IEEE
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 1
Secrecy Transmit Beamforming for
Heterogeneous Networks
Tiejun Lv, Senior Member, IEEE, Hui Gao, Member, IEEE, and Shaoshi Yang, Member, IEEE
Abstract—In this paper, we pioneer the study of physical-layer
security in heterogeneous networks (HetNets). We investigate se-
cure communications in a two-tier downlink HetNet, which com-
prises one macrocell and several femtocells. Each cell has multiple
users and an eavesdropper attempts to wiretap the intended
macrocell user. First, we consider an orthogonal spectrum allo-
cation strategy to eliminate co-channel interference, and propose
the secrecy transmit beamforming only operating in the macro-
cell (STB-OM) as a partial solution for secure communication
in HetNet. Next, we consider a secrecy-oriented non-orthogonal
spectrum allocation strategy and propose two cooperative STBs
which rely on the collaboration amongst the macrocell base station
(MBS) and the adjacent femtocell base stations (FBSs). Our first
cooperative STB is the STB sequentially operating in the macrocell
and femtocells (STB-SMF), where the cooperative FBSs individu-
ally design their STB matrices and then feed their performance
metrics to the MBS for guiding the STB in the macrocell. Aiming
to improve the performance of STB-SMF, we further propose the
STB jointly designed in the macrocell and femtocells (STB-JMF),
where all cooperative FBSs feed channel state information to
the MBS for designing the joint STB. Unlike conventional STBs
conceived for broadcasting or interference channels, the three pro-
posed STB schemes all entail relatively sophisticated optimizations
due to QoS constraints of the legitimate users. To efficiently use
these STB schemes, the original optimization problems are refor-
mulated and convex optimization techniques, such as second-order
cone programming and semidefinite programming, are invoked to
obtain the optimal solutions. Numerical results demonstrate that
the proposed STB schemes are highly effective in improving the
secrecy rate performance of HetNet.
Index Terms—Beamforming, femtocell, nonconvex optimiza-
tion, heterogeneous network, physical-layer security, semidefinite
programming (SDP).
I. INTRODUCTION
W
ITH the rapid proliferation of smart phones, tablets and
machine-to-machine communications, there is an ever-
increasing demand for seamless wireless coverage, extremely
high mobile data rate and reliable secrecy performance [1].
Manuscript received July 24, 2014; revised December 18, 2014; accepted
February 19, 2015. This work is financially supported by the National Nat-
ural Science Foundation of China (NSFC) (Grant No. 61271188 and Grant
No. 61401041), the Fundamental Research Funds for the Central Universities
(Grant No. 2014RC0106), and the Beijing Municipal Science and Technol-
ogy Commission Research Fund Project (Grant No. D151100000115002).
(Corresponding author: Shaoshi Yang).
T. Lv and H. Gao are with the School of Information and Communication
Engineering, Beijing University of Posts and Telecommunications, Beijing
100876, China (e-mail: lvtiejun@bupt.edu.cn; huigao@bupt.edu.cn).
S. Yang is with the School of Electronics and Computer Science, Univer-
sity of Southampton, SO17 1BJ Southampton, U.K. (e-mail: sy7g09@ecs.
soton.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSAC.2015.2416984
Aiming to effectively enhance the spectral and/or energy ef-
ficiency of wireless networks, it has been suggested that the
deployment density of various network-nodes should increase
[2], [3], and smart access-point activation and resource man-
agement are essential to utilize the dense network-nodes [4].
Therefore, heterogeneous network (HetNet) [5], [6] has been
attracting great research interests, and it is regarded as one of
the most promising techniques for providing higher network
capacity and wider coverage. HetNet is supported by various
types of base stations with different transmit power budgets.
Macrocell base stations (MBSs) provide public access and wide
area coverage up to a few kilometers to all the marcocell users
(MUs). Small cell base stations, such as femtocell base stations
(FBSs), are typically overlaid on the existing macrocells and in-
stalled in the building or indoor environment close to femtocell
users (FUs). It is noted that the network architecture of HetNet
becomes more open and diverse compared to the conventional
single-tier cellular networks, which makes the information ex-
change more susceptible to eavesdropping. Recently, physical-
layer security (PLS) has been proposed as a family of viable
techniques to secure wireless communications [7], [8], and it
also has the potential to tackle the security problem encountered
in HetNet.
Traditionally, the security problem in wireless networks was
mainly studied at higher layers using key-based cryptographic
methods [9]. This conventional wisdom relies on the assump-
tion that the eavesdropper is not computationally powerful to
break the secret key. However, as the computational capability
of wireless devices develops rapidly, perfect security can be
hardly guaranteed with the key-based solutions. It is reasonable
to argue that security measures should be invoked at all layers
where they can be implemented in a cost-effective manner.
Notably, the physical layer has remained almost ignored for
security in the past. The basic idea of PLS is to exploit the
randomness of wireless channel for secure message trans-
mission [10]. The authors in [8], [11], [12] investigated the
PLS in single-antenna fading channels. Since then, the secure
communication in multi-antenna channels has been extensively
studied [13]–[19] and in particular, practical and robust multi-
antenna secrecy beamforming schemes were investigated in
[19] very recently. Secure broadcasting with more than two
receivers were considered in [20]–[22]. Other related works in
the contexts of the multiple-access channel with confidential
messages [23], the Gaussian multiple-access wiretap channel
[24], and the cognitive multiple-access channel with confiden-
tial messages [25] have also been reported. Recently, there
are growing research interests in the secrecy communication
over interference channels, where the interference may be
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IEEE
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2 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
potentially exploited for improving the secrecy performance.
More specifically, in [26], the authors studied the inner and
outer bounds for the secrecy capacity regions of a two-user
interference network where the receivers are potentially eaves-
droppers. The secrecy rate of a two-user interference network
with an external eavesdropper was investigated in [27]. The
MIMO Gaussian interference channel with confidential mes-
sages was studied in [28] using game-theoretic approach. The
authors of [ 29] addressed the problem of minimizing the trans-
mit power with imperfect channel state information (CSI) in a
K-user multiple-input single-output interference network, and
the so-called “S-procedure” was applied. It should be noted that
the existing works on PLS mainly focus on traditional network
architectures, and the research on PLS for HetNet is still largely
missing.
Because of the densely overlaid network architecture, there
is ubiquitous interference of various types existing in HetNet
[30]. From the viewpoint of PLS, deliberately introducing in-
terference can be beneficial for the secrecy rate performance of
the system [10]. Inspired by this insight, the interference should
be utilized, rather than avoided, to improve the secrecy rate in
HetNet using techniques such as proper spectrum allocation
and cooperative beamforming. To elaborate a little further,
motivated by the inter-cell interference coordination techniques
[31]–[35], spectrum allocation can be rearranged dynamically
in conjunction with various levels of cooperation between the
network nodes, such as the MBS and FBSs, to generate the
desired co-channel interference (CCI) to the eavesdropper. As
a result, judicious cooperative beamforming schemes may be
designed to cope with CCI for the sake of improving the secrecy
rate performance in HetNet.
In this paper, a two-tier downlink HetNet system is consid-
ered, where MBS and FBSs serve the corresponding legitimate
MUs and FUs, and an MU acts maliciously as an eavesdropper
to wiretap another legitimate MU. For the considered scenario,
we propose three secrecy transmit beamforming (STB) schemes
in conjunction with two spectrum allocation schemes for secure
communications in the HetNet, assuming different degrees of
cooperation among the network nodes. As an initial s tudy, we
first consider the conventional orthogonal spectrum allocation
(OSA) strategy [36], where orthogonal spectrum resources are
allocated to the MBS and the adjacent FBSs to eliminate the
cross-tier interference and the interference among adjacent
femtocells. Employing OSA, the considered scenario can be
simplified as the secure communication in a broadcasting chan-
nel, and we consider the STB only performed in macrocell
(STB-OM) as a partial solution for the secure communication
in HetNet. It is noted that STB-OM aims to maximize the
secrecy rate of the intended MU subject to the quality of
service (QoS) constraints of the other legitimate MUs, and
no cooperation between the MBS and FBSs is necessary. In-
spired by the fact that friendly interference can help secure
communication [10], we deliberately introduce interference in
the HetNet with the secrecy-oriented non-orthogonal spectrum
allocation (SONOSA) strategy, which dynamically changes the
local pattern of the underlay OSA. Specifically, some coop-
erative FBSs adjacent to the eavesdropper are assigned with
the same frequency resource as MBS, while the OSA strategy
still applies to the non-cooperative FBSs. Consequently, CCI is
deliberately introduced around the eavesdropper to enable more
effective cooperative STB. Specifically, two STB schemes are
proposed in conjunction with SONOSA, where MBS performs
STB in collaboration with its cooperative co-channel FBSs.
Firstly, a STB scheme is proposed to improve STB-OM with
a little cross-tier cooperation, which is sequentially performed
in macrocell and femtocells (STB-SMF). In this scheme, each
cooperative FBS designs its STB to altruistically maximize the
generated interference to the eavesdropper while serving its
own FUs. Then each cooperative FBS calculates a performance
metric and feeds it back to the MBS to facilitate the STB
in macrocell, and the MBS can still use the STB-OM with
minor modification. To improve the overall performance of
STB-SMF, another STB is proposed with the limited cross-
tier cooperation, which is jointly performed in macrocell and
femtocells (STB-JMF). In this scheme, each cooperative FBS
feeds its CSI back to the MBS for the joint STB, which aims
to guarantee the QoS requirements of both MUs and FUs while
enhancing the secrecy rate of the intended MU.
For the sake of clarity, the main contributions of this paper
are summarized as follows:
1) Upon adopting the OSA strategy, an STB-OM scheme is
proposed to secure the broadcast channel of the macrocell,
where the confidential message and the common messages
are simultaneously transmitted. In particular, an iterative
algorithm is proposed to maximize the secrecy rate while
satisfying the QoS of the common messages. To handle the
complicated optimization problem, we transform the orig-
inal nonconvex problem into a second-order cone program
(SOCP) with the aid of a first-order Taylor approximation.
The approximation can be improved with each iteration.
Therefore, a local optimum of the original optimization
problem can be obtained in several iterations. It is noted
that the proposed STB-OM is different from the con-
ventional STB schemes in the broadcasting channel [37],
[38], where only the confidential message transmission is
considered. Furthermore, the STB-OM is applicable to the
general single cell scenarios and does not need cooperation
between the MBS and FBSs, which also initiates our
cooperative STB exploiting CCI.
2) Based on the SONOSA strategy, a STB-SMF scheme
is proposed to improve the secrecy rate of STB-OM
while guaranteeing the QoS requirements of legitimate
MUs. Different from the traditional jamming sources [39],
the cooperative FBSs still serve their FUs while helping
the MBS. To enhance the secrecy rate performance of the
intended MU, the cooperative FBSs selflessly increase
the interference power towards the eavesdropper without
considering the QoS of their FUs, and the optimization
problem is efficiently solved by SOCP. It is worth point-
ing out that each cooperative FBS designs its STB with
local CSI, and only a scalar is fed back to the MBS
for its STB in macrocell, where the MBS can still adopt
STB-OM. Therefore, the STB-SMF scheme imposes very
little overhead for the cross-tier cooperation, and is com-
patible with STB-OM.
IEEE
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LV et al.: SECRECY TRANSMIT BEAMFORMING FOR HETEROGENEOUS NETWORKS 3
3) Employing SONOSA strategy, an STB-JMF scheme is
proposed to strike a better balance between the secret-rate
performance of the intended MUs and the QoS require-
ments of the legitimate MUs and FUs. It is noted that
such complicated optimization is nonconvex, and we opt
for reformulating it into a tractable two-stage problem.
Specifically, we first fix the signal-to-interference-plus-
noise ratio (SINR) of the eavesdropper to formulate the
inner stage problem, which can be further transformed
into a tractable semidefinite program (SDP) by applying
the semidefinite relaxation technique. Then, we perform a
one-dimensional search to solve the outer stage problem,
which finds the most suitable SINR of the eavesdropper to
optimize the original objective. It is noted that the MBS
only needs to collect the CSI from its cooperative FBSs
for this joint STB, and such cross-tier cooperation imposes
acceptable overhead for the backhaul. Furthermore, unlike
the altruistic STB of the cooperative FBSs in STB-SMF,
the STB-JMF shceme guarantees the QoS of the FUs
in the cooperative FBSs.
The rest of this paper is organized as follows. In Section II,
the downlink HetNet system model and the corresponding
spectrum allocation strategies are presented, and we derive
SINR expressions of various network nodes for the following
beamforming design. Based on the two spectrum allocation
strategies, three STB schemes are proposed in Section III,
where the related optimization problems are formulated and
solved. In Section IV, simulation results show the effectiveness
of the proposed algorithms. Finally, conclusions and future
directions are provided in Section V.
Notations: Bold upper and lower case letters denote matrices
and vectors, respectively. Transpose and conjugate transpose
are denoted by (·)
T
and (·)
H
, respectively, while E{·} repre-
sents expectation. Tr(·) is the trace operator, ·represents the
Euclidean norm, |·|denotes the mode of a complex number,
and rank(·) stands for the rank of a matrix. X 0 indicates
that X is Hermitian positive semidefinite. C represents the
field of complex numbers. Re(·) and Im(·) denote the real
part and the imaginary part of a complex number, respectively.
Additionally, the integer set {1, 2,...,K} is abbreviated as
[1,K]. CN(μ, σ
2
) denotes a complex Gaussian variable with
mean μ and variance σ
2
.
II. S
YSTEM MODEL
We consider a downlink HetNet as shown in Fig. 1. There
is one N
M
-antenna MBS at the center, and M single-antenna
MUs are randomly distributed throughout the macrocell cover-
age area, where we have N
M
>M, while the single-antenna
eavesdropper intends to wiretap the confidential message trans-
mitted to a legitimate MU. Additionally, FN
F
-antenna FBSs
are spatially distributed according to a homogeneous Poisson
point process and each FBS aims to serve K single-antenna
FUs, where we have N
F
>K. To simplify the analysis, we
assume that the transmit power of each FBS is fixed and equal,
denoted by P
F
. Similar to that of the FBSs, the transmit power
of the MBS is assumed to be P
M
. Other relevant variables are
defined in Table I.
Fig. 1. Downlink HetNet system model, comprising a macrocell and N
femtocells. The macrocell consists of a MBS, M legitimate MUs and an
eavesdropper. Each FBS serves K FUs.
TABLE I
L
IST OF THE MAJOR VARIABLES
Two spectrum allocation strategies are developed in this
paper, i.e., the OSA strategy and the SONOSA strategy.
Serving as the underlay spectrum allocation strategy, OSA
allocates orthogonal spectrum resources to the MBS and the
adjacent FBSs to eliminate the cross-tier interference as well as
the interference among adjacent femtocells [36]. Building upon
OSA, SONOSA dynamically changes the local pattern of OSA
to enable advanced cooperative STB schemes. Specifically,
the SONOSA strategy assigns the same frequency resource
occupied by the MBS to the FBSs which are adjacent to the
eavesdropper, as shown in Fig. 2. Employing SONOSA, the
co-channel FBSs can work in collaboration with the MBS to
generate interference to the eavesdropper while serving their
own FUs.
IEEE
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4 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
Fig. 2. An example for OSA and SONOSA, where the polygons with the same
color denote the femtocells with the same frequency resource, the apple-green
triangle is MBS, the cell phone is the eavesdropped MU and the ear denotes
the eavesdropper. It is noted that OSA is the underlay strategy, and SONOSA
dynamically changes the local pattern of OSA. Three apple-green femtocells
are assigned with the same frequency resource as the macrocell to generate
CCI against the eavesdropper.
Considering SONOSA, we assume that there are N
(1 ≤ N<F) cooperative FBSs employing CCI to improve the
secrecy rate of the eavesdropped MU. Let us denote the n-th
cooperative FBS of the MBS as FBS
n
and the m-th MU as
MU
m
, then the received signal at MU
m
is given by
y
m
= h
m
w
m
s
m
+
M
q=1,q=m
h
m
w
q
s
q
+
N
n=1
K
k=1
h
n,m
w
nk
s
nk
+ n
m
,m∈ [1,M], (1)
where h
m
∈ C
1×N
M
and h
n,m
∈ C
1×N
F
denote the channel
vector from the MBS to MU
m
and the channel vector from
the FBS
n
to MU
m
, respectively.
1
w
m
∈ C
N
M
×1
and s
m
represent the precoding vector and the message symbol
intended for MU
m
, respectively. Similarly, w
nk
∈ C
N
F
×1
and s
nk
are the precoding vector and the message signal
intended for the k-th FU of the n-th cooperative FBS, denoted
as FU
nk
. n
m
is the Gaussian noise following independent
and identically distributed (i.i.d.) CN(0,σ
2
M
) at MU
m
.The
precoding vectors for the MUs satisfy the power constraint
of
M
m=1
w
m
2
= P
M
and the precoding vectors for
the FUs in a femtocell satisfy the power constraint of
K
k=1
w
nk
2
= P
F
. Without loss of generality, we assume
1
In this paper, we just assume perfect CSI as our first step to get fundamental
insights into the physical layer security problem in HetNet. We will consider a
more practical model including imperfect CSI in our future work.
that there is an eavesdropper wiretapping MU
1
,
2
therefore the
received signal at the eavesdropper is given by
y
E
= h
E
w
1
s
1
+
M
m=2
h
E
w
m
s
m
+
N
n=1
K
k=1
h
n,E
w
nk
s
nk
+ n
E
, (2)
where h
E
∈ C
1×N
M
denotes the channel vector from the MBS
to the eavesdropper, h
n,E
∈ C
1×N
F
is the channel vector
from FBS
n
to the eavesdropper, and n
E
is the Gaussian noise
obeying i.i.d. CN(0,σ
2
E
) at the eavesdropper. Furthermore, the
received signal at FU
nk
can be formulated as
y
nk
= h
n,nk
w
nk
s
nk
+
K
t=1,t=k
h
n,nk
w
nt
s
nt
+
N
p=1,p=n
K
t=1
h
p,nk
w
pt
s
pt
+
M
m=1
h
nk
w
m
s
m
+ n
nk
, (3)
where h
n,nk
∈ C
1×N
F
is the channel vector from FBS
n
to
FU
nk
, h
nk
∈ C
1×N
M
is the channel vector form MBS
n
to FU
k
,
and the Gaussian noise n
nk
at FU
nk
follows i.i.d. CN(0,σ
2
F
).
To facilitate the analysis of secrecy rate performance, we
define the SINR of MU
m
as
SINR
m
=
|h
m
w
m
|
2
A
m
,m∈ [1,M], (4)
where
A
m
=
M
q=1,q=m
|h
m
w
q
|
2
+
N
n=1
K
k=1
|h
n,m
w
nk
|
2
+ σ
2
M
.
Similarly, the SINR of the eavesdropper is represented as
SINR
E
=
|h
E
w
1
|
2
B
E
, (5)
where
B
E
=
M
m=2
|h
E
w
m
|
2
+
N
n=1
K
k=1
|h
n,E
w
nk
|
2
IFT
sum
+σ
2
E
,
and IFT
sum
is the sum of the additional interference tempera-
ture from all the cooperative FBSs to the eavesdropper. Finally,
the SINR of the FU
nk
is written as
SINR
nk
=
|h
n,nk
w
nk
|
2
C
nk
,n∈ [1,N],k∈ [1,K], (6)
2
Similar to [40], we focus on the beamforming design in this paper. The
identification problem—how to identify which MU has been intercepted by
the eavesdropper—is challenging and important, which will be investigated
in detail in our future work. In principle, this problem can be solved by
authentication: the MBS may broadcast some test messages to each MU in a
round-robin manner, and ask each of them to feed back what has been listened.
For the wiretapped MU, the MBS will receive feedback from two sources.
IEEE
Proof
LV et al.: SECRECY TRANSMIT BEAMFORMING FOR HETEROGENEOUS NETWORKS 5
where
C
nk
=
K
t=1,t=k
|h
n,nk
w
nt
|
2
+
N
p=1,p=n
K
t=1
|h
p,nk
w
pt
|
2
+
M
m=1
|h
nk
w
m
|
2
+ σ
2
F
.
After the above preliminary derivations, we will propose
three STB schemes in the next section to maximize the secrecy
rate of the intended MU
1
.
III. S
ECURITY TRANSMIT BEAMFORMING
SCHEMES FOR HetNet
In this section, we propose three secrecy communication
schemes to improve the secrecy rate of HetNet by jointly
considering the spectrum allocation strategy and the transmit
beamforming. Firstly, based on the OSA strategy, we propose
the STB-OM scheme as a partial solution for secure commu-
nication in HetNet. Then, we employ the SONOSA strategy to
propose the STB-SMF scheme, which improves STB-OM with
secrecy-oriented CCI generated by the altruistic cooperative
FBSs. At last, aiming at a balanced system performance, we
propose the STB-JMF scheme, which optimizes the security-
rate of the intended MU while satisfying the QoS constraints
of both legitimate MUs and FUs. In the remaining part of this
section, we will discuss each STB scheme in detail. Note that
in all the three proposed schemes, we assume that the local CSI
of the MUs and of the eavesdropper is available at the MBS,
3
and each FBS knows the local CSI of its own femtocell.
A. Secrecy Transmit Beamforming Only Performed in
Macrocell (STB-OM)
Let us first discuss the STB-OM scheme that relies on
the OSA strategy. Because different frequency resources are
allocated to the MBS and FBSs, no CCI exists in this scheme.
As shown in Fig. 3, the MBS serves multiple legitimate MUs,
and we assume that MU
1
is wiretapped by the eavesdropper.
Our goal is to maximize the secrecy rate of MU
1
while guar-
anteeing the QoS, i.e., SINR, requirements of other legitimate
MUs. The proposed STB-OM scheme is aiming at the secrecy
rate maximization. Unfortunately, this optimization problem,
formulated as (7a) to (7c), is non-convex and hence prohibitive
computational complexity may be incurred for finding its opti-
mum solution. As a compromise, we employ a low-complexity
iterative algorithm [41] which conservatively approximates the
original problem as several tractable SOCP subproblems. In the
remaining part of this subsection, the details of the problem
formulation and solution are provided.
Initially, the secrecy rate optimization problem of STB-OM
can be formulated as
3
Similar to [14], [15], [19], and [37], we assume that the CSI of the
eavesdropper is also available at the MBS to make the STB more tractable.
Fig. 3. An example channel model for the STB-OM scheme, consisting of
one MBS, M =2MUs and one eavesdropper wiretaps the first MU. As the
OSA is employed, the system is equivalent to a broadcast system. The solid
lines indicate useful data streams, and the dash line indicates the interference
stream.
max
{w
m
}
M
m=1
log(1 + SINR
1
) − log(1 + SINR
E
) (7a)
s.t. SINR
m
≥ γ
m
,m∈ [2,M], (7b)
M
m=1
w
m
2
≤ P
M
, (7c)
where the received SINRs from (4) and (5), that are associated
with MU
m
and the eavesdropper, can be simplified as
SINR
m
=
|h
m
w
m
|
2
σ
2
M
+
M
q=1,q=m
|h
m
w
q
|
2
, (8)
and
SINR
E
=
|h
E
w
1
|
2
σ
2
E
+
M
m=2
|h
E
w
m
|
2
+ IFT
sum
, (9)
respectively, when the OSA strategy is adopted. Note that
the IFT
sum
in this STB-OM is zero, because OSA does not
introduce CCI. The constraint (7b) is the QoS requirements
of the other legitimate MUs, i.e., MU
m
,m∈ [2,M], and (7c)
represents the total transmit power constraint at the MBS. To
make the above problem more tractable, we introduce a pair
of slack variables t
1
and t
2
. Then, the original problem can be
equivalently reformulated as
max
{w
m
}
M
m=1
,t
1
,t
2
log(t
1
)+log(t
2
) (10a)
s.t. 1+SINR
1
≥ t
1
, (10b)
1+SINR
E
≤ 1/t
2
, (10c)
SINR
m
≥ γ
m
,m∈ [2,M], (10d)
M
m=1
w
m
2
≤ P
M
. (10e)
Without loss of generality, in the following, we assume σ
2
M
=
σ
2
E
= σ
2
F
= σ
2
=1. Substituting (8) and (9) into the above
