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Beamforming and Power Control for Multi-Antenna
Cognitive Two-Way Relaying
Kommate Jitvanichphaibool, Ying-Chang Liang, and Rui Zhang
Institute for Infocomm Research, A∗STAR,
1 Fusionopolis Way, Singapore 138632
{kjit,ycliang,rzhang}@i2r.a-star.edu.sg
Abstract— This paper considers a cooperative and cognitive
radio (CCR) system where two secondary users (SUs) exchange
their information through a “cognitive” relay station (RS) via
the two-way relaying. The SUs share the same spectrum with a
primary user (PU) while maintaining the interference power at
the PU under a certain level. In order to enhance the achievable
sum rate, the cognitive RS exploits the channel state information
(CSI) of channel links from the RS to PU and from the RS to SUs
to determine the relay beamforming (BF) and the transmit power
levels for the RS and SUs. The structures of the optimal relay BF
and suboptimal BF schemes based on the subspace projection are
presented. Both orthogonal and non-orthogonal projection are
considered. In addition, power control algorithms are proposed to
satisfy the transmit power constraints as well as the interference
power constraints. Numerical results are provided to compare the
performance of the optimal relay BF with that of the suboptimal
ones and also to justify the benefit of the optimal power allocation.
I. INTRODUCTION
Spectrum scarcity in wireless networks due to fixed spec-
trum allocation becomes a major problem that has triggered
a broad range of research activities. One solution to this
problem is increasing the spectrum utilization efficiency of
wireless systems by adopting the innovative idea of cogni-
tive radio (CR), which allows the secondary users (SUs) to
dynamically access the licensed spectrum originally allocated
to the primary users (PUs) [1]. The major challenge for CR
networks is to ensure the quality-of-service (QoS) of PUs
while trying to maximize the throughput of SUs. When SUs
are allowed to use the spectrum concurrently with a PU, the
resultant interference power at the PU has to be kept below
a certain threshold [2]. This constraint limits the allowed
transmit power of SUs and thus the throughput of SUs. In
order to handle this issue, effective technologies such as multi-
antenna transmission [3], [4] and wireless relaying [5] can
be employed to provide throughput enhancement, coverage
extension, and power saving for CR networks.
The idea of using a single-antenna relay station (RS) to
implement the one-way relaying in CR networks, sometimes
called cognitive relaying, has attracted a great deal of at-
tention lately (see, e.g., [6] and references therein). The
results obtained show the throughput improvement of SUs.
In order to further increase the spectrum efficiency, the multi-
antenna and/or two-way relaying technology can be applied.
Combining the well-studied multi-antenna technology and the
two-way relaying provides a promising means to improve the
spectrum utilization efficiency of SUs [7], [8]. Therefore, the
optimal design of a multi-antenna cognitive two-way relaying
in a cooperative and cognitive radio (CCR) network is worth
investigating.
In this paper, we envision a CCR system where a cognitive
RS helps two SUs to exchange their information via the
two-way relaying. The RS, equipped with multi-antenna, is
cognitive in the sense that it can obtain the channel state
information (CSI) on the channels from the RS to PU and
SUs, and design relay beamforming (BF) based upon such
CSI to maximize the achievable sum rate of SUs. In addition,
in order to satisfy the transmit power constraints at the SUs
and RS, as well as the interference power constraints at the
PU, transmit power controls at the RS and SUs are necessary.
In this paper, we present both optimal and suboptimal relay
BF structures as well as a centralized power control algorithm
to fulfill all the required power constraints.
The rest of the paper is organized as follows. Section
II provides the details of the system model. Section IV
presents the problem formulation for obtaining the optimal
relay BF. Section V proposes suboptimal BF schemes. Section
VI presents the power control algorithm. Section VII shows the
simulation results. Finally, Section VIII concludes the paper.
Notation: Bold-face letters are used to denote matrices and
vectors. Let XT,XH,X−1, and X†denote the transpose,
Hermitian, inverse, and pseudo inverse of matrix X, respec-
tively. We represent the trace of matrix Xas Tr(X).Imand
0m×ndenote m×midentity matrix and m×nzero matrix,
respectively. For matrices and vectors, “≤” is used to indicate
the component-wise inequality. We denote |·|and ·as
the scalar norm and the Euclidean norm, respectively. (x)+
indicates the maximum between a real number xand zero.
We define E{X}as the expectation of X.
II. SYSTEM MODEL
The system of interest is composed of one PU, two SUs,
and a “cognitive” RS as shown in Fig. 1. The PU and SUs
are equipped with a single antenna each. The RS, equipped
with M(M≥3) antennas, is employed to assist in the
communications between SUs via the two-way relaying. We
assume that the RS has the perfect CSI on all the channels
between the RS and SUs as well as the PU, and exploits
such information to determine the optimal or suboptimal relay
BF as well as the transmit power levels for the RS and SUs.
978-1-4244-2948-6/09/$25.00 ©2009 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
(b)2nd time-slot
Relay station
S econ dary u ser
Primaryuser
Interference signal
Desired signal
SU 2
SU 1
PU
RS
SU 2
SU 1
PU
RS
(a) 1 st time-slot
Fig. 1. System model for the cooperative and cognitive radio network.
Practically, the RS can obtain the required CSI via learning
and/or training. It is assumed that all the channels remain
unchanged during both the periods for obtaining CSI at the
RS and exchanging information between SUs via the RS.
For the practical purpose, the half-duplex transmission is
assumed. Furthermore, we assume that the time-division du-
plex (TDD) is employed. The two-way relaying requires two
time-slots to exchange information between two SUs denoted
as SU1and SU2. In the first time-slot, SU1and SU2transmit
their corresponding signals s1and s2to the RS simultaneously.
Let P1and P2denote the transmit powers of SU1and SU2,
respectively. The received signal at the RS is given by
yr=h1P1s1+h2P2s2+nr(1)
=H˜s+nr,(2)
where h1and h2are M×1channel vectors from SU1to RS
and from SU2to RS, respectively. We denote H=[h1,h2],
and ˜s =[
√P1s1,√P2s2]T. It is assumed that each element
in the additive white noise vector nris independent circularly
symmetric complex Gaussian (CSCG) random variable (RV)
with zero mean and variance σ2, denoted as CN(0,σ
2). Define
P=[P1,P
2]Tand ¯
P=[¯
P1,¯
P2]T, where ¯
P1and ¯
P2are the
transmit power constraints for P1and P2, respectively. The
transmit power constraint is such that
P≤¯
P.(3)
At the PU, the received signal due to both SUs is
z1=g1P1s1+g2P2s2+v1,(4)
where g1and g2are channel coefficients from SU1to PU and
from SU2to PU, respectively. The additive noise at the PU is
denoted as v1∼CN(0,σ
2). We assume that the interference
power due to SUs is limited by η, i.e.,
|g1|2P1+|g2|2P2≤η. (5)
At the RS, the received signal is processed by a BF matrix
to generate the transmitted signal
u=Ayr,(6)
where AisaBFmatrixofsizeM×M. In order to satisfy
the relay power constraint ¯
Pr, the following must be assured.
Ah12P1+Ah22P2+Tr(AAH)σ2≤¯
Pr.(7)
In the second time-slot, the RS broadcasts the processed
signal to SUs and PU. Assuming channel reciprocity justified
by the TDD mode, the received signals at SU1and SU2are
represented respectively as follows:
˜x1=hT
1Ah2P2s2+hT
1Ah1P1s1+hT
1An +w1,(8)
˜x2=hT
2Ah1P1s1+hT
2Ah2P2s2+hT
2An +w2,(9)
where wi∼CN(0,σ
2),i=1,2. In (8) and (9), the first
term is the desired signal while the second term is the self-
interference from the first time-slot.
Assuming that hT
1Ah1and hT
1Ah2are perfectly known
at SU1via channel training and estimation [9], the self-
interference can then be eliminated [10]. The same method is
also applied at SU2. After taking care of the self-interference,
the interference-free signals at SU1and SU2become
x1=hT
1Ah2P2s2+hT
1An +w1,(10)
x2=hT
2Ah1P1s1+hT
2An +w2,(11)
respectively. The received signal at the PU from the RS is
expressed as
z2=fAh1P1s1+fAh2P2s2+fAnr+v2,(12)
where v2∼CN(0,σ
2), and fis a 1×Mchannel vector
from RS to PU. The interference power at the PU due to the
transmitted signal from the RS is limited by η, i.e.,
|fAh1|2P1+|fAh2|2P2+σ2fA2≤η. (13)
Assuming that s1and s2follow the Gaussian distribution
with zero-mean and unit variance, the achievable rate at SU1
and SU2can be written as
r1=1
2log21+ |hT
1Ah2|2P2
(hT
1A2+1)σ2,(14)
r2=1
2log21+ |hT
2Ah1|2P1
(hT
2A2+1)σ2,(15)
respectively. Note that the factor 1/2 appears because the
information exchange takes two time-slots.
III. PROBLEM FORMULATION
In this section, the problem formulation is provided in
details. The main objective is to determine the optimal relay
BF matrix and the optimal power allocation so as to maximize
the sum rate of SU1and SU2as well as satisfy the constraint
in (3), (5), (7), and (13). This optimization problem can be
formulated as follows (Problem 1):
max
A,P
1
2log21+ |hT
1Ah2|2P2
(hT
1A2+1)σ2
+1
2log21+ |hT
2Ah1|2P1
(hT
2A2+1)σ2(16)
s.t.P≤¯
P,
|g1|2P1+|g2|2P2≤η,
Ah12P1+Ah22P2+Tr(AAH)σ2≤¯
Pr,
|fAh1|2P1+|fAh2|2P2+σ2fA2≤η.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
In general, the above joint BF and power allocation problem
is a non-convex optimization problem, which renders the
problem hard to be solved. However, it is readily observed
that the objective function in the above maximization problem
is a concave function with respect to (w.r.t.) Pwhen Ais
given. Hence, a convex optimization method can be employed
to determine the optimal value of P. For a given P, the optimal
BF matrix can be obtained via some dedicated methods as
shown later in this paper. Therefore, an iterative algorithm
that updates the relay BF matrix and the power allocation
iteratively is applicable for solving Problem 1.
IV. OPTIMAL RELAY BEAMFORMING
Although solving for the optimal relay BF matrix Aopt
directly from Problem 1 for some given power allocation P
is rather difficult, the general structure of Aopt can still be
obtained. Let the singular-value decomposition (SVD) of H
be given by
H=UΣVH,(17)
where Uand Vare M×2and 2×2matrices with orthogonal
column vectors, and Σis a 2×2diagonal matrix. For a given
P, the structure of the optimal BF matrix can be expressed as
Aopt =U∗BoptUH,(18)
where Bopt is a 2×2complex matrix. Using the proof in [7],
it can be shown that the optimal BF matrix in (18) minimizes
the relay transmit power as well as the interference power at
the PU in the second time-slot. It is observed that solving for
Aopt is equivalent to determining Bopt, which can be obtained
by performing an exhaustive search over all quantized 2×2
complex matrices. To avoid a brute-force search, suboptimal
relay BF schemes based on the subspace projection method
are proposed next.
V. P ROJECTION-BASED RELAY BEAMFORMING
In this section, suboptimal relay BF schemes are designed
to cope with the interference at the PU in the second time-
slot. Let us consider projecting HTonto the subspace of fH
as shown below.
Hproj =HT(IM−θˆ
fˆ
fH),(19)
where ˆ
f=fH
f. The parameter θ(0≤θ≤1) controls
the amount of projection onto the null space of fH. Hence,
by adjusting θappropriately, the relay BF designed based
on Hproj plays a tradeoff between maximizing the power of
the signal in the direction of HTand reducing the resultant
interference power at the PU. With different values of θ,two
special cases are considered: when θ=0, the signal power
is maximized in the direction of HTregardless of f, while
when θ=1, the signal power is exclusively assigned in the
null space of fH.
The SVD of Hproj is expressed as
Hproj =UprojΣproj VH
proj,(20)
where Uproj and Vproj are 2×2and M×2matrices with
orthogonal column vectors, and Σproj is a 2×2diagonal
matrix. Using (20), a BF matrix that has similar structure to
the optimal one can be written as
A=VprojBUH,(21)
where Bis a 2×2complex matrix. For a given P, finding B
still requires an exhaustive search over all possible 2×2com-
plex matrices. In order to reduce the computational complexity,
we observe that, based on (18), the optimal matrix Aopt can
be envisioned as a form of joint receive and transmit BF. From
this observation, suboptimal BF matrices that provide similar
structure to the one in (18) without requiring any numerical
search are proposed. The general structure of the proposed
suboptimal BF matrices is as follows.
A=AtxFA rx ,(22)
where Arx and Atx are the receive and transmit BF, respec-
tively. The data switching matrix Fis employed to ensure that
an estimate of s2and that of s1are forward to SU1and SU2,
respectively, and is thus defined as
F=01
10
.
Suboptimal BF schemes based on orthogonal and non-
orthogonal projection are given next.
A. Orthogonal Projection (θ=1)
We consider suboptimal BF schemes that ensure no inter-
ference to the PU in the second time-slot. To achieve this goal,
the transmit BF must place a null in the direction of the PU.
This can be achieved by projecting HTonto the null space of
fH, which results in
H⊥=HT(IM−ˆ
fˆ
fH).(23)
The SVD of H⊥is given by
H⊥=U⊥Σ⊥(V⊥)H,(24)
where U⊥and V⊥are 2×2and M×2matrices with
orthogonal column vectors, and Σ⊥is a 2×2diagonal matrix.
It can be verified that fV⊥=01×2. Hence, a matrix Athat
causes zero interference to the PU in the second time-slot and
maintains the structure of the optimal BF matrix is
A=V⊥BUH.(25)
Since fA =01×M, the constraint (13) can be removed.
To avoid the brute-force search for B, two suboptimal BF
schemes are presented as follows.
1) Maximal Ratio Reception - Orthogonally Projected Max-
imum Ratio Transmission (MRR-OPMRT): Based on the SVD
of Hand H⊥, a suboptimal BF matrix that satisfies the
structure of the matrix Ain (25) is shown below.
A=α(H⊥)HFHH(26)
=αV⊥Σ⊥(U⊥)HFVΣUH,(27)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
where αis employed to ensure that the relay power constraint
in (7) is satisfied. For the MRR-OPMRT scheme, B=
αΣ⊥(U⊥)HFVΣ. The receive BF is HH, which maximizes
the receive signal-to-noise ratio (SNR) at the RS. The transmit
BF is (H⊥)Hthat nullifies the interference at the PU and
maximizes the power of the signal projected onto the null
subspace of fH.
2) Zero-Forcing Reception - Orthogonally Projected Zero-
Forcing Transmission (ZFR-OPZFT): A BF matrix that has
the property of the matrix in (25) and satisfies the zero-forcing
(ZF) criterion to remove the interference between the two SUs
is derived as follows.
The receive BF, Arx , is determined from the following
optimization problem:
min
Arx
E{Arxyr−s2}(28)
s.t.ArxH=I2,
where s=[s1,s
2]T. Solving the above minimization problem
using the Lagrange multiplier method results in
Arx =H†.(29)
For the transmit BF, Atx, we solve the problem below.
min
Atx
E{ˆs −FA rxyr2}(30)
s.t.HTAtx =I2,
fA =01×M,
where ˆs =HTAyr+w, with w=[w1,w
2]T. Notice that
the relay power constraint (7) is not included in the above
optimization problem even though it is relevant to A.This
constraint can be handled by applying an appropriate scaling
factor αto the obtained Asuch that the relay power constraint
is satisfied. After solving the optimization in (30), we obtain
Atx =(H⊥)†.(31)
Combining (29) and (31) as well as applying a suitable
scaling factor result in the following BF matrix:
A=α(H⊥)†FH†(32)
=αV⊥(Σ⊥)−1(U⊥)HFVΣ−1UH.(33)
For the BF matrix with the zero-forcing criterion, we obtain
B=α(Σ⊥)−1(U⊥)HFVΣ−1. It is observed that the differ-
ence between the ZFR-OPZFT and the MRR-OPMRT lies in
the diagonal matrices between V⊥and UH.
B. Non-orthogonal Projection (θ=1)
Although the interference at the PU in the second time-
slot can be completely removed by using the BF schemes
proposed in the previous section, allocating power solely to
the signal projected onto the null space of fHis ineffective
when the PU is able to tolerate higher interference power [3].
Two suboptimal BF schemes are then presented as follows.
1) Maximal Ratio Reception - Projected Maximum Ratio
Transmission (MRR-PMRT): Based on (20), the suboptimal
BF matrix that allocates non-zero power to the signal in the
direction of HTas well as the signal projected onto the null
subspace of fH(i.e., 0<θ<1)isgivenby
A=αHH
projFHH(34)
=αVprojΣproj UH
projFVΣUH.(35)
It is readily seen from (35) that B=αΣprojUH
projFVΣ.An
exhaustive search for θcan be performed to determine the
suboptimal matrix in (34) so as to maximize the achievable
sum rate.
2) Maximal Ratio Reception - Maximum Ratio Transmis-
sion (MRR-MRT): When the power is only allocated to the
signal in the direction of HT(i.e., θ=0),thetransmitBFis
the MRT. Hence, the suboptimal BF becomes the MRR-MRT
scheme that is also given in [7] and expressed as
A=αH∗FHH(36)
=αU∗ΣVTFVΣUH,(37)
where B=αΣVTFVΣ. When the interference power
constraints are inactive, the performance of the MRR-MRT
is close to that of the optimal relay BF for a given P[7].
VI. POWER CONTROL ALGORITHM
In this section, algorithms for determining the optimal pow-
ers allocated to SU1and SU2for a given optimal/suboptimal
relay BF are presented.
A. Optimal Beamforming Case
For a given A, Problem 1 can be solved using the Lagrange
duality method [11]. Let us introduce non-negative dual vari-
ables λ1and λ2associated with P1and P2in constraint (3),
respectively. Also, λ4,λ3and λ5are assigned as dual variables
corresponding to the relay transmit power constraint (7) and
the interference power constraints (5) and (13), respectively.
Denoting λ=[λ1,λ
2,λ
3,λ
4,λ
5]T, the Lagrange dual
problem of Problem 1 can be written as
min
λ≥0
max
P
2
i=1
ri−λ1(P1−¯
P1)−λ2(P2−¯
P2)
−λ3|g1|2P1+|g2|2P2−η−λ4Ah12P1
+Ah22P2+Tr(AAH)σ2−¯
Pr−λ5−η
+|fAh1|2P1+|fAh2|2P2+σ2fA2.(38)
The dual problem can be efficiently solved using the ellipsoid
method [12]. In order to determine the optimal value of P,
we solve the above maximization problem. Since the objective
function in (38) is concave w.r.t. P, the global optimal for P1
and P2can be obtained. Hence, the duality gap, defined as the
difference between the optimal value of the primal problem
and that of the dual problem, is zero. Applying the Karush-
Kuhn-Tucker (KKT) conditions, the optimal P1and P2are
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
determined as
P∗
1=1
β(λ1+λ3˜g1+λ4ψ6−λ5ψ8)−ψ4
ψ2+
,(39)
P∗
2=1
β(λ2+λ3˜g2+λ4ψ5−λ5ψ9)−ψ3
ψ1+
,(40)
where the following notations are used: ˜g1=|g1|2,˜g2=|g2|2,
ψ1=|hT
1Ah2|2,ψ2=|hT
2Ah1|2,ψ3=(hT
1A2+1)σ2,
ψ4=(hT
2A2+1)σ2,ψ5=Ah22,ψ6=Ah12,ψ7=
Tr(AAH)σ2,ψ8=|fAh1|2,ψ9=|fAh2|2,ψ10 =σ2fA2,
and β=2·ln(2).
The algorithm for solving the dual problem in order to
obtain the optimal power allocation for a given BF matrix
is summarized below (Algorithm 1).
•Initialize λ.
•Repeat
–Calculate P∗
1(λ)and P∗
2(λ)using (39) and (40),
respectively.
–Update λusing the ellipsoid method with P∗
1(λ)−
¯
P1,P∗
2(λ)−¯
P2,˜g1P∗
1(λ)+˜g2P∗
2(λ)−η,ψ6P∗
1(λ)+
ψ5P∗
2(λ)+ψ7−¯
PR, and ψ8P∗
1(λ)+ψ9P∗
2(λ)+
ψ10 −ηas the sub-gradients for λ1,λ2,λ3,λ4, and
λ5, respectively.
•Until λconverges
Using Algorithm 1, an iterative algorithm for obtaining
the optimal relay BF matrix as well as the optimal power
allocation for Problem 1 can be realized.
B. Suboptimal Beamforming Case
For a given projection-based BF matrix A, Problem 1 can
be generally reformulated as (Problem 2):
max
P,θ,α
1
2log21+ |hT
1Ah2|2P2
(hT
1A2+1)σ2
+1
2log21+ |hT
2Ah1|2P1
(hT
2A2+1)σ2(41)
s.t.P≤¯
P,
|g1|2P1+|g2|2P2≤η,
Ah12P1+Ah22P2+Tr(AAH)σ2≤¯
Pr,
|fAh1|2P1+|fAh2|2P2+σ2fA2≤η.
In general, Problem 2 is a non-convex problem. However, for
given θand α, the objective function in Problem 2 is a concave
function w.r.t. P, hence, Algorithm 1 can be employed to
determine the optimal value of P.
Since the upper bound of αdepends on the constraints (5)
and (13), it can be verified that αis in the following range.
0<α<minα(U)
1,α
(U)
2,(42)
where
α(U)
1=¯
Pr
Tr(˜
A˜
AH)σ2,α
(U)
2=η
σ2f˜
A2.(43)
−20 −15 −10 −5 0 5
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Interference power allowed at PU (dB)
Average sum rate (bits/s/Hz)
Optimal BF
MRR−PMRT
MRR−MRT
MRR−OPMRT
ZFR−OPZFT
Fig. 2. Comparison of the average sum rate for the optimal and suboptimal
BF schemes.
0 0.5 1 1.5 2
0.5
1
1.5
2
2.5
3
Average sum rate (bits/s/Hz)
Distance between SU1 and RS
OPA
EPA
Fig. 3. Comparison of the average sum rate between the optimal and equal
power allocation.
The matrix ˜
Arepresents a suboptimal BF matrix excluding α.
For a suboptimal BF based on the orthogonal projection, α(U)
1
is the upper bound of α. Note that any value of αthat causes
Tr(AAH)σ2>¯
Pror σ2fA2>ηis not considered. Using
an exhaustive search for θand αthat maximizes the sum rate,
the corresponding Pand Aare then obtained.
VII. SIMULATION RESULTS
In this section, numerical results are provided to illustrate
the performance of the proposed suboptimal BF schemes as
well as the power control algorithm. The PU and SUs are
equipped with single antenna while the RS employs three
antennas. The distances between SU1and SU2, and that
between each SU and the PU are 2 and 3 units, respectively.
Each channel coefficient composes of both small-scale fading
and distance-dependent attenuation components. The small-
scale fading is assumed to be Rayleigh distributed with zero-
mean and unit-variance. The distance-dependent attenuation
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
has the path-loss exponent equal to 4. The transmit power
constraints for SUs and RS are assumed to be equal. All the
channels involved are assumed to have independent elements
distributed as CSCG RVs each with zero mean and unit
variance.
Fig. 2 shows the performance of the optimal BF as well
as the proposed suboptimal ones when the optimal power
allocation is employed. Here, the RS is assumed to be located
at the center between SU1and SU2. The average sum rate
corresponding to the maximum interference power allowed at
the PU (i.e., η) is used as the performance metric. The transmit
power constraint is set at 15 dB.
For suboptimal BF schemes, it is observed that the MRR-
PMRT is superior than the others due to its ability to efficiently
allocate power between the signal in the direction of HTand
that in the null space of fH. Note that the increase in the
performance gap between the MRR-PMRT and the optimal
BF for large value of ηdoes not imply that the MRR-PMRT
is unfavorable since the low interference regime is of particular
interest in cognitive radio networks compared to the moderate
to high interference regime. As observed, the performance of
the MRR-PMRT is closer to that of the MRR-MRT when the
interference power allowed at the PU increases. Due to its
inability to assign a fraction of power to the signal in the null
space of fH, the MRR-MRT can only transmit with relatively
low power at the low interference regime in order to maintain
the interference level at the PU under a certain threshold.
For suboptimal BF schemes based on the orthogonal projec-
tion, both MRR-OPMRT and ZFR-OPZFT perform reasonably
well when the interference power allowed at the PU is rather
low. It is observed that the MRR-OPMRT performs better
than the ZFR-OPZFT. The gain is more pronounced when
the PU can tolerate more interference. This result can be
explained as follows. For the ZFR-OPZFT, the ZFR suppresses
the interference between s1and s2and separates s1from s2
at the RS, while the OPZFT mitigates the interference caused
by s1at SU1and that caused by s2at SU2. In contrast,
the MRR-OPMRT maximizes the signal powers forwarded
to s1and s2by applying matched-filter (MF)-based receive
and transmit BF, but it does not perform any interference
suppression at the RS. Note that the interference between
s1and s2can be completely removed at their receivers by
the self-interference cancelation. Therefore, it seems that the
MRR-OPMRT benefits from this operation, while the ZFR-
OPZFT does not gain any advantage from its interference
suppression at the RS (though the receivers do not need to
implement the interference mitigation and are thus simplified).
Note that both schemes outperform the MRR-MRT at low
interference regime.
The justification of employing the optimal power allocation
(OPA) over the equal power allocation (EPA) is shown in
Fig. 3. Only the MRR-PMRT is considered in the figure. The
transmit power for the EPA is determined by maximizing the
sum rate when both P1and P2are equal. Here, the transmit
power constraint and the interference power constraint are 15
and -10 dB, respectively. The average sum rate associated with
the distance between SU1and RS is used as a performance
metric. As expected, the OPA provides higher throughput than
the EPA at all distances since the OPA opportunistically takes
advantage of the channel variation. It is observed that the gain
decreases when the RS is placed close to the middle between
two SUs since the values of the channel gain from SU1to RS
and that from SU2to RS become close. As a result, the OPA
does not offer significant gain over the EPA.
VIII. CONCLUSIONS
In this paper, we study a cooperative and cognitive radio
system where a cognitive RS aids two SUs in exchanging
their information while maintaining the interference power
at a PU under a certain threshold. In order to obtain high
spectrum efficiency, the two-way relaying is employed. We
provide the structure of the optimal relay BF that maximizes
the achievable sum rate, and propose projection-based sub-
optimal BF schemes with less computational complexity. In
particular, based on the orthogonal projection, two suboptimal
BF schemes namely the MRR-OPMRT and ZFR-OPZFT are
given. In order to optimally allocate the power between the
signal transmitted through the channel link from the RS to SUs
and that transmitted in the null space of the channel link from
the RS to PU, the MRR-PMRT based on the non-orthogonal
projection is proposed. In addition, power control algorithms
based on the Lagrange duality are also given to ensure no
violation on the transmit power constraints as well as the
interference power constraints. Numerical result shows that
the MRR-PMRT performs favorably compared to the optimal
relay BF at the low interference regime.
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.
