On the energy efficient multiple-pair communication in massive MIMO relay networks

Abstract

In this paper, we consider multiple-pair communication in massive MIMO relay network, wherein K single antenna source nodes deliver their messages to the corresponding K single antenna destination nodes with the help of one relay provisioned with N(N >> K) antenna array. And the energy efficient multiple-pair communication in Massive MIMO relay network through the precoding at both sources and relay is addressed. It is shown that, given the channel state information at the source nodes and the relay, the zero-forcing precoding at all source nodes, the zero-forcing reception and zero-forcing transmission (ZFR/ZFT) or the zero-forcing reception and maximum ratio transmission (ZFR/MRT) at relay can be employed to mitigate inter-pair interference. The asymptotical analysis shows that, the required transmit power at relay can be made inversely proportional to the number of relay antennas without sacrificing the achieved energy efficiency. And the optimal power allocation problem is further formulated to address the power allocation design at all source nodes and the relay according to the large-scale fading for a better energy efficiency, when fulfilling some predefined sum rate performance requirements.

Full text

On the Energy Efficient Multiple-Pair
Communication in Massive MIMO Relay Networks
Do Dung Nguyen, Qingchun Chen
nguyendodung1985@gmail.com, qcchen@swjtu.edu.cn
Southwest Jiaotong University, Chengdu, 610031, China
Abstract—In this paper, we consider multiple-pair communica-
tion in massive MIMO relay network, wherein Ksingle antenna
source nodes deliver their messages to the corresponding Ksingle
antenna destination nodes with the help of one relay provisioned
with N(NK)antenna array. And the energy efficient
multiple-pair communication in Massive MIMO relay network
through the precoding at both sources and relay is addressed. It
is shown that, given the channel state information at the source
nodes and the relay, the zero-forcing precoding at all source
nodes, the zero-forcing reception and zero-forcing transmission
(ZFR/ZFT) or the zero-forcing reception and maximum ratio
transmission (ZFR/MRT) at relay can be employed to mitigate
inter-pair interference. The asymptotical analysis shows that,
the required transmit power at relay can be made inversely
proportional to the number of relay antennas without sacrificing
the achieved energy efficiency. And the optimal power allocation
problem is further formulated to address the power allocation
design at all source nodes and the relay according to the large-
scale fading for a better energy efficiency, when fulfilling some
predefined sum rate performance requirements.
I. INTRODUCTION
MULTIPLE-input multiple-output (MIMO) is vital for
wireless communication to realize high data rate trans-
mission over multipath fading channels. MIMO provides ex-
traordinary throughput without additional power consumption
or bandwidth expansion. Recently, it is shown that there is
a great potential of using massive array antennas to fur-
ther enhance MIMO technology. Massive MIMO provides
a promising and effective approach to substantially mitigate
interference and fast fading for the increased system capacity
[1]–[3]. Moreover, it is also unveiled that the application of
array antennas at each base station (BS) in a non-cooperative
cellular network can effectively suppress intra-cell interference
without sophisticated beamforming design [4], [5]. In addition,
the efficient use of large antenna array gives rise to either
improved reliability or transmit power saving at the BS [6].
In [5] the spectrum and energy efficiency of massive MU-
MIMO systems were investigated to show that, the transmit
power can be made inversely proportional to the square-root
of the number of BS antennas.
The joint use of massive MIMO and relay can realize
the benefits of both techniques [4], [9]. For instance, the
massive MIMO relaying can be utilized to expand cover-
age and improve spectral efficiency. However, the inter-pair
interference will degrade the achieved performance, which
requires the transmission design to be handled carefully [7]–
[9]. In [7], several low-complexity beamforming schemes were
proposed to realize block-diagonalization. To maximize the
energy efficiency of the MIMO interference channel, it is
This work was jointly supported by the NSFC under Grant No. 61271246
and the National High Technology Development 863 program of China under
Grant No.2015AA01A710.
proposed in [8] to jointly design the beamforming matrices
for each transmit-receive pair. Multiple-pair communication
in amplify-and-forward Massive MIMO relaying network was
investigated in [9] to unveil the asymptotically achievable rate
in different power-scaling cases.
In this paper, we consider the multiple-pair communication
for massive MIMO relay network as well. The message
delivery from source to destination subsumes two phases,
namely the relay receiving phase and the relay transmit phase.
In the relay receiving phase, all Ksource nodes transmit
simultaneously the precoded signal to the relay; while in
the relay transmit phase, all received signals at the relay
will be precoded by using zero-forcing reception/maximum
ratio transmission (ZFR/MRT) or zero-forcing reception/zero-
forcing transmission (ZFR/ZFT) before being forwarded to
all Kdestination nodes. The optimal precoding design in
terms of the energy efficiency at both Ksources and relay is
presented. It is shown that, orthogonal sub-channels between
Ksource nodes and Kdestination nodes can be realized, when
ZFR/ZFT design is employed. Moreover, the transmit power at
relay can be made inversely proportional to the number Nof
relay antennas without sacrificing the performance. Similar to
the optimal power allocation assumed in [10], we investigate
the optimal power allocation at all source nodes and the relay
to maximize the energy efficiency. The simulation results are
presented to verify the proposed energy efficient multiple-pair
communication design and optimal power allocation method
in the massive MIMO relay system. The remainder of this
paper is organized as follows. Section II presents the system
model. The multiple-pair precoding and relay precoding design
is addressed in Section III. The asymptotical analysis are
presented in Section IV. In Section V, we consider the optimal
power allocation issue. Simulations results are presented in
Section VI and Section VII concludes the paper.
Notation: Throughout the paper, we use upper (lower)
case boldfaces to denote matrices (vectors). The superscripts
T, and Hstands for the transpose and conjugate-transpose,
respectively. Aij denotes the (i;j)-th entry of matrix A, and
INis the N×Nidentity matrix. The expectation operation and
the Euclidean norm are denoted by E{.}and ., respectively.
II. SYSTEM MODEL
As illustrated in Fig.1, let us consider a multiple-pair one-
way relay networks consisting of Ksynchronized single
antenna sources {AK},Ksingle antenna destinations {BK}
and one relay provisioned with N(NK)antennas. It is
assumed that all Ksources are synchronized to deliver mes-
sage to their corresponding Kdestinations with the assistance
of the relay, and there is no direct path between Ksource
nodes and Kdestination nodes. Meanwhile, we assume that
2016 3rd National Foundation for Science and Technology Development Conference on Information and Computer Science
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Fig. 1. Massive MIMO relay system model.
Ksources, Kdestinations and the relay know the channel
state information (CSI) of all the related links.
A. Relay Receiving Phase
In the first phase, Ksource nodes {AK}transmit simulta-
neously to relay, and the received signal at the relay is
yR=H1Wx +nR,(1)
where x=[x1,x
2, ..., xK]Tare the transmitted symbols by K
sources, xk=√pt,kskand pt,k denotes the transmit signal and
the transmit power at Ak, respectively, where E{|sk|2}=1.
W=[w1,w2,···,wK]denotes the K×Kprecoding matrix,
and wkis the k-th column vector. H1=[h11,h12 , ..., h1K]
is the N×Kmatrix channel between the Ksources and
the relay. The additive white Gaussian noise nR∈CN×1is
assumed to be zero mean with co-variance matrix σ2
nIN.
B. Relay Transmit Phase
In the second relay transmit phase, the received signal yR
in the first phase will be processed with a precoding matrix
F, namely, ˜yR=FyR, before being forwarded to all K
destination nodes {BK}. Then the received K×1signal at
Kdestinations {BK}will be
yB=HH
2FyR+nB,(2)
where H2is the N×Kchannel matrix between relay and K
destinations. The received signal at Bkis
yBk=√pt,khH
2kFH1wksk+
K

i=1,i=k
hH
2kFH1√pt,iwisi
+hH
2kFnR+nBk,(3)
where the first item represents the desired message from Ak
to Bk, the second item represents the inter-pair interference
from Ai,i=k.h2k∈CN×1is the k-th column of H2.nBk
is the additive white Gaussian noise at Bkwith zero mean
and covariance σ2
n. The average transmit power Prat relay is
Pr=Tr
E˜yR˜yH
R
=Tr
FH1WWHHH
1P2
t+σ2
nINFH,(4)
where Pt=diag{√pt,1,√pt,2, ..., √pt,K },P2
t=Pt·Pt.
As a result, the instantaneous terminal-to-terminal signal-
to-interference-noise ratio (SINR) at Bkis
γk=√pt,k hH
2kFH1wk
2
K

i=1,i=khH
2kFH1√pt,iwi
2+hH
2kF2σ2
n+σ2
n
.
(5)
So the overall achievable rate can be calculated as below
R=E1
K+1
K

i=1
C(γk),(6)
where C(γk)log2(1 + γk)represents the instantaneous
achievable rate of each terminal-pair. The factor 1/(K+1)
corresponds to the loss by the assumed two-phase transmission
scheme and the symbol extension for precoding, as illustrated
in (3). Now the energy efficiency, which is defined as the
achievable sum rate divided by the total transmit power [6],
is given by
ηEE =R
K
i=1 pt,i +Pr
,(7)
Our goal in this paper is to use {wi}and Fto maximize
the energy efficiency of the system. More specifically, the
optimized problem can be reformulated as below
(wopt
i,Fopt) = arg max
wi,F
ηEE
s.t. wi2=1
TrFH1WWHHH
1P2
t+σ2
nINFH=Pr.(8)
The above optimization problem is to achieve the effectiveness
in terms of both the sum rate and the energy consumption
for the multiple-pair massive MIMO relaying system through
the optimization of wiand F. Due to the non-convex nature
of the objective function, it is difficult to derive the closed-
form optimal solution. When the relay is provisioned with
a very large number of antennas, the channels tend to be
asymptotically orthogonal. We will derive the asymptotically
optimal solutions of wiand Fin Section V.
III. PRECODING DESIGN
A. Precoding Design at Source
Given the known H1, with the property of reduced singular
value decomposition (SVD), we have
H1=ˆ
U1ˆ
Λ1ˆ
VH
1,(9)
where ˆ
U1∈CN×Kand ˆ
V1∈CK×Kare unitary matrices,
and ˆ
Λ1=diag{λ11,λ
12, ..., λ1K}.
In order to eliminate the inter-pair interference, given the
known H1, we may let wi=ˆ
v1ifor i=1,2, ..., K, where
ˆ
v1iis the i-th column of ˆ
V1. Then the received signal at relay
can be rewritten as
yR=ˆ
U1ˆ
Λ1Pts+nR,(10)
where s=[s1,s
2, ..., sK]T. And the received signal at Bkis
yBk=√pt,khH
2kFˆ
u1kλ1ksk+
K

i=1,i=k
hH
2kFˆ
u1i√ptiλ1isi
+hH
2kFnR+nBk,(11)
where ˆ
u1kis the k-th column of ˆ
U1.
B. Precoding Design at Relay
We consider two types of precoding at relay, name-
ly, the zero-forcing reception/maximum ratio transmission
(ZFR/MRT) scheme and the zero-forcing reception/zero-
forcing transmission (ZFR/ZFT) one, especially in the regime
of very large N.
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1) ZFR/MRT at Relay: In this case, F=Fmrt 
αmrtH2ˆ
UH
1ˆ
U1−1ˆ
UH
1, where αmrt is chosen to satisfy the
average power constraint at the relay, namely
αmrt =Pr
TrP2
tˆ
Λ2
1HH
2H2+σ2
nHH
2H2.(12)
And the received signal at all Kdestinations is
yB=αmrtHH
2H2ˆ
Λ1Pts+αmrtHH
2H2ˆ
nR+nB,(13)
where ˆnR=(
ˆ
UH
1ˆ
U1)−1ˆ
UH
1nR.The nRis also Gaus-
sian distributed with a zero mean and a covariance matrix
ˆ
UH
1ˆ
U1−1Hσ2
n. The received signal at Bkwould be
yBk=αmrt √pt,k hH
2kH2λ1ksk
+
K

i=1,i=k
αmrthH
2kH2√pt,iλ1isi
+αmrthH
2kH2ˆnR+nBk.(14)
As a result, the received SINR at Bkis
γmrtk=αmrt pt,kλ1k
hH
2kH2

2
K

i=1,i=k
αmrtpt,i λ1i
hH
2kH2

2
+αmrt
hH
2kH2

2
σ2
n+σ2
n
.
(15)
2) ZFR/ZFT at Relay: In this case, F=Fzf 
αzf H2HH
2H2−1ˆ
UH
1ˆ
U1−1ˆ
UH
1, where the coefficient of
αzf should be chosen to fulfill the average transmit power
constraint at relay, namely
αzf =



Pr
TrP2
tΛ12(HH
2H2)−1+σ2
n(HH
2H2)−1.(16)
Now the received signal at Kdestinations will be
yB=αzf PtΛ1s+αzf ˆ
UH
1ˆ
U1−1ˆ
UH
1nR+nB.(17)
And the received signal at Bkis
yBk=√ptkαzf λ1ksk+αzf ˆ
nR+nBk.(18)
It could be noted that, by using the ZFR/ZFT based precoding
strategy at relay, we can realize the end to end multiple-
pair communications without inter-pair interference. Hence,
the SNR at Bkis
γzfk=pt,kα2
zf λ2
1k
α2
zf σ2
n+σ2
n
.(19)
IV. ASYMPTOTICAL ANALYSIS
We have assumed ZFR/MRT and ZFR/ZFT at the relay to
forward the received signal to Kdestination. In both cases, the
achievable terminal-to-terminal (t-2-t) sum rate can be given
by the (6). From (7), we may note that, in order to maximize
the energy efficiency ηEE, we may try to maximize the sum
rate Rfor the given transmit power constraint pt,k and Pr. Let
us see the case that the number of antenna Nat relay tends to
infinity. Before we consider the system with very large N, let
us review two results about random vectors in [11] as follows:
Let x=[x1, ..., xn]Tand y=[y1, ..., yn]Tbe two mutually
independent n×1vectors, whose elements are independent
and identically distributed zero-mean random variables with
variances σ2
xand σ2
y, respectively. According to the law of
large number, we have
xHx
n
a.s
−−→ σ2
xand xHy
n
a.s
−−→ 0as n→∞,(20)
where a.s
−−→ denotes the almost sure convergence.
A. ZFR/MRT at the Relay
Proposition 1: With the power-scaling Pr=Er/N , when
Eris fixed and Ntends to infinity, we have
γmrtk
a.s
−−−−→
N→∞
pt,kλ2
1k
σ2
nTrP2
tΛ2
1D2+σ2
nTrD2
Erη2
2k
+1
.(21)
Proof: In this case, the received signal at Bkis
yBk=Nαmrt√pt,k hH
2kH2λ1ksk
N
+Nαmrt
K

i=1,i=k
hH
2kH2√pt,iλ1isi
N
+NαmrthH
2kH2ˆnR
N+nBk.(22)
In the very large Nregime, we may apply the law of large
number (20). In this case, the limit of amplification coefficient
becomes
Nαmrt =



Er
TrP2
t
ˆ
Λ2
1HH
2H2
N+σ2
nHH
2H2
N
a.s
−−−−→
N→∞ Er
TrP2
tΛ12D2+σ2
nD2.(23)
The first item in (22) can be rewritten as
Nαmrt√pt,k hH
2kH2λ1ksk
N=Nαmrt√pt,k
K

i=1
hH
2kh2iλ1ksk
N
a.s
−−−−→
N→∞ Er
TrP2
tΛ12D2+σ2
nD2η2kλ1ksk.(24)
In the same way, the second item in (22) is
Nαmrt
K

i=1,i=k
hH
2kH2√pt,iλ1isi
N=Nαmrt
K

i=1,i=k
hH
2kh2i√pt,iλ1isi
N
a.s
−−−−→
N→∞ 0.(25)
Similarly, the third item in (22) can be written as
NαmrthH
2kH2ˆnR
N=Nαmrt
K

i=1
hH
2kh2iˆnR
N
a.s
−−−−→
N→∞ Er
TrP2
tΛ12D2+σ2
nD2η2kˆnR,(26)
where ˆnR∼CN(0,σ
2
n).Substituting (24), (25) and (26) into
(22), with nBk∼CN(0,σ
2
n), the asymptotic SINR can be con-
cluded. 
2016 3rd National Foundation for Science and Technology Development Conference on Information and Computer Science
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B. ZFR/ZFT at the Relay
Proposition 2: With the power-scaling Pr=Er/N , when
Eris fixed and the number of relay Ngoes to infinity, we
have
γzfk
a.s
−−−−→
N→∞
pt,kλ2
1k
σ2
nTrP2
tΛ2
1D−1
2+σ2
nTrD−1
2
Er+1
.(27)
Proof: With ZF processing, we have
h2kFzf ˆui=αzf δki,(28)
where δki =1when k=iand 0otherwise. Thus, the received
signal at Bkis
yBk=√pt,kαzf λ1k sk+αzf ˆ
UH
1ˆ
U1−1ˆ
UH
1knR+nBk,
(29)
where [A]kis the k-th row of the matrix A. The received
SNR at Bkis
γzfk=pt,kα2
zf λ2
1k
α2
zf ˆ
UH
1ˆ
U1−1kkσ2
n+σ2
n
.(30)
By letting Er=NPr,αzf can be rewritten as
αzf
a.s
−−−−→
N→∞ 



Er
TrP2
tΛ12(D2)−1+σ2
n(D2)−1.(31)
Substituting (31) into (30), we obtain the SNR in (27). 
By using massive MIMO relay, we can establish inter-
ference free connection between Ksource-destination pairs.
Moreover, it can be observed from (21) and (27) that, the
use of massive MIMO relay can give rise to a more energy
efficient multiple-pair communications. It is worth noting that,
these proposed schemes are applied according to the amplify-
and-forward (AF) protocol in the multiple-pair relaying system
with perfect CSI assumption, thus the transmit power at the
relay can be scaled down by a factor 1/N for the given fixed
rate. Compared with the AF protocol is low implementation
complexity compared with the data transmission according
to decode-and-forward (DF) protocol in [5], there is a lower
implementation complexity. Moreover, the transmit power can
only be scaled down with a factor of 1/√Nby employing the
relaying protocol in [5] and [6].
V. O PTIMAL POWER ALLOCATION
In this section, we assume that the transmit power pt,k at
different source is different, and we aim at the power allocation
issue to maximize the energy efficiency, subject to a predefined
sum rate requirement and the maximal allowed transmit power
at all sources and the relay. The power allocation problem can
be formulated as follows
maximize ηB
EE
subject to RB≥RB
o
0≤pt,k ≤pto,k=1, ...K (32)
0≤Pr≤Pro,
where Rois the required sum rate, pto and Pro stands for the
maximal allowed transmit power at Bkand relay, respectively.
The superscript “B”refers to either ZFR/MRT or ZFR/ZFT
scheme. The above problem is equivalent to
minimize K
k=1 pt,k +Pr
subject to K
k=1 (1 + γB
k)≥2(K+1)RB
o
γB
ko ≤γB
k,k=1, ...K (33)
0≤pt,k ≤pto,k=1, ...K
0≤Pr≤Pro.
In (33), the objective function and the inequality constraints
are posynomial functions. By following [ [13], Lemma 1] we
can have the following approximation
K

k=1
(1 + γk)≈
K

k=1
νkγak
k,(34)
where νkγak
kis used to approximate 1+γknear a point
˜γk, where ak˜γk(1 + ˜γk)−1and ν˜γ−ak
k(1 + ˜γk).Now
the optimization problem (33) can be approximated by a
geometric program (GP) problem [12]. By using a similar
method in [13], the following Algorihtm 1 can be utilized to
solve (33).
Algorithm 1
1. Initialization: Set i=1; initialize the value of γkas γk,1
for k=1, ..., K; choose the maximum number of iteration
L, a tolerance , and coefficient α(it is used to control the
approximation accuracy in (34)).
2. Iteration:
i) Compute ak,i =γk,i(1 + γk,i)−1and νk,i =
γ−ak,i
k,i (1 + γk,i).
ii) For Ldo
minimize K
k=1 pt,k +Pr
subject to K
k=1 νk,iγak,iB
k≥2(K+1)RB
o
γB
ko ≤γB
k,k=1, ...K
0≤pt,k ≤pto,k=1, ...K
0≤Pr≤Pro,
α−1γk,i ≤γk≤αγk,i.
3. Check: If maxk|γk,i −γ∗
k|<or i=L, stop; otherwise,
go to step 4.
4. Set: i=i+1,γk,i =γ∗
k, go to step 2.
VI. SIMULATION RESULTS
In the simulations, we assess the achieved system perfor-
mance of multiple-pair communication in the massive MIMO
relay network; the transmit power of each terminal is set to
be pt=1dB, Er=20dB and σ2
n=1. We assume that
SNR is defined by the SNR pt, and the number of source
pairs K=10. Moreover, the network is considered under
a practical scenario, in which all sources and destinations
are located uniformly at random with radius (from center to
vertex) of 1000m. We assume that no terminal is closer to the
relay than ro= 100m. The large-scale fading [D2]kk =η2k
is set by η2k=zk/(1 + (rk/ro)l), where zkis a log-
normal random variable with standard deviation σdB, rkis
the distance between the destination nodes Bkand the relay,
2016 3rd National Foundation for Science and Technology Development Conference on Information and Computer Science
260

Fig. 2. The achieved sum rate versus the number of relay antennas, pt=
1dB, Er= 20dB, UPA.
Fig. 3. The achieved energy efficiency versus the number of relay antennas,
pt=1dB, Er=20dB, UPA.
and lis the path loss exponent. In all simulations, we assume
K≤10.Wesetσ=8dB and l=3.8, as recommended in
[14]. And the following three large-scale fading realizations
are considered:
System I: [D2]K
k=1 = [0.8246 0.7975 1.1880 2.0163 1.0389
0.3591 0.9716 1.9107 0.6881 0.9826];
System II: [D2]K
k=1 = [1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0];
System III: [D2]K
k=1 = [0.6782 0.8962 3.0042 0.9735 3.8457
1.5298 3.0618 0.7213 2.5379 1.8901].
The achieved sum rate and the energy efficiency with
different number of relay antennas are illustrated in Fig. 2 and
Fig. 3, where uniform power allocation (UPA) at all sources
is assumed. It is noted that, although the transmit power of
each source terminal is small, the achievable sum rate and
the energy efficiency curvature are fairly steep. As expected,
effective multiple source-destination pair communications can
be supported to realize better energy efficiency and larger
sum rate when more antenna number is available at relay.
Moreover, we may note that, the achieved energy efficiency of
the massive MIMO relay network depends on the large-scale
fading characteristics. When dissimilar large-scale fading is
assumed, just like the case in System I and System III, the
ZFR/ZFT scheme outperforms the ZFR/MRT scheme in terms
Fig. 4. The achieved sum rate over transmit power at sources, Er=20dB,
UPA, System I.
Fig. 5. The energy efficiency versus the sum rate with different power
allocation schemes, N= 300,E
r=10pt,p
t=[−2 : 20]dB.
of the achievable rate and the energy efficiency. However, the
difference tends to diminish when similar large-scale fading
parameters are assumed, just like the case in System II setup.
This complies with the asymptotical analysis in Section IV that
the achieved performance will depend only on the large-scale
fading characteristics. In Fig. 4, we can see that, there will be
a significant increase in the achieved sum rate by increasing
the number of antennas at relay. Meanwhile, unless within
very high SNR region, the ZFR/ZFT scheme outperforms
the ZFR/MRT scheme. Even within high SNR region, the
difference in the achieved sum rate between ZFR/MRT and
ZFR/ZFT is limited. Since in wireless relay network, the
transmit power at source is basically limited, which suggests
the advantages of the ZFR/ZFT, especially within low to
moderate transmit power region.
Finally, we will assess the difference in the energy efficiency
for the desired achievable sum rate with the uniform power
allocation and the optimal power allocation. The large-scale
fading coefficients are chosen as follows: D2=diag{0.8251
0.7964 1.1878 2.0085 1.0286 0.3587 0.9623 1.9005 0.6920
0.9729}, which is a snapshot of the practical setup for Fig.5,
while =0.01,N= 300,α=0.15,L=5,γko, and Er=
10ptwith pt=[−2 : 20]dB are assumed in Algorithm 1 for
2016 3rd National Foundation for Science and Technology Development Conference on Information and Computer Science
261

Fig. 6. The required relative transmit power at all sources for the given sum
rates of RZFR/MRT and RZF R/ZF T .
Fig. 7. The required total transmit power at all sources and the transmit
power at relay for the given sum rates of RZFR/M RT and RZFR/ZFT .
the optimized power allocation determination. Here uniform
power allocation implies that all sources and the relay use
their maximal transmit powers, i.e.,pt=pto,∀k=1, ..., K,
and Pr=Pro. We can observe from Fig. 5 that, for the given
desired sum rate, the optimal power allocation will lead to
a much better energy efficiency. This implies that, by using
the proposed OPA, less transmit power is needed to realize the
desired sum rate by some traffic requirements, which is highly
desirable in wireless relay network. Basically, the ZFR/MRT
outperforms the ZFR/ZFT in terms of the achieved energy
efficiency for the given sum rate. However, the difference tends
to be smaller for a larger sum rate requirement.
In order to clearly illustrate the improved energy ef-
ficiency for a given achievable sum rate with the OPA,
we use the relative transmit power, which is defined as
the optimal transmit power/uniform transmit power ra-
tio. And the relative transmit powers at K=10
sources nodes are illustrated in Fig. 6, wherein the same
large-scale fading coefficient in Fig. 5 is assumed, and
four uniform transmit power settings are considered, i.e.,
pt={−2dB(0.6310W); 1dB(1.2589W); 4dB(2.5119W)
7dB(5.0119W)}; the desired sum rates are RZF R/M RT =
{0.6908; 1.0974; 1.6328; 2.2970}(bps/Hz),RZF R/ZF T =
{0.5627; 0.9716; 1.5121; 2.19534}(bps/Hz), respectively. At
first, one may note that, the relative transmit powers at K
source nodes are almost proportional to the large-scale fading
D2,i.e., larger large-scale fading implies a larger relative
transmit power (smaller transmit power saving) for the desired
achievable sum rate requirement. The total transmit power
at all Ksource nodes PS=K
i=1 ptivs relay (Pr)for
the aforementioned four settings are illustrated in Fig. 7. It is
noted that, for both the ZFR/ZFT and the ZFR/MRT schemes,
significant transmit power can be saved at all source nodes
and the relay for a target sum rate, when comparing with the
UPA.
VII. CONCLUSION
In this paper, the massive MIMO one-way relaying system
is considered to support simultaneous multiple-pair commu-
nications. It is proposed to jointly employ the SVD-based
precoding at all source nodes and the ZFR/ZFT(MRT)-based
precoding at relay to completely eliminate the mutual inter-
ference among multiple pair channels. It is shown that, the
use of massive antenna at relay can be exploited to enable
the energy efficient multiple pair relay transmission, where
we have shown that the increase in the number of antennas at
relay can not only cancel out small-scale fading, but also give
rise to the increased sum rate and improved energy efficiency.
In addition, the energy efficiency of the system can be further
improved by introducing the optimal power allocation scheme.
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