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Physical Communication ( )
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Physical Communication
journal homepage: www.elsevier.com/locate/phycom
Full length article
Interference mitigation for cognitive radio MIMO systems based onpractical precoding
Zengmao Chen a, Cheng-Xiang Wang a,, Xuemin Hong b, John Thompson c,Sergiy A. Vorobyov d, Feng Zhao e, Xiaohu Ge f
aJoint Research Institute for Signal and Ima ge Processing, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH1 4 4AS,
United Kingdomb School of Information Science and Technology, Xiamen University, Xiamen 361005, ChinacJoint Research Institute for Signal and Imag e Processing, Institute for Digital Communications, University of Edinburgh,Edinburgh, EH9 3JL, United Kingdomd Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 2V4, Canadae Department of Science and Technology, Guilin University of Electronic Technology, Guilin 541004, ChinafDepartment of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
Article history:
Received 15 February 2012
Received in revised form 27 April 2012
Accepted 29 April 2012
Available online xxxx
Keywords:
Cognitive radio
Interference mitigation
MIMO
Precoding
a b s t r a c t
In this paper, we propose two subspace-projection-based precoding schemes, namely, full-
projection (FP)-and partial-projection (PP)-based precoding, for a cognitiveradio multiple-
input multiple-output (CR-MIMO) network to mitigate its interference to a primary
time-division-duplexing (TDD) system. The proposed precoding schemes are capable of
estimating interference channels between CR and primary networks, and incorporating
the interference from the primary to the CR system into CR precoding via a novel sensingapproach. Then, the CR performance and resulting interference of the proposed precoding
schemes are analyzed and evaluated. By fully projecting the CR transmission onto a null
space of the interference channels, the FP-based precoding scheme can effectively avoid
interfering the primary system with boosted CR throughput. While, the PP-based scheme
is able to further improve the CR throughput by partially projecting its transmission onto
the null space.
2012 Elsevier B.V. All rights reserved.
1. Introduction
A cognitive radio (CR) [14] system may coexist with
a primary network on an either interference-free orinterference-tolerant basis [5,6]. For the former case, the
CR system only exploits the unused spectra of the primarynetwork. While, for the latter case, the CR system is al-
lowed to share the spectra assigned to primary network
Corresponding author. Tel.: +44 131 451 3329.E-mail addresses: [email protected] (Z. Chen),
[email protected] (C.-X. Wang), [email protected]
(X. Hong), [email protected] (J. Thompson),
[email protected] (S.A. Vorobyov), [email protected] (F. Zhao),
[email protected] (X. Ge).
under the condition of not imposing detrimental interfer-ence on the primary network. Therefore, the interferencefrom the CR network to the primary system (CR-primary
interference) should be carefully managed and canceled inorder to protect the operation of the primary system. Var-ious interference mitigation (IM) techniques applicable toCR networks have been reported in [7]. As for multiple an-tenna CR networks, transmit beamforming [812] and pre-coding in [1315] are effective approaches to proactivelycancel the CR-primary interference. On one hand, it steersthe CR transmission to avoid interfering with the primarynetwork. On the other hand, it exploits the diversity or themultiplexing gain of the CR system to enhance the reliabil-ity or efficiency of the CR network.
However, in [815], perfect or partial channel stateinformation (CSI) of CR interference channels to primary
1874-4907/$ see front matter 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.phycom.2012.04.007
http://dx.doi.org/10.1016/j.phycom.2012.04.007http://www.elsevier.com/locate/phycomhttp://www.elsevier.com/locate/phycommailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.phycom.2012.04.007http://dx.doi.org/10.1016/j.phycom.2012.04.007mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://www.elsevier.com/locate/phycomhttp://www.elsevier.com/locate/phycomhttp://dx.doi.org/10.1016/j.phycom.2012.04.0077/28/2019 Interference Mitigation MIMO
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2 Z. Chen et al. / Physical Communication ( )
Fig. 1. A CR MIMO transmitterreceiver pair coexists with a primary TDD system.
network (CR-primary interference channels) is required at
the CR transmitter (Tx) side to guarantee no/constrained
interference to the primary system. Therefore, extra sig-
naling between primary and CR networks is inevitable toobtain the CSI, which jeopardizes the applicability of these
beamforming and precoding schemes. A more practical
precoding schemesensing projection (SP)-based precod-ing, which learns the CSI using subspace estimation [16]and does not require a priori CSI, has been proposed for
a CR multiple-input multiple-output (MIMO) link coexist-
ing with a primary time-division-duplexing (TDD) system
in [17,18]. However, such a precoding scheme does not
account for the interference from primary Txs to the CRreceiver (Rx) (primary-CR interference), which leads to a
CR throughput loss. In [19,20], it is proposed to remove
the primary-CR interference at the CR Rx via null-space Rx
beamforming, which sacrifices the CR throughput as well.Moreover, the CR network in [19,20] has to work in a TDD
mode aligned with the primary system in order to facilitate
the null-space Rx beamforming.In this paper, two enhanced SP-based precoding sche-
mes, namely, full-projection (FP)- and partial-projection(PP)-based precoding, are proposed for CR MIMO systems
by incorporating the primary-CR interference. As the name
suggests, the FP-based scheme nulls the CR transmission
by fully projecting the transmission onto the estimated
null space of the CR-primary interference channels. Insteadof removing the primary-CR interference using null-space
Rx beamforming, the proposed precoding schemes account
for the primary-CR interference via sensing. This, on one
hand, improves the CR throughput, and on the other hand,introduces more flexibility into the CR deployment, i.e.,
the CR network does not have to work in a TDD mode asin [19,20]. The PP-based precoding can further improve the
CR throughput by projecting the CR transmission onto a
subspace that partially spans the estimated null space of
the CR-primary interference channels. As a result, the CRthroughput is further improved at the cost of introducing
extra interference to the primary network.
The remainder of this paper is organized as follows. The
system model is given in Section 2. The working principleof the SP-based precoding is introduced in Section 3. Then,we propose two new precoding schemes in Section 4.
The performance of the proposed precoding schemes is
evaluated in Section 5. Finally, we conclude the paper inSection 6.
Notation: Vectors are denoted by bold-face lower-caseletters, e.g., x, and bold-face upper-case letters are used
for matrices, e.g., X. For a matrix X, Tr{X}, XH, and X
denote its trace, Hermitian transpose and pseudoinverse,respectively. E{} stands for the statistical expectationoperator. Cxy denotes the space of x y matrices withcomplex entries.
2. System model and problem formulation
We consider a CR system shown in Fig. 1, where a CRTxRx pair shares the same spectrum with a primary TDD
network. Multiple antennas are mounted at the CR nodes
and possibly at each of the primary users. The CR Tx, CRRx, primary base station (BS) and the kth primary user
are equipped with Mt, Mr, Mbs and Mk (k = 1, . . . , K)antennas, respectively. Block-fading channels are assumedfor the primary and CR systems.
For a narrowband transmission, the received symbol atthe CR Rx can be expressed as
y = HFs + n + z (1)
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Fig. 2. System diagram for the proposed precoding schemes.
wherey CMr1 is the received signal vector at the CR Rx,s CMt1 and F CMtMt are the transmit informationvector with E{ssH} = I and precoding matrix of the CRTx, respectively, H CMrMt is the channel matrix fromthe CR Tx to CR Rx, whose elements are independent andidentically distributed (i.i.d.) complex Gaussian randomvariables with zero mean and variance 2H, and n C
Mr1
stands for the additive white Gaussian noise (AWGN)vector with zero mean and covariance matrix E{nnH} =2n I. Moreover, z C
Mr1 denotes the interference fromthe primary network to CR Rx. It can be expressed as
z =
Hurxu, during primary uplinkHdrxd, during primary downlink (2)
where Hur CMr
Kk=1 Mk and Hut C
MtK
k=1 Mk (seeFig. 1) represent the interference channels from all the Kactive primary users to CR Rx and to CR Tx, respectively,during primary uplink. Similarly, Hdr C
MrMbs in(2) together with Hdt C
MtMbs (see Fig. 1) standfor the interference matrices from the primary BS toCR Rx and to CR Tx during primary downlink. All theseinterference matrices (Hur, Hut, Hdr and Hdt) have i.i.d.complex Gaussian random elements with zero mean andcovariances 2ur,
2ut,
2dr and
2dt, respectively. Moreover,
xu CK
k=1M
k
1
and xd CM
bs
1
are the transmittedsignal vectors of all the K primary users and primary BS,respectively. We define the interference covariance matrixas Z E{zzH}.
3. Principle of SP-based precoding
The precoding problem for CR transmission can beexpressed as the following optimization problem [14]
maxF
log2 det
I +
HFFHHH
2n
(3)
subject toTr
{FF
H
} Pcr (4)Tr{GkFF
HGHk } k k = 1, . . . , K. (5)
In (5), Gk CMkMt is the channel matrix from the
CR Tx to the kth primary user. Thus, the channel matrixfrom the CR Tx to all primary users becomes HHut =
[GT1 , . . . , GTK]
T due to channel reciprocity. The constraintson the CR transmission power and the maximum allowedinterference perceived at each primary user are given by(4) and (5), respectively.
The projected channel singular value decomposition(SVD) or P-SVD precoding has been proposed in [14] as asuboptimal solution for the optimization problem (3)(5).It can be expressed as
F = U
(I 1 )+ 1
2 (6)
where ()+ max(0, ), denotes the power level fora water-filling (WF) algorithm, and U and originatefrom the SVD of the effective CR channel matrix H
H H(I UGUHG ), (7)
with H = V1/2
UH, and UG in (7) is from another SVD
HHut = VG1/2
G UHG , which is estimated via sensing in the SP
precoding [17,18] as shown in Fig. 2. It is worth noting thatthe P-SVD precoding given in (6) actually guarantees that
Tr{GkFFHGHk } = 0 (k = 1, . . . , K), i.e., no interference
is introduced to primary users. This eventually tightensthe constraint (5). Therefore, the P-SVD precoding is asuboptimal solution for the optimization problem (3)(5).
By analogy with the multiple signal classification tech-nique [16], the signal covariance matrix is decomposedinto signal and noise subspaces to estimate UG, that is
Rut =1
LS
LSi=1
rut(i)rHut(i) (8)
= UUH (9)
= UGGUHG + UnnU
Hn . (10)
In (16), rut(i) = Hutxu(i)+n(i) is the ith received symbol atthe CR Tx, and its estimated covariance matrix is denoted
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as Rut. An eigenvalue decomposition is then performed on
Rut in (17), where = diag(1, . . . , Mt) is a diagonal
matrix with descendingly ordered eigenvalues of Rut and
U CMtMt contains the corresponding eigenvectors. The
matrix Rut is further decomposed into interference and
noise components in (18) with UG and Un being the first
Kp = rank(Hut) and the remaining (Mt Kp) columns ofU, respectively, and G and n being their correspondingeigenvalue matrices. A rank estimate for Kp can be carried
out by using, e.g., an Akaike information criterion (AIC)or minimum description length (MDL) estimator [21]. Thesensing phase is followed by a CR transmission, where a
precoding matrix obtained from (6) is applied.
The merit of the SP precoding over the P-SVD approachis that no CSI is required due to the interference spaceestimation in (16)(18). However, both of the precoding
algorithms in [17,18] do not consider the interference fromthe primary network to the CR receiver, which eventually
leads to rate loss for the CR link.
4. Proposed precoding schemes
In this section, we elaborate the CR precoding duringthe primary downlink.1 When incorporating the primary-CR interference, the precoding problem for the CR Tx
during the primary downlink can be expressed as follows
maxF
log2 det
I +
HFFHHH
Z + 2n I
(11)
subject to Tr{FFH} Pcr (12)
Tr{GkFF
H
G
H
k } k, k = 1, . . . , K. (13)The constraints on the CR transmission power and the
maximum allowed interference perceived at each primaryuser are given by (12) and (13), respectively. In (13), Gk C
MkMt is the channel matrix from the CR Tx to the kth
primary user. Thus, the channel matrix from the CR Tx toall primary users becomes HHut = [G
T1 , . . . , G
TK]
T due tochannel reciprocity.
Then, the precoding matrix for CR transmission during
the downlink can be written as [22]
Fd = Ud (dI 1d )
+
12 (14)
where d is the power level for the water-filling algorithmand Ud is obtained through the following eigenvaluedecomposition (EVD)
UddUHd = H
H(Z +
2n I)
1H
= (I UGUHG )
HHH(Z + 2n I)1H(I UGU
HG ). (15)
Similar to the P-SVD precoding, the precoding matrixgiven by (14) is a suboptimal solution for the optimization
problem (11)(13) due to the fact that it tightens theconstraint (13) by forcing k to 0.
1 A similar precoding for the primary uplink can be easily obtained,
which is ignored here for brevity.
In (15), the effective CR channel matrix is definedas H H(I UGU
HG ), where UG is estimated by
decompositing the CR received signal covariance matrixinto signal and noise subspaces. It can be expressed as
Rut =1
LS
LS
i=1 rut(i)rHut(i) (16)
= UUH (17)
= UGGUHG + UnnU
Hn . (18)
In (16), rut(i) = Hutxu(i)+n(i) is the ith received symbol atthe CR Tx, and its estimated covariance matrix is denotedas Rut. An EVD is then performed on Rut in (17), where =diag(1, . . . , Mt) is a diagonal matrix with descendingly
ordered eigenvalues of Rut. It is further decomposed into
interference and noise components in (18) with UG and Unbeing the first Kp = rank(Hut) and the remaining (Mt Kp)
columns of U, respectively, and G and n being their
corresponding eigenvalue matrices.It can be seen from (14) and (15) that in order toobtain the CR precoding matrix, the interference-plus-noise covariance matrix Rur Z +
2n I needs to be
estimated at the CR Rx, besides the estimation of theinterference subspace UGU
HG at the CR Tx.
4.1. Full-projection-based precoding
To enable the estimation of UGUHG and Rur, we propose
an enhanced precoding scheme, which is demonstrated inFig. 2. Each CR cycle consists of sensing and transmissionphases. We name the CR transmission during the primary
downlink as T1 and uplink as T2. For T1, the space UGU
H
G isestimated at theCR Tx during the primary uplink accordingto (16)(18) over LS1 symbols. The estimation of Rur isperformed at the CR Rx at the beginning of the primarydownlink for a batch ofLS2 symbols via a procedure similarto (16). After obtaining these two estimates, the CR Txstarts transmission T1 using the precoding matrix obtainedby (14). Then T2 follows immediately after T1 but rightbefore the sensing phase for the next CR cycle. The CRprecoding matrix for T2 can be obtained by other twosensing sessions concurrent with the sensing phase for T1.This precoding scheme fully projects its transmission ontothe estimated null space of the CR-primary interferencechannels. Therefore, it is termed as FP precoding.
It can be seen from Fig. 2 that the proposed FP precodingscheme shifts the CR cycle of the SP precoding rightwardsin time. By doing this, several benefits are obtained.Firstly, introducing CR Rx sensing phases improves theCR throughput by incorporating the interference-plus-noise covariance matrix into precoding. Secondly, shiftingthe CR cycle diverts part of the CR transmission fromthe primary downlink to the uplink which reduces thetime that primary Rxs expose themselves to CR-primaryinterference. This is beneficial to the primary network,since primary users are usually more susceptible tointerference than the primary BS.
Theoretically, the proposed FP precoding can com-
pletely mitigate the CR-primary interference if there is noerror in the interference space estimation (18). However,
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its IM ability degrades rapidly when the CR interference-to-noise ratio, INR 2ut/
2n , drops below a threshold.
This is due to the fact that in (18) some components in thenoise subspace may swap with those in the interferencesubspace when the noise amplitude n is relatively largecompared to the interference channel gain ut. This phe-nomenon is known as a subspace swap2 [25].
For low INR, the interference subspace has a highprobability to swap with the noise subspace. When asubspace swap happens, (15) can be rewritten as
UddUHd (I UnU
Hn )
HHH(Z + 2I)1H(I UnUHn )
= UGUHG H
H(Z + 2I)1HUGUHG (19)
which means that Fd and HHut span the same space. Thus, the
average CR-primary interference at low CR INR becomes
IFPl = E{Tr{HHutFdF
Hd Hut}} Pcr
2ut. (20)
This suggests that the average interference power atprimary users is proportional to the channel gain between
CR and primary users at low CR INR.The average CR-primary interference in the high CR INR
regime can be expressed as
IFPh = E{Tr{HHutUd(dI
1d )
+UHd Hut}} (21)
= E{Tr{HHut(Ud Ud)(dI 1d )
+
(Ud Ud)HHut}} (22)
E{Tr{HHut(XHHut)
NHUd(dI
1d )+Ud
HN(HHutX)Hut}} (23)
= 2n PcrE{Tr{HHut(X
HHut)(HHutX)
Hut}} (24)
=2n Pcr
LS1Tr{Qu} (25)
where (22) is due to the fact that HHutUd = 0; (23) is
obtained using the fact that Ud Ud (XHHut)
NHUdfor high INR [26] with X [xu(1),xu(2) , . . . ,xu(LS1)],and N [n(1), n(2) , . . . , n(LS1)]; (24) follows from theindependence of XHHut and N and E{N
HYN} = 2n Tr{Y}I
for any matrix Y. Note that Qu E{xuxHu } in (25) is
the transmit covariance matrix for the primary user. Aninteresting fact can be observed from (25) that at high CRINR the average CR-primary interference does not depend
on the interference channel Hut. It is proportional to thechannel noise 2n and inversely proportional to the sensinglength LS1.
4.2. Partial-projection-based precoding
The PP precoding works in a similar manner to theabove proposed FP precoding except for the selection ofthe interference space. For the downlink CR precoding, a
subspace UmUHm partially spanning the interference space
is obtained by choosing m eigenvectors corresponding to
2 The lower bound on the probability of the subspace swap has been
investigated in [23,24].
the first m largest eigenvalues of in (17), where m canbe determined according to various criteria. One candidatecriterion is
Mmini=m+1
i
mi=1
i
rt/d (26)
with Mmin min(Mt,K
k=1 Mk). We call rt/d the trivialover dominant interference ratio (TDIR). This selectionprocess chooses m dominant interference subchannels toform an estimate of the interference space and ignoresthe other (Mmin m) trivial ones. Finally, substituting the
estimated subspace UmUHm for UGU
HG , the precoding matrix
Fd for the downlink CR transmission can be obtained via(14). However, we may fail to find a value of m satisfying(26). In this case, the proposed FP precoding is used.
The joint probability density function (PDF) of the
ordered eigenvalues
[1, 2, . . . , Mmin ] ofRut, with1 2 Mmin
2n is [27]
f(1, 2, . . . , Mmin )
=1
PpMmin
f
1
2n
Pp,
2 2
n
Pp, . . . ,
Mmin 2
n
Pp
(27)
where Pp is the transmission power of each primary user
antenna and f(1, 2, . . . , Mmin ) with 1 2
Mmin is given by
f(1, 2, . . . , Mmin )
=
Mmini=1
ei MmaxMmini
Mmin 1i=1
Mmin
j=i+1
(i j)2
Mmini=1
(Mmax i)!Mmini=1
(Mmin i)!
(28)
with Mmax max(Mt,K
k=1 Mk). Therefore, the probabil-ity for the occurrence of(26) is
pm = Sf(1, 2, . . . , Mmin ) d1 d2 dMmin (29)
where S {(1, 2, . . . , Mmin )| (26) 1 2
Mmin 2
n }.In other words, for the PP precoding scheme the
probabilities of using the genuine PP (m satisfying (26)exists) and using FP are pm and (1 pm), respectively.
Therefore, the CR Tx uses (1 pm)K
k=1 Mk + pmm
andK
k=1 Mk degrees of freedom (DoF) for IM in the PPand FP precoding schemes, respectively. This means thatcompared to the proposed FP precoding the PP precoding
scheme transfers pm(K
i=1 Mk m) DoF from interferencemitigation to CR transmission, which leads to a higherthroughput for the CR link. It can be seen from (27)(29)
that in the large INR regime, pm is fixed for a given noisepower 2n and Pp. Considering the fact from (25) that at
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Fig. 3. CR throughput under different precoding schemes ( Mt = Mr =4, Mbs = 2, K = 2, M1 = M2 = 1, LS1 = LS2 = LT2 = 50, LT1 =350, 2H =
2ut = 1, Pcr = 1, and rt/d = 0.1).
high INRs the average interference power of FP IFPh is fixed
and the average interference power resulting from real
PP IPP is proportional to the square of the interference
channel gain 2ut, the overall average interference of the PP
precoding IPPh = pmIPP+(1pm)I
FPh is linearly proportional
to 2ut for large INRs.
5. Numerical results & discussions
Consider a scenario where a CR MIMO system coexists
with a primary TDD system which has one 2-antenna
BS and two single-antenna users. We assume that thenumber of antennas for primary users is known to the
CR system. Therefore, the rank estimation of Kp used in
(18) is not needed in our simulations. Each CR node is
equipped with four antennas. The primary network works
as a downlink-broadcast and an uplink multiple-access
system. The transmission power of the CR and primary
networks is 1. All the obtained results are averaged over
2000 simulation runs.
First, we evaluate the throughput of the CR systemwith theproposed precodingschemes overdifferent valuesof signal-to-noise ratios, SNR 2H/
2n . In Fig. 3, the
throughputs (average mutual information in (11)) of thetwo proposed precoding schemes are compared with thatof the SP precoding of [17,18] and the P-SVD precodingwith perfect CSI of [14]. It can be seen that the proposed
FP/PP precoding schemes lead to higher CR throughputthan the SP precoding, and the throughput gain becomeslarger as the SNR increases.
Fig. 4 evaluates the impact of CR INR on the CRthroughput and the resulting CR-primary interferenceunder different precoding schemes. It has the same setupas that of Fig. 3 with 2n = 10
4. By comparingFig. 4(a) with Fig. 4(b), it can be seen that the proposedFP/PP precoding schemes outperform the SP counterpartat low INRs, since they lead to higher CR throughputwithout introducing extra interference. At high INRs, boththe proposed FP and SP precoding schemes have fixedinterference, and there is a fairly good agreement between
the derived andsimulated interference of the FP precoding.Another phenomenon which can be seen from Fig. 4(b)is that the interference of the SP precoding is slightlysmaller than that of the FP precoding. This is due to thefact that the sensing of the SP precoding is longer than theuplink sensing of the FP precoding. Moreover, at high INRsthe interference of the proposed PP precoding is linearlyproportional to the CR INR, which supports our analysis inSection 4.2.
6. Conclusions
In this paper, two SP-based precoding schemes, namely,
FP and PP precoding, have been proposed for CR MIMO sys-tems to mitigate the CR-primary interference and improvethe CR throughput. These two precoding schemes are capa-ble of estimating the CSI of primary-CR interference chan-nels and can account for the primary-CR interference viaa novel sensing approach. Therefore, no extra signaling isrequired between primary and CR systems, which conse-quently eases the deployment of CR networks. The perfor-mance of the proposed precoding schemes has also been
a b
Fig. 4. (a) CR throughput and (b) resulting interference of different precoding schemes (Mt = Mr = 4, Mbs = 2, K = 2, M1 = M2 = 1, LS = 100, LS1 =LS2 = LT2 = 50, LT1 = 350,
2H = 1, Pcr = 1, rt/d = 0.1, and
2n = 10
4).
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Z. Chen et al. / Physical Communication ( ) 7
evaluated. It has been demonstrated that the FP precod-ing can boost the CR throughput without introducing extraCR-primary interference in the low INR regime. The PP pre-coding can further improve the CR throughput if the pri-mary system can tolerate some extra interference.
Acknowledgments
The authors acknowledge the support from the RCUKfor the UKChina Science Bridges Project: R&D on (B)4GWireless Mobile Communications. Z. Chen, C.-X. Wang,and J. Thompson acknowledge the support from the Scot-tish Funding Council for the Joint Research Institute inSignal and Image Processing between the University ofEdinburgh and Heriot-Watt University, as part of theEdinburgh Research Partnership in Engineering and Math-ematics (ERPem). Z. Chen and S. A. Vorobyov acknowledgethe support from the National Science and EngineeringResearch Council (NSERC) of Canada. F. Zhao acknowledgesthe support from the National Natural Science Founda-tion of China (NSFC) (Grant No.: 61172055). C.-X. Wangand F. Zhao acknowledge the support of the Key Lab-oratory of Cognitive Radio and Information Processing(Guilin University of Electronic Technology), Ministry ofEducation, China (Grant No.: 2011KF01). X. Ge acknowl-edges the support from the NSFC (Grant No.: 60872007),National 863 High Technology Program of China (GrantNo.: 2009AA01Z239), Hubei Provincial Science andTechnology Department (Grant No.: 2011BFA004), andthe Ministry of Science and Technology (MOST) of China,International Science and Technology Collaboration Pro-gram (Grant No.: 0903).
References
[1] S. Haykin, Cognitive radio: brain-empowered wireless communica-tions, IEEE J. Sel. Areas Commun. 2 (2005) 201220.
[2] I.F. Akyildiz, W.Y. Lee, M.C. Vuran, S. Mohanty, NeXt genera-tion/dynamic spectrum access/cognitive radio wireless networks: asurvey, Comput. Netw. 13 (2006) 21272159.
[3] Q. Zhao, B.M. Sadler, A survey of dynamic spectrum access, IEEESignal Process. Mag. 3 (2007) 7989.
[4] X. Hong, C.-X. Wang, H.-H. Chen, Y. Zhang, Secondary spectrumaccess networks: recent developments on the spatial models, IEEEVeh. Technol. Mag. 2 (2009) 3643.
[5] C.-X. Wang, X. Hong, H.-H. Chen, J. Thompson, On capacityof cognitive radio networks with average interference powerconstraints, IEEE Trans. Wireless Commun. 4 (2009) 16201625.
[6] X. Hong, C.-X. Wang, M. Uysal, X. Ge, S. Ouyang, Capacity analysis ofhybrid cognitive radio networks with distributed VAAs, IEEE Trans.Veh. Technol. 7 (2010) 35103523.
[7] X. Hong, Z. Chen, C.-X. Wang, S.A. Vorobyov, J. Thompson, Cognitiveradio networks: interference cancellation and management tech-niques, IEEE Veh. Technol. Mag. 4 (2009) 7684.
[8] J. Zhou, J. Thompson, Linear precoding for the downlink of multipleinput single output coexisting wireless systems, IET Commun. 6(2008) 742752.
[9] T.K. Phan, S.A. Vorobyov, N.D. Sidiropoulos, C. Tellambura, Spectrumsharing in wireless networks via QoS-aware secondary multicastbeamforming, IEEE Trans. Signal Process. 6 (2009) 23232335.
[10] G. Zheng, K.-K. Wong, B. Ottersten, Robust cognitive beamformingwith bounded channel uncertainties, IEEE Trans. Signal Process. 12(2009) 48714881.
[11] L. Zhang,Y.-C.Liang, Y.Xin, H.V. Poor,Robustcognitive beamformingwith partial channel state information, IEEE Trans. WirelessCommun. 8 (2009) 41434153.
[12] G. Zheng, S. Ma, K.-K. Wong, T.-S. Ng, Robust beamforming incognitive radio, IEEE Trans. Wireless Commun. 2 (2010) 570576.
[13] L. Bixio, G. Oliveri, M. Ottonello, M. Raffetto, C.S. Regazzoni,Cognitiveradios with multiple antennas exploiting spatial opportunities, IEEETrans. Signal Process. 8 (2010) 44534459.
[14] R. Zhang, Y.-C. Liang, Exploiting multi-antennas for opportunisticspectrum sharing in cognitive radio networks, IEEE J. Sel. Top. Sign.Proces. 1 (2008) 88102.
[15] G. Scutari, D.P. Palomar, S. Barbarossa, Cognitive MIMO radio:competitive optimality design based on subspace projections, IEEESignal Process. Mag. 6 (2008) 4659.
[16] R. Roy, T. Kailath, ESPRIT-estimation of signal parameters viarotational invariance techniques, IEEE Trans. Acoust. Speech SignalProcess. 7 (1989) 984995.
[17] H. Yi, H. Hu, Y. Rui, K. Guo, J. Zhang, Null space-based precodingscheme for secondary transmission in a cognitive radio MIMOsystem using second-order statistics, in: Proc. IEEE ICC, 2009.
[18] R. Zhang, F. Gao, Y.-C. Liang, Cognitivebeamforming made practical:effective interference channel and learning-throughput tradeoff,IEEE Trans. Commun. 2 (2010) 706718.
[19] H. Yi, Nullspace-based secondary joint transceiver scheme forcognitive radio MIMO networks using second-order statistics, in:Proc. IEEE ICC, 2010.
[20] F. Gao, R. Zhang, Y.-C. Liang, X. Wang, Design of learning-basedMIMO cognitive radio systems, IEEE Trans. Veh. Technol. 4 (2010)17071720.
[21] O. Somekh, O. Simeone, Y. Bar-Ness, W. Su, Detecting the numberof transmit antennas with unauthorized or cognitive receivers in
MIMO systems, in: Proc. IEEE MILCOM, 2007.[22] Z. Chen, S.A. Vorobyov, C.-X. Wang, J. Thompson, Pareto regioncharacterization for rate control in multi-user systems and Nashbargaining, IEEE Trans. Automatic Control 57 (12) (2012).
[23] J. Thomas, L. Scharf, D. Tufts, The probability of a subspace swap inthe SVD, IEEE Trans. Signal Process. 3 (1995) 730736.
[24] M. Hawkes, A. Nehorai, P. Stoica, Performance breakdown ofsubspace-basedmethods: prediction and cure, in: Proc. IEEE ICASSP,2001.
[25] D.W. Tufts, A.C. Kot, R.J. Vaccaro, The analysis of threshold behaviorof SVD-based algorithms, in: Proc. XXIst Annu. Asilomar Conf.Signals. Syst. Comput., 1987.
[26] F. Li, H. Liu, R.J. Vaccaro, Performance analysis for DOA estimationalgorithm: unification, simplification and observations, IEEE Trans.Aerosp. Electron. Syst. 4 (1993) 11701184.
[27] M. Chiani, M.Z. Win, A. Zanella, R.K. Mallik, J.H. Winters, Bounds andapproximations for optimum combining of signals in the presence
of multiple co-channel interferers and thermal noise, IEEE Trans.Commun. 2 (2003) 296307.
Zengmao Chen received his B.Sc. degree fromNanjing University of Posts & Telecommunica-tions (NUPT), China, and his M.Eng. degree fromBeijing University of Posts and Telecommunica-tions (BUPT), China, in 2003 and 2006, respec-tively, and his Ph.D. degree from Heriot-WattUniversity, UK, in 2011.
Dr. Chen is now a Post-doc Research Asso-ciate with the Joint Research Institute for Signaland Image Processing, Heriot-Watt University,UK and the Network Manager for the UK-China
ScienceBridges: R&D on (B)4G Wireless Mobile Communications project.From September 2009 to December 2009, he was a visiting researcher
in the University of Alberta, Canada. From 2006 to 2007, he worked as aResearch DesignEngineer in Freescale Semiconductor (China) Ltd. His re-search interestsinclude: cognitive radio networks, MIMO communicationsystems, interference modeling, and interference cancellation.
Cheng-Xiang Wang received his B.Sc. andM.Eng. degrees in Communication and Informa-tion Systems from Shandong University, China,in 1997 and2000, respectively, and hisPh.D. de-gree in Wireless Communications from AalborgUniversity, Denmark, in 2004.
He has been with Heriot-Watt University,Edinburgh, UK, since 2005, first as a Lecturer,then asa Readerin 2009,and then waspromotedto a Professorin Wireless Communications since2011. He is also an Honorary Fellow of the Uni-
versity of Edinburgh, UK, a Chair Professor of Shandong University, aGuestProfessor of Huazhong Universityof Scienceand Technology,an Ad-junct Professor of Guilin Un iversity of Electronic Technology, and a Guest
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Researcher of Xidian University, China. He was a Research Fellow at theUniversity of Agder, Grimstad, Norway, from 2001 to 2005, a Visiting Re-searcher at Siemens AG-Mobile Phones, Munich, Germany, in 2004, anda Research Assistant at Technical University of HamburgHarburg, Ham-burg, Germany, from 2000 to 2001. His current research interestsincludewireless channel modeling and simulation, green communications, cog-nitive radio networks, vehicular communication networks, mobilefemto-cell networks, cooperative (relay) MIMO communications, and (beyond)4G wireless communications. He has edited 1 book and published 1 book
chapterand over 150papersin refereed journals andconference proceed-ings. He is leading several projects funded by EPSRC, Mobile VCE, and in-dustries, including the RCUK funded UKChina Science Bridges: R&D on(B)4G Wireless Mobile Communications.
Prof. Wang is currently serving as an Associate Editor for IEEE Trans-actions on Vehicular Technology, an Editor for Wireless CommunicationsandMobile ComputingJournal(John Wiley & Sons)and Securityand Com-munication Networks Journal (John Wiley & Sons), and a Scientific BoardMember for InTech (Open Access Publisher). He also served as an Edi-tor for IEEE Transactions on Wireless Communications (20072009) andHindawi Journal of Computer Systems, Networks, and Communications(20072011). He was the leading Guest Editor for IEEE Journal on Se-lected Areas in Communications, Special Issue on Vehicular Communica-tions and Networks. He served or is serving as a TPC member, TPC Chair,and General Chairfor morethan 60 international conferences.He receivedtheIEEE Globecom10 Best Paper Award in 2010 andthe IEEE ICCT11 BestPaper Awards in 2011. Dr Wang was listed in Dictionary of International
Biography 2008 and 2009, Whos Who in the World 2008 and 2009,Great Minds of the 21st Century 2009, and 2009 Man of the Year. Heis a Senior Member of the IEEE, a Fellow of the IET, a Fellow of the HEA,and a member of EPSRC Peer Review College.
Xuemin Hongreceived his B.Sc. degree in Com-munication Engineering from Beijing Informa-tion Science and Technology University, China,in 2004 and his Ph.D. degree in Wireless Com-municationsfrom Heriot-Watt University, UK, in2008. Since July 2011, he has been an AssociateProfessorwith theSchoolof Information Scienceand Technology, Xiamen University,China. FromAugust 2009 to July 2011, he was a Post-docResearch Associate with the Joint Research In-stitute for Signal and Image Processing, Heriot-
Watt University, UK. From January 2009 to July 2009, he was a Post-docResearch Fellow with the Department of Electrical and Computer Engi-neering, University of Waterloo, Canada. From 2004 to 2005, he was af-filiated with the Centre for Telecommunication Research, Kings CollegeLondon, UK.
Dr.Hongsresearch interestsinclude MIMOand cooperative systems,wireless radio channel modeling, cognitive radio networks, and (beyond)4G wireless communications. He has published more than 20 technicalpapers in major international journals and conferences and 1 book chap-ter in the area of wireless communications.
John Thompson received his B.Eng. and Ph.D.degrees from the University of Edinburgh in1992 and 1996, respectively. From July 1995to August 1999, he worked as a postdoctoralresearcher at Edinburgh, funded by the UK
Engineering and Physical Sciences ResearchCouncil (EPSRC) and Nortel Networks. He wasappointedas a lecturer atwhat isnow theSchoolof Engineering at the University of Edinburgh in1999. He was recently promoted to a Professorand a personal chair in Signal Processing and
Communications.Prof. John S. Thompsons research interests currently include energy
efficient communications systems, antenna array techniques and multi-hop wireless communications. He has published over 200 papers todate including a number of invited papers, book chapters and tutorialtalks, as well as co-authoring an undergraduate textbook on digitalsignal processing. He is overall project leader for the 1.2M EPSRC Islayproject involving four universities which investigates efficient hardwareimplementation of complex algorithms. He is also the academic deputyleaderfor the2M EPSRC/Mobile VCEGreen Radio project,which involvesa number of international communication companies. He is currently
editor-in-chief of the IET Signal Processing journal and was a technicalprogram co-chair for the Globecom conference in Miami in December2010.
Sergiy A. Vorobyovreceived the M.Sc. and Ph.D.degrees in systems andcontrol from Kharkiv Na-tional Universityof RadioElectronics, Ukraine, in1994 and 1997, respectively.
Since 2006, he has been with the Depart-ment of Electrical and Computer Engineering,University of Alberta, Edmonton, AB, Canadawhere he becamean AssociateProfessorin 2010and Full Professor in 2012. Since his gradu-
ation, he also occupied various research andfacultypositionsat the Kharkiv National Univer-
sity of Radio Electronics, Ukraine; the Institute of Physical and Chemi-cal Research (RIKEN), Japan; McMaster University,Hamilton, ON, Canada;Duisburg-Essen University and the Darmstadt University of Technology,Germany; and the Joint Research Institute between the Heriot-Watt andEdinburgh Universities, UK. He also held visiting positions at the Tech-nion, Haifa, Israel, in 2005 and the Ilmenau University of Technology, Il-menau, Germany, in 2011. His research interests include statistical andarray signal processing, applications of linear algebra, optimization, andgame theory methods in signal processing and communications, estima-tion, detection, and sampling theories, and cognitive systems.
Dr. Vorobyov is a recipient of the 2004 IEEE Signal Processing Soci-ety Best Paper Award, the 2007 Alberta Ingenuity New Faculty Award,the 2011 Carl Zeiss Award (Germany), and other awards. He was an As-sociate Editor for the IEEE TRANSACTIONS ON SIGNAL PROCESSING from2006 to 2010 and for the IEEE SIGNAL PROCESSING LETTERS from 2007
to 2009. He is a member of the Array and Multi-Channel Signal Process-ing and Signal Processing for Communications and Networking TechnicalCommittees of IEEE Signal Processing Society. He has served as a TrackChair in Asilomar 2011 and as a Technical Co-Chair in the IEEE CAMSAP2011.
Feng Zhao was born in 1974. He received hisPh.D. degree in Communication and Informa-tion Systems from Shandong University, China,in 2007. Now he is a Research Associate in theSchool of Information and Communications ofGuilin University of Electronic Technology. Hisresearch interests include wireless communica-tion systems, information processing, and infor-mation security. He has published more than
30 papers in journals and international confer-ences.
Xiaohu Ge is currently a Professor with the De-partment of Electronics and Information Engi-neering at Huazhong University of Science andTechnology (HUST), China. He received his Ph.D.degree in Communication and Information En-gineering from HUST in 2003. He has worked atHUST since Nov. 2005. Prior to that, he workedas an assistant researcher at Ajou University(Korean) and Politecnico Di Torino (Italy) fromJan. 2004 to Oct. 2005. He was a visiting re-searcher at Heriot-Watt University, Edinburgh,
UK from June to August 2010. His research interests are in the area of
mobile communications, traffic modeling in wireless networks, greencommunications, and interference modeling in wireless communications.He has published about 50 papers in refereed journals and conferenceproceedings and has been granted about 10 patents in China. He is lead-ing several projects funded by NSFC, China MOST, and industries. Heis taking part in several international joint projects, such as the RCUKfunded UKChina Science Bridges: R&D on (B)4G Wireless Mobile Com-munications and the EU FP7 funded project: Security, Services, Network-ing and Performance of Next Generation IP-based Multimedia WirelessNetworks.
Prof. Ge is currently serving as an Associate Editor for InternationalJournal of Communication Systems (John Wiley & Sons) and KSII Trans-actions on Internet and Information Systems. Since 2005, he has beenactively involved in the organization of more than 10 international con-ferences, such as Publicity Chair of IEEE Europecomm 2011 and Co-Chairof workshop of Green Communicationof Cellular Networksat IEEE Green-Com 2010. He is a Senior Member of the IEEE, a Senior member of the
Chinese Institute of Electronics, a Senior memberof the China Institute ofCommunications,and a memberof theNSFCand ChinaMOST Peer ReviewCollege.