This paper investigates the power allocation and outage performance of MIMO fullduplex relaying (MFDR), based on orthogonal spacetime block codes (OSTBC), in cognitive radio systems. OSTBC transmission is used as a simple means to achieve multiantenna diversity gain. Cognitive MFDR systems not only have the advantage of increasing spectral efficiency through spectrum sharing, but they can also extend coverage through the use of relays. In cognitive MFDR systems, the primary user experiences interference from the secondary source and relay simultaneously, owing to full duplexing. It is therefore necessary to optimize the transmission powers at the secondary source and relay. In this paper, we propose an optimal power allocation (OPA) scheme based on minimizing the outage probability in cognitive MFDR systems. We also analyse the outage probability of the secondary user in noiselimited and interferencelimited environments in Nakagamim fading channels. Simulation results show that the proposed schemes achieve performance improvements in terms of reducing outage probability.
1. Introduction
C
ognitive radio (CR)
[1]
is becoming one of the most promising technologies for efficient spectrum utilization. Spectrum sharing methods in CR can be classified in two categories: spectrum overlay and spectrum underlay. Recently, spectrum underlay sharing protocols have drawn increasing interest
[2]
[3]
. The underlay paradigm allows cognitive (secondary) users to utilize the licensed spectrum if the interference caused to the primary users is below a prescribed interference threshold. Because of the constraint on transmitted power, the performance of cognitive underlay protocols degrades significantly in fading environments. One efficient method to improve the performance of the secondary network is to use a cooperative relay
[4]
[5]
[6]
. It is well known that the cooperative cognitive relay is able to mitigate signal fading arising from multipath propagation and, at the same time, improve the outage performance of wireless networks.
In essence, the relay systems can be classified into two categories: halfduplex relaying (HDR) systems, where the relay receives and retransmits the signal on orthogonal channels, and fullduplex relaying (FDR) systems, where the reception and retransmission at the relay occur at the same time on the same channel. FDR systems have been examined for their ability to effectively prevent capacity degradation due to additional use of time slots
[7]
[8]
.
The multipleinput multipleoutput (MIMO) technology provides another approach to combat fading. It can offer antenna diversity without requiring additional bandwidth or transmitting power. OSTBC transmission
[9]
[10]
is a simple way to obtain a multiantenna diversity gain. It reduces complexity and only requires linear processing at the receiver end. Performance analysis for OSTBC transmission in a nonspectrum sharing scenario with decodeandforward (DF) and amplifyand forward (AF) relays has been presented in
[9]
and
[10]
, respectively. The authors in
[11]
consider cognitive AF relaying networks for spectrum sharing, based on distributed OSTBC. In particular, they derive the exact closedform expression for outage probability. On the other hand,
[12]
reports on the outage performance of MIMO cognitive DF relaying systems that use OSTBC transmission over Rayleigh fading channels. It has been verified that the cognitive relay network using OSTBC can achieve full degree of diversity. However, these prior works only consider cognitive MIMO halfduplex relaying (CogMHDRD ). To the best of our knowledge, no work has been carried out on cognitive MIMO fullduplex relaying (CogMFDR). Furthermore, the use of FDR nodes introduces interference problems that are inherent to the full duplex approach
[8]
. The primary user receives interference from the secondary source and relay, simultaneously. Consequently, in order to satisfy an interference constraint, the transmission powers at the secondary source and relay have to be lower than the transmission power of the CogMHDRD . Arbitrarily reducing the transmission power, however, deteriorates performance for the secondary user (SU). Thus, to improve the performance of the SU in a CogMFDR, optimal power allocation is essential.
Our goal in this paper is to study an optimal power allocation scheme and evaluate the outage performance of the CogMFDR based on OSTBC. We build upon the work of
[12]
, in which the secondary source (
SU_{TX}
), relay (
SU_{R}
), and the destination (
SU_{D}
) are assumed to be equipped with multiple antennas. This configuration corresponds to the scenario where the base station (i.e.,
SU_{TX}
) communicates with the user (i.e.,
SU_{D}
) with the help of relay nodes (i.e.,
SU_{R}
); because of the system’s size and complexity, the base station and relay nodes can have multiple antennas for better performance. To minimize outage probability, an optimal power allocation scheme is proposed based on this scenario. The corresponding probability of the secondary system is also evaluated in a Nakagamim fading channel. Such models have been extensively studied in various wireless communication systems because they capture physical channel phenomena more accurately than Rayleigh and Rician models. In summary, the major contributions of this paper are as follows:
1) We propose an OPA scheme to minimize the outage probability of the secondary user network. This concerns the power allocation problem for the CogMFDR based on a OSTBC system.
2) Exact outage probabilities are derived in noiselimited and interferencelimited environments in Nakagamim fading channels. These are validated through simulations.
3) The performance of the CogMFDR system deteriorates in the presence of interference because of full duplexing. The proposed OPA scheme can help to alleviate this issue and achieve maximum performance gain.
In the sequel, the paper is organized as follows. In Section 2, the system model is described. In Section 3, an OPA scheme is proposed and the exact outage probability is derived for two restrictive environments. Simulation results are provided in Section 4 and Section 5.
2. System Model
The system model is shown in
Fig. 1
. In this figure, the primary transmitter
PU_{TX}
and receiver
PU_{RX}
are equipped with only one antenna. The secondary source node
SU_{TX}
, the secondary relay node
SU_{R}
, and secondary destination node
SU_{D}
are equipped with
N_{S}
antennas,
N_{R}
antennas and
N_{D}
antennas, respectively. Secondary user coexists with the primary user (PU) in an underlay approach. Additionally,
SU_{R}
adopts the DF cooperative protocol to assist the
SU_{TX}
with data transmission, in FDR node. Similar to
[12]
, we assume that
SU_{TX}
and
SU_{R}
use the same OSTBC(s), which means
N_{S}
=
N_{R}
=
N_{D}
=
N
. The entire transmission is accomplished in two phases.
Cognitive MIMO FullDuplex Relay Network based on Orthogonal SpaceTime Block Codes
In the first phase, the
SU_{TX}
encodes the
K
symbols,
x
_{1}
,
x
_{2}
,...
x
_{K}
, selected from a signal constellation using the OSTBC matrix,
Letter
L
denotes the block length and each codeword
contains the signal transmitted from the
ith
antenna at the
lth
symbol interval.
is a linear combination of
x
_{1}
,
x
_{2}
,...
x
_{K}
and their conjugates
According to a property of the coding matrix, any pair of columns taken from
G_{s}
is orthogonal. The
SU_{TX}
transmits the encoded signals to the
SU_{R}
over
N
antennas and
L
symbol intervals. The power of each codeword at
SU_{TX}
is
denotes the expectation operator. We assume that channel fading is quasistatic, i.e., the fading coefficients are constant during the block length of an OSTBC codeword, and will change independently every
L
intervals. The signal matrices received at
SU_{R}
are
where
denotes the
SU_{TX}
→
SU_{R}
channel matrices. Symbol
denotes the noise matrices at
SU_{R}
in the first phase.
If a relay node,
SU_{R}
cannot decode the source message correctly, transmission is not performed during the second phase. Otherwise, during the second phase,
SU_{R}
encodes the source message using the same OSTBC and forwards the encoded signal matrix
to
SU_{D}
over
N
antennas and
L
symbol intervals. The power of each codeword at
SU_{R}
is
The signal received at
SU_{D}
is expressed as
where
denotes the
SU_{R}
→
SU_{D}
channel matrices. The noise matrices at
SU_{D}
during the second phase are denoted by
As shown in
Fig. 1
, there are three sources of interference at
SU_{R}
and
SU_{D}
in CogMFDR. Firstly, because of full duplexing, the retransmission signal at the FDR node interferes with the signal received via the
H_{rr}
channel. This is called echo interference
[8]
. Meanwhile,
SU_{D}
also receives interference from
SU_{TX}
over the
H_{sd}
channel. Secondly, in a spectrum sharing system, nodes
SU_{R}
and
SU_{D}
experience interference from
PU_{TX}
as well. By applying a noise whitening filter at the nodes, the effective noise approximates white Gaussian
[13]

[16]
. Thirdly,
PU_{RX}
in CogMFDR also receives interference from
SU_{TX}
and
SU_{R}
over channels
h_{sp}
and
h_{rp}
, respectively. In summary, the channel gains are as follows:
where
denotes the squared Frobenius norm. In order to control the power of the secondary nodes, we assume that the secondary system can obtain perfect channel state information (CSI) about the interference link between
SU_{TX}
and
PU_{RX}
. The secondary user can share the primary user’s spectrum, as long as the amount of interference inflicted on the primary receiver is below a predetermined interference power threshold (IPT) value
Q
.
For a comparison, we consider the CogMHDR with diversity (CogMHDRD). In CogMHDRD,
SU_{TX}
→
SU_{D}
link is considered for transmission in the first phase. Similarly to
[12]
, the signal matrices received at the
is given by
where
denotes the
SU_{TX}
→
SU_{D}
channel matrices. Symbol
denotes the noise matrices at
SU_{D}
. Meanwhile, the transmission powers of
SU_{TX}
and
SU_{R}
are constrained by
where
are the channel gains between
PU_{RX}
and the
ith
transmit antenna at
SU_{TX}
, and the channel gains between
PU_{RX}
and the
ith
transmit antenna at
SU_{R}
, respectively.
P_{s}
=
NE_{s}
and
P_{r}
=
NE_{r}
are the total transmission powers of
SU_{TX}
and
SU_{R}
respectively.
However, in CogMFDR,
SU_{TX}
and FDR node
SU_{R}
, transmit their signals simultaneously on the same spectrum. Thus,
PU_{RX}
receives interference from
SU_{TX}
and
SU_{R}
simultaneously. In this case, the transmission powers of
SU_{TX}
and
SU_{R}
should be constrained by
3. Optimal Power Allocation And Outage Probability Analysis in CogMFDR
In this section, we study an optimal power allocation (OPA) scheme for CogMFDR. We begin by comparing the performances of CogMHDRD without joint power allocation and CogMFDR with the EPA scheme. Building on this result, we propose an OPA scheme capable of minimizing the SU outage probability of CogMFDR. We then analyse the outage probabilities in noiselimited and interferencelimited environments.
The fading coefficients of all channels are identical and independently distributed (i.i.d.) Nakagamim random variables. Therefore,
follow Gamma distributions with parameters (1/
β_{sp},m_{sp}N
) and (1/
β_{rp},m_{rp}N
), respectively. Similarly,
follow Gamma distributions with parameters (1/
β_{sd},m_{sd}N^{2}
), (1/
β_{rd},m_{rd}N^{2}
), (1/
β_{sr},m_{sr}N^{2}
) and (1/
β_{rr},m_{rr}N^{2}
). The probability density function (PDF) and cumulative distributed function (CDF) of a gamma random variable
g
with parameter (1/
β,m
) are given by
where
γ
(
α, x
) is the incomplete gamma function
[17]
and
β
=
m
/Ω. In order to investigate the effect of interference due to full duplexing, we assume that the parameters of all channel gains, with the exception of
b_{rr}
and
b_{sd}
, are unity. This ensures a fair comparison between CogMFDR and CogMHDRD .
 3.1 Comparison of Outage Performance of CogMHDRD and CogMFDR with EPA Scheme
 A. Outage Analysis for CogMHDRD
In this type of system,
SU_{TX}
and
SU_{R}
must satisfy the interference power constraints (5) and (6). The maximum allowed transmission powers at
SU_{TX}
and
SU_{R}
can be expressed as
where
P_{s}^{H}
and
P_{r}^{H}
are the transmission powers of
SU_{TX}
and
SU_{R}
in the CogMHDRD, respectively. Similarly to
[12]
, the squaring method proposed in
[18]
is used to decode OSTBCs. We can then obtain the received signaltonoise ratios (SNRs) at
SU_{R}
and
SU_{D}
from (1), (2), (4) and (10) as follows
where
are SNRs for the link
SU_{TX}
→
SU_{R}
,
SU_{R}
→
SU_{D}
and
SU_{TX}
→
SU_{D}
respectively.
and the code rate of OSTBC is
r
=
K/L
. The noise powers
are defined by
where
are the noise variances at
SU_{R}
and
SU_{D}
, respectively,
are the noise variances from
PU_{TX}
to
SU_{R}
and
SU_{D}
, respectively. Consider that
where
g_{rd}
and
a_{rp}
are Gamma distributions with parameters (1,
N^{2}
) and (1,
N
), respectively. Therefore, the PDF of
can be developed as
We define
η_{H}
as the required SNR in CogMHDRD. Similarly to
[12]
, the outage probability of the secondary system when the
SU_{R}
cannot correctly decode the source message is given by
where (eq1) uses expression
Accordingly, the outage probability of the secondary system when the
SU_{R}
can correctly decode the source message is given by
Where
(eq2) uses
[17, eq. 341)]
, and
φ
(
a,b,c,d
,
y
_{0}
,
y
_{1}
) is defined as follows
With (eq3) follows the partial fraction in
[17, eq.362)]
and (eq4) uses
[17, eq. 341)]
. Therefore, the total outage probability
of CogMHDRD, which is the sum of (16) and (17), is given by
 B. Outage Analysis for CogMFDR with EPA Scheme
As discussed above,
SU_{TX}
and
SU_{R}
CogMFDR must satisfy the interference constraint (7). A simple way (not optimal) to ensure satisfaction of the interference constraint is to set the predetermined interference threshold to half the value of the CogMHDRD threshold. The transmission powers of
SU_{TX}
and
SU_{R}
written as
P_{s}^{E}
and
P_{r}^{E}
, are given by
This scheme is referred to as ‘Equal Power Allocation’ (EPA). The received SNR at the
SU_{R}
and
SU_{D}
can be expressed as
Similarly to (15), we can calculate
as follows
The outage probability for the
SU_{TX}
→
SU_{R}
link can be derived as
where
and
η_{F}
is the required SNR in CogMFDR. (eq5) uses the binomial theorem under the integral, while (eq6) uses
[17, eq.311)]
and
[17, eq. 3931)]
. Similarly, we can get the outage probability for the
SU_{R}
→
SU_{D}
link as follows
where
The outage probability is
where
are defined in (25) and (26).
 3.2 Outage Analysis for CogMFDR with OPA Scheme
To derive the OPA values
at
SU_{TX}
and
SU_{R}
in CogMFDR, the outage probability of
SU
is obtained by solving the optimization problem.
In (28), the received SNRs at
SU_{R}
and
SU_{D}
are
As shown in (29) and (30), the interference due to full duplexing is added to the received signals at
SU_{R}
and
SU_{D}
. Because the outage probability is determined by the worst instantaneous received SNR in (28), the optimization problem can be reformulated as
When the sum of the transmission powers at
SU_{TX}
and
SU_{R}
is constrained, the outage probability is minimized when the SNRs at
SU_{R}
and
SU_{D}
are identical, i.e.,
as in
[19]
. Thus, the transmission powers of
SU_{TX}
and
SU_{R}
, which minimize the outage probability, satisfy
The OPA values
in (32), are the roots of a quadratic equation. Because
it follows that
where
In the above,
consist of the channel gains for all links, the noise powers at the
SU_{R}
and
SU_{D}
, and the interference threshold. The EPA scheme does not satisfy the SNR balancing, because it only considers
a_{sp}
and
a_{rp}
. The OPA scheme, however, ensures that the SNR condition is satisfied at
SU_{R}
and
SU_{D}
. This minimizes the outage probability of
SU
subject to the interference constraint (7). To verify the performance improvement using the OPA scheme, we record the outage probability in two environments that vary in the presence of noise and interference: the noiselimited and the interferencelimited ones.
 A. Outage Probability in a Noise Limited Environment
In a noiselimited environment, the interference terms in (29) and (30) are negligible. The SNRs at
SU_{R}
and
SU_{D}
are respectively approximated as follows:
where
are the SNRs at
SU_{R}
and
SU_{D}
, and
are the OPA values at
SU_{TX}
and
SU_{R}
. It follows from relations (33) and (34) that
In (36) and (37),
consist of the channel gains
g_{sr}
,
g_{rd}
,
a_{sp}
and
a_{rp}
, the noise powers at the
SU_{R}
and
SU_{D}
, and the interference threshold. The SNR balancing condition is satisfied, and that guarantees that the outage probability of the secondary user is minimized in the noiselimited environment. Therefore, the received SNRs at
SU_{R}
and
SU_{D}
are given by
The outage probability of the secondary user in the noiselimited environment can be written as
The overall outage probability can thus be obtained in closed form as
where
For a detailed derivation of (40), please refer to Appendix A.
 B. Outage Probability in an InterferenceLimited Environment
In the interferencelimited environment, the received interference powers at
SU_{R}
and
SU_{D}
are higher than the noise powers. Similar to (29) and (30), the noise powers are negligible and the SNRs are approximated by
where
are the SNRs at
SU_{R}
and
SU_{D}
, respectively. It follows that (33) and (34) can be rewritten as
where
are the OPA values at
SU_{TX}
and
SU_{R}
in the interferencelimited environment. These power allocations minimize the outage probability of the secondary user by satisfying the SNR balancing condition. The SNRs at
SU_{R}
and
SU_{D}
can then be expressed as
It is interesting to note that as shown in (44), the IPT value Q, the channel gains
a_{sp}
and
a_{rp}
do not affect the SNRs at
SU_{R}
and
SU_{D}
. This is because the transmission powers of
SU_{TX}
and
SU_{R}
, which satisfy the interference constraint (7) in CogMFDR, directly interfere with
SU_{D}
and
SU_{R}
. Thus, the overall outage probability is given by
where
,
e
_{1}
=
N
^{2}
+
i
 1,
e
_{2}
=
N
_{2}
+
m_{rr}N
^{2}
+ (1 +
i

j
),
e
_{3}
=
N
^{2}
+
i

j
, and
φ
(a,b) is defined as in (54). The derivation process of (45) is provided in Appendix B.
4. Numerical Simulations
In this section, MonteCarlo simulations are executed and the impact of factors on outage performance is examined. Based on the above analysis, the factors which affect the outage performance are as follows: a. the IPT value
Q
; b. the mean interference channel fading exponents
m_{rr}
and
m_{sd}
; c. the additive noise variance
and the interference power
d. the number
N
of antennas in the SU nodes.
We set the rate threshold of cognitive relay networks to
R_{th}
= 1
bit / s / Hz
. The OSTBC rate is assumed to be the greatest achievable value, see e.g.,
[20]
, which is given by
where
N
= 2
M
(when
N
is even) or
N
= 2
M
 1 (when
N
is odd). Furthermore, we set the channel parameters
Ω_{rr}
=
Ω_{sd}
= 1.
Fig. 2
shows the outage probabilities in CogMHDRD and CogMFDR using the EPA scheme with respect to
m_{rr}
and
m_{sd}
, where
N
= 3 . In this figure, we set
η_{F}
= 2
^{Rth}
1 in CogMFDR and
η_{H}
= 2
^{2Rth}
1 in CogMHDRD. This is because only half the resources are utilized in CogMHDRD. The noise power is set at
As shown in
Fig. 2
, the outage performance of CogMFDR improves as the interference channel gains (
m_{rr}
and
m_{sd}
) decrease as we would expect. Because, the worse the interference channel gains are, the smaller interference power introduced by FDR would be added at the receive nodes, therefore, the better outage performance would be. When compared with CogMFDR, the outage probability of CogMHDRD is inversely proportional to the channel gain
m_{sd}
due to the
SU_{TX}
→
SU_{D}
link is considered for transmission. Meanwhile, the performance gain between CogMFDR and CogMHDRD would decrease when Q increases. This is because the interference power, which has a bad effect on the outage performance, would be larger when Q increases. However, the proposed EPA scheme cannot alleviate the effect of this interference.
SU outage probabilities in CogMHDRD and CogMFDR using the EPA scheme with respect to m_{rr} and m_{sd}
SU outage probabilities of CogMFDR using the OPA and EPA schemes.
Fig. 3
shows the secondary user outage probabilities in CogMFDR using the OPA and EPA schemes, respectively. We set
m_{rr}
=
m_{sd}
= 20
dB
and
As can be seen in the figure, the outage probabilities decrease as the number of antenna increases for both schemes. The outage probability of CogMFDR with EPA scheme decreases more slowly than that of CogMFDR with OPA scheme or CogMHDRD as Q increases, it even has a worse performance compared to the CogMHDRD when the SNR is high. This is because the increase in SNR causes the interference effect to become dominant relative to the noise effect. It denotes CogMFDR only has a better performance than CogMHDRD in low SNR region due to the interference introduced by fullduplex. These results further validate the investigation of FDR and HDR in ref
[8]
. However, despite the fact that a floor occurs in the high SNR region owing to local interference, the floor in the OPA scheme occurs at a higher SNR region than in the EPA scheme. This is because the OPA scheme balances the SNRs at
SU_{R}
and
SU_{D}
. Therefore, the proposed OPA scheme can help to achieve full performance gain in CogMFDR.
SU outage probabilities of CogMFDR using the OPA and EPA schemes with respect to
Fig. 4
shows the outage probabilities of CogMFDR using the OPA and EPA schemes, with respect to the interference power from
PU_{TX}
. In this figure, we assume additive noise variance,
It can be observed that the outage performance of the OPA scheme is superior to that of the EPA scheme, as expected. This performance gain becomes more evident with increasing the number of antennas. Meanwhile, it is verified that the simulated outage probability perfectly matches the theoretical one derived for the noiselimited environment, when the interference power is large.
SU Outage probabilities of CogMFDR using the OPA and EPA schemes with respect to m_{rr} and m_{sd}
Fig. 5
shows the outage probabilities of CogMFDR as functions of the mean interference channel gain
m_{rr}
and
m_{sd}
, when the OPA and EPA schemes are used. It is assumed that
and
Q
=10
dB
. As shown in
Fig. 5
, the outage performance using the EPA scheme is more vulnerable to the interference channel gain than using the OPA one. This can be mainly attributed to the fact that only the channel gains
a_{sp}
and
a_{rp}
are considered in the EPA scheme. On the other hand, the OPA scheme in CogMFDR performs SNR balancing which makes it robust to such interference. It can also be observed that the simulated outage probability with the OPA scheme agrees with the theoretical outage probability of the interference limited environment when the interference channel gain is large.
Fig. 6
shows the outage probabilities of the secondary user with respect to the interference threshold. We set
As mentioned before, when the interference threshold increases,
SU_{TX}
and
SU_{R}
can raise their transmission powers so that the secondary user’s throughput increases. However, in CogMFDR, any increase in the transmission power leads to an increase in interference observed at
SU_{R}
and
SU_{D}
. Hence, in
Fig. 6
, a high interference threshold indicates an interferencelimited environment. This demonstrates that the outage probability using the OPA scheme follows closely the outage analysis of the interferencelimited environment. Otherwise, when the interference threshold is small, the outage probability using the OPA follows the outage analysis of the noiselimited environment.
SU outage probabilities of CogMFDR using the OPA scheme with respect to Q
5. Conclusion
In this paper, we proposed an OPA scheme to minimize the overall outage probability of CogMFDR and then derived the outage probabilities for the secondary user in noiselimited and interferencelimited environments. The results obtained were further used to confirm that the proposed CogMFDR outperform the conventional CogMHDRD with regards to the outage probability when the SNR or the interference power is low. Simulation results demonstrated that using the OPA scheme in CogMFDR can improve the performance gain that full duplexing offers. Moreover, it also confirmed that the simulated outage probability values agree perfectly with the theoretical ones, in both the noiselimited and interferencelimited environments.
In reality, as we all know, the system is more likely to operate in low SNR region than in high SNR region, especially for the power limited system where the transmit power is limited by the IPT value. Therefore, the proposed CogMFDR and OPA scheme are more valuable for the practical application than conventional schemes.
BIO
Jia Liu received the M.S. degree in electronics and information engineering from Guilin University of Electronic Technoloy, Guilin, China, in 2008. He is currently working toward the Ph.D. degree in electrical engineering at the School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China. His research interests include cognitive radio, relay, wireless network coding, et al.
Guixia Kang received the M.S. degree from Tianjin University, Tianjin, China, and the Ph.D. degree in electrical engineering from Beijing University of Posts and Telecommunications (BUPT), Beijing. She was a research scientist in the Future Radio Concept Department of Siemens, Munich, Germany. She is currently a Professor with BUPT. Her interests include the research, development and standardization of 3G and beyond 3G (B3G) wireless communications systems as well as wireless sensor networks.
Ying Zhu received the M.S. degree in electronics and information engineering from Guilin University of Electronic Technoloy, Guilin, China, in 2009. She is currently working toward the Ph.D. degree in electrical engineering at the School of Beijing University of Posts and Telecommunications, Beijing, China. Her research interests include cognitive radio , relay, and information theory.
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