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Int. J. Electron.Commun. (AE) 67 (2013) 10791085

Contents lists available at ScienceDirect

InternationalJournal ofElectronics andCommunications (AE)

journal homepage: www.elsevier .com/ locate /aeue

RF beamforming for MIMO cognitive user

J. Ahmadi-Shokouh, H. Keshavarz

School of Electrical & Computer Engineering, University of Sistanand Baluchestan, Zahedan, Iran

a r t i c l e i n f o

Article history:Received 17 October 2012Accepted 25 June 2013

Keywords:Cognitive networksMIMO systemsRF beamforming

a b s t r a c t

Using Multiple Input Multiple Output (MIMO) architecture in cognitive radio (CR) secondary usersimproves the system performance in terms ofinterference cancellation and data rate enhancement butat the expense ofadding complexity and cost. A solution to reduce this complexity is employing radio

frequency (RF) beamforming networks at the transmitter/receiver front-ends. In this paper, we considera MIMO secondary user equipped with such RF beamforming network. Moreover, we find the trans-mit/receive optimum RF beamforming network for a MIMO spatial multiplexing system. We evaluatethe performance ofthe optimally designed RF beamforming technique over a Rician channel via com-puter simulations. The simulation results are assessed for different RF beamforming structures and thenumber ofprimary transmitters which cause interference on the secondary receiver.

2013 Elsevier GmbH. All rights reserved.

1. Introduction

Cognitive radio (CR) is a new class of wireless systems thatare able to reliably sense the spectral environment over a widebandwidth, detect the presence/absence of legacy users, so-called

primary users; i.e. those which have spectrum license, and use thespectrum only if the communication does not interfere with pri-maryusers.AlthoughresearchdoneonCRnetworksmostlyassumesingle antenna used at both primary and secondary transceivers,recent advances in using multiple antennas at both sides of a wireless communication link promise significant performanceimprovements by exploiting the effect of fading and multipathenvironments. For example, exploiting multiple antenna systemfor opportunistic spectrum sharing in CR networks is investigatedin [16]. In all these papers, a transmit beamforming is performedat the secondary user and the beamforming parameters are opti-mized subject to different criteria. For example, in a most recentpaper[6] thecognitive achievablecapacitybasedon thepeak trans-mit power at the secondary user and the peak interference powerat the primary user is optimized. Although Multi-Input and Multi-Output (MIMO) communication systems provide very high datarates with low error probabilities, these advantages are obtainedat the expense ofhaving highsignal processing tasks andhardwarecosts. The increased hardware cost is mainly due to having mul-tiple radio frequency (RF) chains (one for each antenna element).A MIMO system with the same number of RF chains and antennaelements is called full-complexity MIMO system.

Corresponding author. Tel.: +98 5418056540.E-mail addresses:[email protected], [email protected]

(J. Ahmadi-Shokouh), [email protected] (H. Keshavarz).

RF chain is the expensive, bulky and complex part of the radioarchitecture in a wireless system due to having many RF elec-tronic elements includinglow noiseamplifier(LNA), mixers, filters,analog-to-digital converter (ADC), etc. On the other hand, antennaelements do not add that cost in comparison to the RF chains to

a radio architecture. Hence, reducing the complexity of the MIMOsystemradioby loweringthenumber ofRF chains, whilethe MIMOperformance is preserved at the same level, is crucial in any MIMOapplication (herein cognitive user). To lower the number of RFchains and provide a low cost MIMO system a RF pre-processingscheme is proposed in [7]. Due to the adaptive beamformingcapabilities, theproposedRFbeamformingmethodshows a signifi-cantly improvedperformance compared to the traditional antennaselection methods for MIMO systems. It is shown in [7] that theoptimum beamforming method can evenachieve the performanceof a full-complexity MIMO system in which the receive antennasare directly connected to the RF chains, and therefore it takes thesame numberof antennas as the receive beamformingMIMO does.In [7], thebeamformingstructureis optimizedbasedon the instan-taneouschannelstatesforspatialmultiplexingMIMOtransmission.A similar RF pre-processing architecture is also used in [8]; how-ever, in which the linear RF pre-processing matrix is tuned onlybased on the large-scale statistics of the channel. Moreover, theperformance of this proposed idea is investigated for when thebeamformer is placed before LNA in [9].

In all these papers, only the noise-dominated fading channel isconsidered. However, in practice the noise is not the only impair-ment that limits thecommunication systemperformance. In manycases, e.g. cognitive radio networks, the channel suffers frominterference from other users and from fading due to destructiveadditioncausedbymultipathpropagation aswell. Readers canfinda general formulation for MIMO capacity when the interference

1434-8411/$ seefrontmatter 2013 Elsevier GmbH. All rights reserved.

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1080 J. Ahmadi-Shokouh,H. Keshavarz/ Int. J. Electron. Commun. (AE) 67 (2013) 10791085

exists in the channel in [10] where both the interference channelmatrix and noise vector entries are considered to be zero-meanand unit variance, independent and identically distributed (i.i.d.)circularly symmetric Gaussian random processes. However, theinterference has normally the following two important featureswhich make it different than noise [11]. First, power angular spec-trum (PAS) of the received interference signals on each antennaelement has a non-uniform spatial distribution. The interferencePAS varies based on the location and transmits power of either thelineof sight (LOS) interference sources or clusters/scattererswhichreflect the rays coming from non line of sight (NLOS) interferencesources. Moreover, the interference covariance matrix is notdiagonal. Considering these features introduces the interference-plus-noise vector as a colored noise with non diagonal covariancematrix. Authors in [12] use such a colored noise for MIMO spatialtransmission calculations. Moreover,moredetails about theMIMOdiversity transmission in a channel with interference can be foundin [13] and [14]. By considering the interference channels with theaforementioned characteristics for the interference, the solutionsproposed in [7] and [8] for the MIMO system equipped with thereceive beamforming are no longer optimum.

In this paper, we investigate on a CR network in which the sec-ondary user hasa MIMO linkwith theRFbeamformingarchitecture

at the transmit and receive sides based on the proposed model in[7]. We willfindtheoptimal solution forthe secondaryuser receiveRF beamforming module considering all constraints exist in theCRspectrum sharing network. The constraints are applied based onthe CRnetwork model used in [1] andthenew onesarisenwiththeproblem definition in this paper.A similar RFpre-processingarchi-tecture is also used in [6]. In [6], an antenna subarray formationscheme is exploited where each RF chain is allocated to a subarrayof antennas.While,wetake the MIMO beamformingmodel used in[7] where each RF chain can be connected to all antennas throughthe RF beamforming network.

The rest of the paper is organized as follows. In Section 2, weintroduce the system model and problem statement. We then findthe optimum RF beamformer matrices for the MIMO spatial multi-

plexingtransmissionstrategyin Sections3. InSection4, a computersimulation is provided in order to support the analytical achieve-ments. Finally, Section 5 concludes the paper.

2. Systemmodel definition and problem statement

In this study, we take the MIMO cognitive network modelproposedin [1]. Thismodel isdepicted inFig.1 while the MIMO sec-ondaryuserisequippedwithRFbeamformingcapability.Accordingto this model, it is assumed that all the primary users and thesecondary user share the same bandwidth for transmission, i.e.spectrum sharing.

2.1. MIMOwith beamforming capability

The MIMO secondary user consists of a NT-element transmitand a NR-element receive array antenna. In this framework thesecondary physical channel, including radio propagation environ-ment and transmit and receive antennas, is modeled by a NRNTmatrix Hs. ThereexistNt

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J. Ahmadi-Shokouh, H. Keshavarz / Int. J. Electron. Commun. (AE) 67 (2013) 10791085 1081

Fig. 3. Interferencemodel.

with the interferers. Hence, the interference-plus-noise, modeledas a vector at the receive antenna array, is given by

z =

K

k=1

aksk + n (1)

wherenCN(0, 2nINs ).Thearrayresponseakof thereceive antennaarray in the direction ofkis given by

ak =

1

e((j2)/0) sin(k)

...

e((j2)/0)(NR1)sin(k)

where and0 = 1/f0arerespectively the antenna spacing andthewave-length. Hence, theinterference-plus-noisecovariancematrixcan be obtained as

Kz= AKsA

+ 2nINR (2)

where

A= [a1,a2, . . . ,aK]T

In (2),Ks = E(ss) represents the interference covariance matrixwhere s= [s1, s2, . . ., sK]T. Asseen,the covariancematrixKzis alwayspositive-definite due to the term 2nINR in (2). In our optimizationproblem, we assume this covariance matrix, i.e. Kz, is fully knownat the receiver side.

2.3. Problem statement

According to theconsidered cognitivenetwork, the noiseat the

secondaryreceivergenerallycontainstheinterferencefromthepri-marytransmitters andcannot be white, consequently.However, incase of using a traditional full-complexity MIMO system for thesecondary user (as assumed in [1]), by applying a noise-whiteningfilter at the secondary receiver and incorporating this filter matrixinto the channel matrix Hs, the equivalent noise at the secondaryreceivercanbeassumedtobeapproximatelywhite Gaussian[14].In this paper, it is shown that the noise-plus-interference filter-ing in order to have a white equivalent noise is no longer validwhen the secondaryuser is using thereceive RF beamforming net-work. In other words, the MIMO channel for a secondaryuser withreceives RF beamforming is not a noise-limited one. Hence, we inthis paper aim to jointly optimize the secondary user transmit-ter and RF beamforming receiver in a spectrum sharing cognitive

network.

3. Spatial multiplexing transmission formulation

In signal transmission system, the Nr1 received signal vectoryfor the secondary user is written as

y= WRHsWTx+WRz (3)

where x is a Nt1 transmitted signal. Hence, the correspondingtransmit-receive Mutual Information (MI) is given by [15]

I= log[det(WRHsWTKxWTHsWR(WRKzWR)1 + INr)] (4)

where Kx is the transmit signal covariance matrix. Without los-ing any generality, we can assume Kx = INt.

2 Now, assuming thatthe channel matrix Hs and the interference covariance matrix Kzare fully known at the secondary system we solve the followingoptimization problem

IM= maxtr(WTW

T)Pt

tr(HkWTWTH

k) Pk fork {1,2, . . . ,K}

maxWR

I (5)

where Pt and Pk a re the total average power available atthe transmitter over a symbol period and the total tolerableinterference-power over all the receive antenna elements for thekth primary receiver, respectively.

3.1. Optimum receive beamformingmatrixWR

To maximize (4) on the beamforming matrix WR, the solutionis first found for the case when no constraint is imposed on WR,i.e.WR C

NrNR . In this case, the Optimum Receive Beamformer forSpatial Multiplexing transmission (OBSM) is given by

WobsmR = argmaxWR

I, (6)

The OBSM matrix,WobsmR , is found through the following theo-rem.

Theorem 1. For a given N RNTchannel matrix Hs and N RNRinterference covariance matrix Kz, the N rNR OBSM matrix repre-

sented in (6) is given by

WobsmR =MUA

1/2z U

z (7)

where M is any N rNr non-singular matrix, and =[INr|0Nr(NRNr)]. The N RNR unitary matrix Uz and N RNRdiagonal matrix z come from the singular value decomposition(SVD)Kz= UzzU

z, andUAis a N RNRunitary matrix coming from

the SVD ofA= UAAUAwhereA=

1/2z U

zHsWTW

TH

sUz

1/2z .

Proof. See Appendix A.

3.2. Optimum transmit beamformingmatrixWT

We do not expect to find a general closed form solution for the

optimumWTbased on the constraints shown in (4). However, weprovide an upper-bound and lower-bound solutions for (4) relax-ing some conditions. Moreover, the optimum solutions for somespecial cases are analytically obtained.

3.2.1. OptimumWTfor upper-bound of IMIn this case, wefind the optimalWTfor whenW

obsmR is provided

and one of the conditionsonWTin theoptimization problem (5) isrelaxed. Substituting (7) into (4) yields an upper-bound for (5) as

Iu,M= maxtr(WTW

T)Pt

log[det(A+ INr)] (8)

2 In fact, the transmit beamforming is performed using the transmit RF beam-

forming networkWT.

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The following theorem provides the optimumWTfor the upperbound of(8).

Theorem 2. Fora givenNRNTchannel matrixHsand the NRNRinterference covariance matrix Kz, the optimal WTwhich maximizesI(WobsmR ) based on the reduced constraints, i.e. (8), is given by

WuT= UB1/2u,TV

B (9)

whereu,Tis aN tNtdiagonal matrix whose non-zero elements aredetermined based on water-filling strategy as follows

[u,T]i,i = (1

2i,B

)+

with chosen to satisfy the following constraint

Nti=1

1

2i,B

+ Pt

and x+ = max(0,x). Moreover, UBandVBare respectivelyNRNRand

NTNTunitary matrices coming from the SVD ofB =1/2z U

zHs =

UBBVB.

Proof. See Appendix B.

3.2.2. OptimumWTfor lower-bound of IMIn this case, we find the optimal WT for when W

obsmR is pro-

vided and one tight extreme condition onWTin the optimizationproblem (5) is applied. In this condition, we set each communica-tion link between thesecondarytransmitantenna element andtheprimary receive antenna element has no loss, i.e. it is mathemati-cally set to one. Moreover, we consider P0 =minPkfor k {1, 2, . . .,K}. According to the above conditions, the lower-bound for (5) isdefined as

Il,M= maxtr(WTW

T)P0

log[det(A+ INr)] (10)

The following theorem provides the optimumWTfor the upper

bound of(10).Theorem 3. Fora givenNRNTchannel matrixHsand the NRNRinterference covariance matrix Kz, the optimal WTwhich maximizesI(WobsmR ) based on the applied constraints, i.e. (10), is given by

WlT= UB1/2l,T VB (11)

wherel,Tis a N tNtdiagonal matrix whose non-zero elements aredetermined based on the water-fillingmethod as follows

[l,T]i,i =

1

2i,B

+


Nti=1

1

2i,B

+

P0

Proof. The proof is similar to the proof for Theorem 2.

4. Computer simulations

4.1. Simulationmodel

A computer simulation is provided in this section in order touphold our theoretical analysis. In our simulations, we evaluatethe performance of the proposed beamforming architecture withdifferent number of antenna elements at the transmit/receive sec-

ondary user system. This evaluation is also performed for when

different number of primary users exists in the channel. A Rician-based statistical channel model [16] is used here to realize thechannel, H. Note that as we focus on the receive part, we assumeNT=Nt=4.

A MIMO system with NR receive antennas and NR receive RFchains. As previously defined, this configuration is called full-complexity MIMO system which is analyzed in [1].

A MIMO system with NRreceive antennas, Nr receive RF chains,anda post-LNA receive FFT-basedBultermatrix implemented byaNrNRPassive LinearNetwork (PLN).The entries of this matrixare fixed and their amplitudes and phases do not change. For therest of this paper we call this system FFT-MIMO.

A MIMO system with NR receive antennas, NrRF chains, andan optimum post-LNA receive beamforming matrix realizedby a NrNR LN whose entries phase and amplitude are fullyadjustable with no-constraint, i.e. whenW= WobsmR .

A MIMO system with Nr receive antennas and Nr receive RFchains.Wecallthis configurationlow-complexityMIMOinwhichthe number of receive antenna terminals and receive RF chainsare the same but equal to the number of receive RF chains usedin receive beamforming scheme.

The statistical channel models are commonly used to evaluatetheperformance of the communications systems via simulation. ARician-based statistical channel model is used here to realize thechannel matrix, H, for a spatially correlated MIMO channel. Thismodel,in whichthereis a strongdirect signal path, i.e. line-of-sight(LOS),betweenthetransmitterandthe receiver,characterizesmostof the wireless channels like indoor clustered wireless environ-ment. In a Rician model, the channel matrix H can be representedas [16]

H =

KfKf+ 1

HLOS +

1

Kf+ 1HNLOS (12)

where HLOS and HNLOS are respectively the LOS and non-line-of-

sight (NLOS) channel components, andKfrepresents the Rician K-factor. In the channel model (12), the LOS component is obtainedas [17]

HLOS = a(LOS,r) a(LOS,t)H

wherea istheantennaarrayresponse,and LOS,randLOS,trepresentrespectively the receive AOA and the transmit angle of departure(AOD) corresponding to the LOScomponent. The NLOS componentof the channel matrix is given by the Kronecker model as [17]

HNLOS = R1/2r HwR

1/2t

where Hw is a NsNtmatrix with complex Gaussian elements.Also, Rrand Rtare respectively the spatial covariance matrices at

the receiver andtransmitter, representing thereceiver/transmittersignal correlation across the antenna elements. In this paper, weobtain the spatial covariance matrices, Rr and Rt, based on theindoor clustered channel model [18].

In our simulation study, 1000 channel matrix realizations areproduced with Nt=Nr= 4. The arbitrary non-singular matrix M isalso chosen as a NrNridentity matrix, M = INr. The mean

3 of(4)over all the channel realizations is shown in Fig. 4 when differentnumber of the primary transmitters interfere the secondary userchannel. It is also assumed that the total power transmitted by allthe primary transmitters is remained constant.

3 Note that this is not a traditional stochastic representation which is used in

information theory.

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Fig. 4. Mean mutual information versus number of primary transmitters.

4.2. Results

In Fig.4, thesolid lines show theoptimumvaluesfor themutualinformation (4) obtained from an exhaustive search method foreach case of with and without beamforming (SNR= 10dB). How-ever, the upper and lower dash lines of the above mentionedoptimum solutions are respectively the upper, i.e. (8), and lower,i.e. (10), bounds of the mutual information. As shown in Fig. 4, atightersolutionband, i.e.upper-to-lowerbound, is providedfor themutual information whena lower number of theprimarytransmit-tersexist inthechannel.Moreover, it is seen that there isnogain ofbeamforming while the number of the primary transmitters goesbeyond a limit. However, this limit happens at a higher number ofthe primary transmitters for when a beamforming network with a

larger number of antenna elements is employed.Tostudythe dominanceeffect of interference, weusea measure

called interference dominance ratio (IDR). This measure is definedasthereceivedinterferencepowerbytheabovenominalreceivertothe noisepower, i.e. IDR= (||Ks||1)/2n, whenthe total interference-plus-noise power PINis assumed to be constant. The mean MI (4),i.e. I(W), averaged on all channel matrix realizations, is plottedversus IDR in Fig. 5 for differentW. In this figure SNR= 10dB, thenumber of interferers is 2, and Kf=5 dB. As this figure shows, the

optimum receive beamforming, i.e. W= WobsmR , achieves the full-complexity MIMOperformance regardless of either interference ornoise dominance. Moreover, a receive beamforming MIMO alwaysoutperforms both the FFT-MIMO and the low-complexity MIMOsystems. Another fact revealed in this figure is the outperforming

of the FFT-MIMO system compared to the low-complexity MIMOone for all IDRs. However, this merit reduces to a no-significantimprovement at low IDRs.

In the next step, we study the effect of LOS link dominance onthe receive beamforming MIMO system performance. The RicianK-factor is used as measure in this regard. As observed from Fig. 6the meanMI decreasesas theK-factor increases(whenthe LOSlinkdominates).Thisis expectedas increasing theLOScomponent leadsto less multipath effect and hence less capacity improvement.

As stated in previous sections, one of the significant benefitsderived from the RF beamforming method is the reduced systemcomplexity and cost via lowering the number of RF chains. In thisstep,weevaluatehow the number of receive RFchainsNrcanaffectthe performance in both spatial multiplexing and diversity trans-

missions. Fig. 7 shows the mean MI versusNr. Again the number of

Fig. 5. MI versusinterference dominanceratio(IDR) when SNR= 10dB, thenumberofinterferers is 2 andKf=5 dB.

Fig. 6. MI versus Rcian Kfactor (Kf) when IDR= 10dB, the number of interferers is2 and SNR= 10dB.

Fig. 7. MI versusnumber of receive RF chains(Nr) whenSNR= 10dB,thenumber of

interferers is 2, IDR= 10dB and Kf=5 dB.

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interferers is2, IDR= 10dB,Kf=5 dB, and SNR= 10dB.Obviously,Nris upper-bounded byNRwhich shows the full-complexity case, i.e.Nr=NR. Inspecting these figure some conclusions can be drawn asfollows

(1) All MIMO methods have the same performance at Nr=NR.This observation reveals that no beamforming technique canimprove the performance of a full-complexity system even in

the presence of interference.(2) Fig. 7 shows that for the spatial multiplexing transmission anoptimum receive beamforming MIMO can achieve the full-complexityperformanceonlyif thenumberof receive antennasis more than the transmit ones, i.e.NrNt.

(3) The FFT-MIMO basically outperforms the low-complexityMIMO for low Nr, whereas low-complexity MIMO is superiorto FFT-MIMO for the Nrclose toNR.

5. Conclusion

In this paper, we investigate on an optimal transmit/receive RFbeamformingstructurefor a MIMOsecondaryuser inCRnetworks.The optimization is performed based on a MIMO spatial multiple-xingtransmission.We propose a closedform analytical solution forthe optimum RF beamforming network at the secondary receiver.We also find upper and lower bounds for this optimum solutionat the secondary transmitter. To evaluate the analytical results, acomputer simulation is employed. We perform the simulation forthe differentnumber of primary transmitters andRF beamformingarchitectures. The results reveal that there is no gain of beamform-ing while the number of the primary transmitters goes beyond a

limit.Moreover, as shown the tightness of theproposed upper andlower bounds for the optimum RF beamforming network at thesecondary transmitters vary with both the antenna elements usedin the transmit/receive arrays and the number of primary trans-mitters. As a future work, one can optimize the RF beamformingparameters based on the cognitive achievable capacity subject tothe peak transmit power at the secondary user and the peak inter-ference power at the primary user.

Appendix A. Proof ofTheorem 1

For the proof ofTheorem 1, we first convert the problem to [7,Theorem 2] and then use the techniques from [7, Appendix B] tocomplete the proof. To proceed this method, it is shown in [19,

Theorem 8.7.1] that there exists a nonsingular NRNR matrix X1such that

X1HsWTWTH

sX

1 = D1

X1KzX1 = INR

(13)

where D1is a NRNRdiagonal matrix. Define Y1=WRX

11 . Substi-

tuting WR =Y1X1into (4) yields

I(Y1) = log[det(Y1D1Y1(Y1Y

1)

1+ INr)].

Now, the OBSM matrix is given byWobsmR = Y1,optX1where

Y1,opt= arg maxY1C

NrNRI(Y1) (14)

According to [7, Theorem 2], theoptimum matrix Y1,optis

Y1,opt=M. (15)

where M is an arbitrary NrNr nonsingular matrix, and =[INr|0Nr(NRNr)].

To find X1, let X2 =1/2z U

zwhere Kz= UzzU

z. Then, define

A= X2HsWTWTH

sX

2. Hence,X1 = U

AX2,whereUAcomesfromthe

SVD ofA= UAAUA, can meet the conditions in (13).

Appendix B. Proof ofTheorem 2

Rewrite A= BWTWTB

where B =1/2z U

zHs. Now, consider

the SVD ofB = UBBVB and WTW

T= UxxU

x where UB, VB, B,

Uxandxare respectively NRNRunitary matrix,NTNTunitarymatrix,NRNTdiagonalmatrix,NTNTunitarymatrix andNTNTdiagonal matrix. Then, using the approach used in [20, Section IV]yields the best Uxas Ux,u =VB. Hence, (8) is rewritten as

Iu,M= maxx:tr(x)Pt

log[det(BxTB

T+ INr)] = max

i,x :tr(x)Pt

Nti=1

log(1+ i,x2i,B) (16)

The water-fillingapproach is then employed to maximize (16).

Hence, the bestx, i.e.x,u, is found as

i,x,u =

1

2i,B

+


Nti=1

1

2i,B

+ Pt.

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