum-rates vs. number of BS
SNR regime only. The similar results with MMSE for
antennas, using the scheduling algorithms are shown in
SUS-AS and DOSUS-AS are observed from Fig. 3(b),
Fig. 5(a) for ZF, Fig. 5(b) for MMSE, Fig. 5(c) for MRT
but here the RUS-AS differ in around 5 bits throughout
and Fig. 5(d) for no precoding case, downlink transmit
the SNR range. The results using MRT, as observed from
power being 15 dB. As is known that increasing the BS
Fig. 3(c) the performances of all the three scheduling
antenna increases diversity gain, the average system
algorithms remain static in the whole SNR range, the
sum-rate shows increasing trend in all the cases.
RUS-AS performing least keeping around 15 bits lower from the other two. Similar trend as in Fig. 3(c) is also
The SUS-AS algorithm show highest results and
seen in Fig. 3(d) for the case of no precoding but with
RUS-AS the lowest. Use of MMSE for M=65 to 150,
average system sum-rate even lowers than the RUS-AS.
DOSUS-AS result is almost the average of RUS-AS and SUS-AS, with significant sum-rate difference between
To compare the performances of ZF, MMSE, MRT,
SUS-AS and DOSUS-AS, between DOSUS-AS and
and no precoding in a particular scheduling case, we plot
RUS-AS. Similar trend is for ZF in Fig. 5(a). More or
the average system sum-rate versus downlink transmit
less similar trends are seen for MRT and no precoding
power in Fig. 4(a) for DOSUS-AS, Fig. 4(b) for SUS-AS,
case as observed in Fig. 5(c) and Fig. 5(d), but here the
and Fig. 4(c) for the RUS-AS algorithm. It is observed
RUS-AS perform much less compared to SUS-AS and
from Fig. 4(a) and Fig. 4(b), that all the cases of
DOSUS-AS.
precoding show similar performances, ZF and MMSE show significant increasing sum-rate, and MRT and no
210 200
220 210 200
210
ZF MMSE MRT Without Precoding
200
190
180 5
Average sum-rate (bits/Hz/s)
ZF MMSE MRT Without Precoding
(b)
190
180
10 15 SNR (dBm)
20
5
10 15 SNR (dBm)
20
(c) ZF MMSE MRT Without Precoding
200 190 SUS-AS DOSUS-AS RUS-AS
180 170
(c)
190
160
200 190 180
SUS-AS DOSUS-AS RUS-AS
170
(d) 195 190 185
SUS-AS DOSUS-AS RUS-AS
180
180 170
210
40 60 80 100 120 140 160 160 40 60 80 100 120 140 160 M Number of BS Antennas M Number of BS Antennas
175
SUS-AS DOSUS-AS RUS-AS
40 60 80 100 120 140 160 M Number of BS Antennas
190
170 165 40 60 80 100 120 140 160 M Number of BS Antennas
Figure-5: Average system sum-rate versus number of BS
180
antennas, for downlink transmit SNR=15dBm, N=64,
170
using (a) ZF, (b) MMSE, (c) MRT, and (d) no precoding,
160 5
200
210
Average sum-rate (bits/Hz/s)
220
220
Average sum-rate (bits/Hz/s)
Average sum-rate (bits/Hz/s)
(a)
(b) 220
Average sum-rate (bits/Hz/s)
attains much higher performance.
Average sum-rate (bits/Hz/s)
cases and in all the scheduling algorithms, ZF precoding
(a) 220
Average sum-rate (bits/Hz/s)
precoding showing static results. Out of all the precoding
10 15 SNR (dBm)
20
for SUS-AS, DOSUS-AS, RUS-AS algorithms.
Figure-4: Average system sum-rate versus downlink
The average system sum-rates vs. number of BS
transmit power, applying (a) DOSUS-AS, (b) SUS-AS
antennas, using the ZF, MMSE, MRT and no precoding
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI are shown in Fig. 6(a) for DOSUS-AS, Fig. 6(b) for
sum-rate shows increasing trend in all the cases. In the cases of SUS-AS and RUS-AS, ZF and MMSE perform similarly, whereas MRT and no precoding show similar
210 200 SUS-AS DOSUS-AS RUS-AS
190 180
trend. The same may be remarked for DOSUS-AS, with
40
considerable difference between ZF and MMSE at the of
the
number
of
210 200 190 180 170
ZF MMSE MRT Without Precoding
40 60 80 100 120 140 160 M Number of BS Antennas
antennas. (b)
Average sum-rate (bits/Hz/s)
Average sum-rate (bits/Hz/s)
(a)
BS
220 210 200 190 180 170
ZF MMSE MRT Without Precoding
40 60 80 100 120 140 160 M Number of BS Antennas
Average sum-rate (bits/Hz/s)
(c) 210 200
ZF MMSE MRT Without Precoding
210 200 190 SUS-AS DOSUS-AS RUS-AS
180 170
60 80 100 120 140 N Number of Users
40 60 80 100 120 140 N Number of Users
(c) Average sum-rate (bits/Hz/s)
mid-range
Average sum-rate (bits/Hz/s)
antenna increases diversity gain, the average system
(b)
200 190 SUS-AS DOSUS-AS
180
RUS-AS
170
160 40
60 80 100 120 140 N Number of Users
(d) Average sum-rate (bits/Hz/s)
being 15 dBm. As is known that increasing the BS
(a) 220
Average sum-rate (bits/Hz/s)
SUS-AS, Fig. 6(c) for RUS-As, downlink transmit power
3
200 190 SUS-AS DOSUS-AS
180
RUS-AS
170 160 40 60 80 100 120 140 N Number of Users
Figure-7: Average system sum-rate versus no. of users, for different scheduling algorithms and using precoding (a) ZF, (b) MMSE, (c) MRT, and (d) no precoding for M=32, and downlink transmit SNR=15dBm.
190 180
To explore the effect of variation of the number of
170
users on the average system sum-rate for M=32, transmit
160
downlink SNR=15 dBm, and λs=8. We observe 40 60 80 100 120 140 160 M Number of BS Antennas
simulation results in Fig. 7 using the three scheduling algorithms, Fig. 7(a) using ZF, Fig. 7(b) using MMSE,
Figure-6: Average system sum-rate versus number of BS
Fig. 7(c) using MRT, and Fig. 7(d) without precoding.
antennas with downlink transmit SNR=15dBm and N=64,
The increase in the total number of users is observed to
for (a) DOSUS-AS, (b) SUS-AS, and (c) RUS-AS
increase the receive diversity gain resulting in increased
algorithm, with ZF, MMSE, MRT and no precoding
average system sum-rates. It is seen that SUS-AS shows
cases.
highest performance and RUS-AS the lowest irrespective of precoding types. Except in the case of MMSE precoding, SUS-AS and DOSUA-AS perform similarly with around 2-5 bits difference. In MMSE the average system sum-rate between SUS-AS and DOSUS-AS widens to around 10 bits from N=60 onward. The variation of the average system sum-rate versus the no. of users are shown in Fig. 8 for three scheduling algorithms with ZF, MMSE, MRT and no precoding case. Fig. 8(a) shows the result with DOSUS-AS, Fig. 8(b) with SUS-AS, and Fig. 8(c) with RUS-AS, with all the four precoding cases. It is observed that average system sum-rate increases with the increase of number of users, SUS-AS performing better than the other two.
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI algorithm-3 is O(1), and of algorithm-1 is
200 190 ZF MMSE MRT Without Precoding
180 170
Average sum-rate (bits/Hz/s)
Average sum-rate (bits/Hz/s)
210
220
Average sum-rate (bits/Hz/s)
200
number of antennas for simultaneous data transmission
ZF MMSE
using TDD mode. The antennas are selected based on
MRT Without Precoding
210
maximum SNR to scheduled users. The three algorithms
200
are considered of low complexity. We observe that the 190
SUS-AS user scheduling with maximum SNR based antenna selection technique enhances the average system
180
40 60 80 100 120 140 N Number of Users (c) 210
where λs is the number of users scheduled with an equal
(b)
(a)
3
ª¯q<= ‡
40 60 80 100 120 140 N Number of Users
sum-rate to the highest extent when ZF precoding scheme is used. We also observe that for given value of
ZF MMSE MRT Without Precoding
N, the increase of M increases the system sum-rate in all the three scheduling algorithms and with any precoding
190
scheme. The same is observed when M is fixed and N is
180
increased. This shows that increase in M or N increases 170
the diversity gain thereby enhancing the system
160
sum-rate.
40 60 80 100 120 140 N Number of Users
Figure-8: Average system sum-rate versus no. of users
Acknowledgements
for (a) DOSUS-AS, (b) SUS-AS, and (c) RUS-AS algorithm, with ZF, MMSE, MRT and no precoding
The authors hereby acknowledge the financial support of
cases, for M=32, downlink transmit SNR=15dBm.
the Ministry of Electronics and Information Technology (Meity) Govt. of India, in this research work (Grant PhD-MLA-4(96)/2015-2016).
5. Conclusion In this paper, we explored how the average system
References
sum-rate of a massive MIMO cellular mobile service depends on the user selection and antenna scheduling
[1] T. L. Marzetta, “Noncooperative Cellular Wireless with Unlimited
algorithms with different precoding schemes.
Numbers of Base Station Antennas,” IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp. 3590-3600, Nov. 2010.
The main objective is to reduce inter-user
[2] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O.
interference by adopting appropriate user selection and
Edfors, and F. Tufvesson, “Scaling Up MIMO: Opportunities and
antenna scheduling algorithms to enhance the average
Challenges with Very Large Arrays,” IEEE Signal Processing
system sum-rate. We consider a slowly fading Rayleigh
Magazine, vol.30, no.1, pp.40-60, 2013.
channel with perfect acquisition of CSI to explore the
[3] E. G. Larsson, O. Edfors, F. Tufvesson and T. L. Marzetta,
system sum-rate capacity of a massive MIMO network.
“Massive MIMO for next generation wireless system,” IEEE
The users are characterized by having both small scale
Communications Magazine, vol. 52, no. 2, pp. 186-195, Feb. 2014.
fading (SSF) due to slowly fading Rayleigh channel and
[4] T. A. Sheikh, J. Bora and M. A. Hussain, “A Survey of Antenna
distance dependent large-scale path loss (LSF). We
and User Scheduling Techniques for Massive MIMO-5G Wireless
studied the system sum-rate variation with variation in
System,” 2017 International Conference on Current Trends in
the downlink transmit power, number of BS antenna, and
Computer, Electrical, Electronics and Communication (CTCEEC),
the number of users.
Mysore, 2017, pp. 578-583, 2017. [5] O. Bai, H. Gao, T. Lv, and C. Yuen, “Low-complexity user
We applied linear precoding schemes such as ZF,
scheduling in the downlink massive MU-MIMO system with linear
MMSE, and MRT and user scheduling algorithms such
precoding," IEEE Int. Conference on Communication, China (ICCC),
as
SUS-AS,
computational
DOSUS-AS, complexity
and of
RUS-AS.
The
pp. 380-384, Oct. 2014.
algorithm-2
and
[6] T. A. Sheikh, J. Bora and M. A. Hussain, “Combined User and
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI st
3
Antenna Selection in Massive MIMO Using Precoding Technique”,
with Imperfect Channel Estimation,” IEEE
International Journal of Sensors, Wireless Communications and
Technology Conference (VTC Spring), Glasgow, Scotland, pp.1-6, Mar.
Control, vol.9, no.1, pp.1-10, 2019.
2015.
[7] G. Lee and Y. Sung, “Asymptotically optimal simple user
[19] Y. Dong, Y. Tang, and K. Zhang, “Improved Joint Antenna
scheduling for massive MIMO downlink with two-stage beamforming,”
Selection and User Scheduling for Massive MIMO System,” 16th IEEE
IEEE 15th International Workshop on Signal Processing Advances in
International Conference on Computer and Information Science
Wireless Communications (SPAWC), Toronto, Canada, pp. 60-64, Jun.
(IEEE/ICIS), Wuhan, China,pp.69-74, May, 2017.
2014.
[20] Y. Gao, W. Jiang, and T. Kaiser, “Bidirectional Branch and Bound
[8] T. A. Sheikh, J. Bora and M. A. Hussain, “Sum-rate Performance of
Based Antenna Selection in Massive MIMO System.” IEEE 26th
Massive MIMO Systems in Highly Scattering Channel with
Annual International Symposium on Personal, Indoor, and Mobile
Semi-orthogonal and Random User selections”, Radioelectronics and
Radio Communications, Hong Kong, China, pp. 563 -568, Sept. 2015.
Communications Systems, Vol. 61, No. 12, pp. 547-555, 2018.
[21] H. Huh, “Large system analysis of multi-cell MIMO Downlink:
[9] Y. Xu, G. Yue, and S. Mao, “User grouping for massive MIMO in
Fairness scheduling and inter-cell cooperation,” Ph.D. dissertation,
FDD system: New design methods and analysis,” IEEE Journals and
Univ. Southern California, Los Angeles, CA, USA, 2012.
Magazines, vol. 2, pp. 947–959, Aug. 2014.
[22] H. Yang and T. Marzetta, “Performance of conjugate and
[10] E. Bjornson, L. Sanguinetti, J. Hoydis and M. Debbah, “Optimal
zero-forcing beamforming in large-scale antenna system,” IEEE
Design of Energy-Efficient Multi-User MIMO System: Is Massive
Journal of Selected Areas of Communication, vol. 31, no. 2, pp.
MIMO the Answer?,” IEEE Transactions on Wireless Communications,
172-179, Feb. 2013.
vol. 14, no. 6, pp. 3059-3075, June 2015.
[23] T. Yoo and A. Goldsmith, “On the optimality of multiantenna
[11] J. Nam, A. Adhikary, J. Y. Ahn, and G. Caire, “Joint spatial
broadcast scheduling using zero-forcing beamforming,” IEEE Journal
division and multiplexing: Opportunistic beamforming, user grouping
on Selected Areas in Communication, vol. 24, no. 3, pp. 528–541, Mar
and simplified downlink scheduling,” IEEE J. Sel. Topics Signal
2006.
Process., vol. 8, no. 5, pp. 876–890, Oct. 2014.
[24] M. Benmimoune, E. Driouch, W. Ajib, and D. Massicotte, “Joint
[12] H. Liu, H. Gao, S. Yang, T. Lv, “Low-complexity downlink user
transmit antenna selection and user scheduling for massive MIMO
selection for massive MIMO system,” IEEE System Journal, vol.11,
system,” 2015 IEEE Wireless Communication and Networking
no.2, pp.1072-1083, Jun 2017.
Conference (WCNC 2015), New Orleans, LA, pp. 381-386, 2015.
[13] Y. Gao, H. Vinck and T. Kaiser, “Massive MIMO Antenna
[25] G. H. Golub and C. F. Van Loan, “Matrix Computations,” 3rd Ed.
Selection: Switching Architectures, Capacity Bounds, and Optimal
Baltimore, MD: The John Hopkins Univ. Press, 1996.
Antenna Selection Algorithms,” IEEE Transactions on Signal
[26] L. Jin, X. Gu, Z. Hu, “Low-Complexity Scheduling Strategy for
Processing, vol. 66, no. 5, pp. 1346-1360, Mar, 2018.
Wireless Multiuser Multiple-Input Multiple-Output Downlink System”
[14] X. Gao, O. Edfors, F. Tufvesson, and E. G. Larsson, “Massive
IET Communications, vol. 5, no.7, pp. 990-995, May, 2011.
MIMO in Real Propagation Environments: Do All Antennas Contribute
[27] B. Lee, L. Ngo and B. Shim, “Antenna group selection based user
Equally?”, IEEE Trans. Commun., vol. 63, no.11, pp. 3917-3928, Nov.
scheduling
2015.
Communications Conference, Austin, TX, 2014, pp. 3302-3307, 2014.
[15] B. Fang, Z.P. Qian, W.S., and W. Zhong, “RAISE: A New Fast
[28] G. Xu, A. Liu, W. Jiang, H. Xiang and W. Luo, “Joint user
Transmit Antenna Selection Algorithm for Massive MIMO System,”
scheduling and antenna selection in distributed massive MIMO systems
Wireless Personal Commun., vol. 80, no. 3, pp. 1147-1157, Feb. 2015.
with limited backhaul capacity,” China Communications, vol. 11, no. 5,
[16] K. Dong, N. Prasad, X.D. Wang, and S.H. Zhu, “Adaptive antenna
pp. 17-30,May 2014.
selection and Tx/Rx beamforming for large-scale MIMO system in 60
[29] X. Liu and X. Wang, “Efficient Antenna Selection and User
GHz channels,” EUSIP Journal Wireless Commun. and Network., vol.
Scheduling in 5G Massive MIMO-NOMA System,” IEEE 83rd
2011, no. 59, pp.1-14., 2011.
Vehicular Technology Conference (VTC Spring), Nanjing, pp.1-5,
[17] Gkizeli M. and Karystinos G.N., “Maximum-SNR Antenna
2016.
Selection Among a Large Number of Transmit Antennas,” IEEE J. Sel.
[30] J. Yan,D. Li, Z. Shi, Y. Guo,W. Wu, “Energy efficient joint user
Topics Signal Process., vol. 8, no. 5, pp. 891-901, Oct. 2014.
scheduling and transmit beamforming in downlink DAS”, Wireless
[18] D. Mi, M. Dianati, S. Muhaidat, and Y. Chen, “A Novel Antenna
Networks, pp-1-15, 2018.
Selection Scheme for Spatially Correlated Massive MIMO Uplinks
[31] Q. Yu, C. Han, L. Bai, J. Choi and X. Shen, “Low-Complexity
for
massive
MIMO
systems,”
81
IEEE
Vehicular
Global
Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI Multiuser
Detection
in
Millimeter-Wave
Systems
Based
on
Opportunistic Hybrid Beamforming,” IEEE Transactions on Vehicular Technology, vol.67, no.10, pp. 10129-10133, 2018, [32] L. Bai, T. Li, Q. Yu, J. Choi, and W. Zhang, “Cooperative Multiuser Beamforming in mm-Wave Distributed Antenna Systems,’ IEEE Transactions on Vehicular Technology, vol.67, no.12, pp. 12394-12397, 2018, [33] B. M. Lee, J. Choi, J. Bang, and B. C. Kang, “An energy efficient antenna selection for large scale green MIMO systems,” IEEE Int. Symp. On Circuits and Systems (ISCAS), pp. 950-953, May 2013.
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Conflict of Interest The authors has no conflict of interest regarding the paper entitle: Capacity Maximizing in Massive MIMO with Linear Precoding for SSF and LSF Channel with Perfect CSI.