Hybrid Procoder and Combiner Design for Secure Transmission in mmWave MIMO Systems
aa r X i v : . [ c s . I T ] A p r Hybrid Procoder and Combiner Design for SecureTransmission in mmWave MIMO Systems
Xiaowen Tian † , Ming Li † , Zihuan Wang † , and Qian Liu ‡ † School of Information and Communication EngineeringDalian University of Technology, Dalian, Liaoning 116024, ChinaE-mail: { tianxw,wangzihuan } @mail.dlut.edu.cn, [email protected] ‡ School of Computer Science and TechnologyDalian University of Technology, Dalian, Liaoning 116024, ChinaE-mail: [email protected]
Abstract —Millimeter wave (mmWave) communications havebeen considered as a key technology for future 5G wirelessnetworks. In order to overcome the severe propagation lossof mmWave channel, mmWave multiple-input multiple-output(MIMO) systems with analog/digital hybrid precoding and com-bining transceiver architecture have been widely considered.However, physical layer security (PLS) in mmWave MIMOsystems and the secure hybrid beamformer design have not beenwell investigated. In this paper, we consider the problem ofhybrid precoder and combiner design for secure transmissionin mmWave MIMO systems in order to protect the legitimatetransmission from eavesdropping. When eavesdropper’s channelstate information (CSI) is known, we first propose a joint analogprecoder and combiner design algorithm which can preventthe information leakage to the eavesdropper. Then, the digitalprecoder and combiner are computed based on the obtainedeffective baseband channel to further maximize the secrecy rate.Next, if prior knowledge of the eavesdropper’s CSI is unavailable,we develop an artificial noise (AN)-based hybrid beamforming ap-proach, which can jam eavesdropper’s reception while maintain-ing the quality-of-service (QoS) of intended receiver at the pre-specified level. Simulation results demonstrate that our proposedalgorithms offer significant secrecy performance improvementcompared with other hybrid beamforming algorithms.
Index Terms —Millimeter wave (mmWave) communications,multi-input multi-output (MIMO), physical layer security (PLS),hybrid precoding, artificial noise (AN).
I. I
NTRODUCTION
Millimeter wave (mmWave) communications, which canprovide orders-of-magnitude wider bandwidth than current cel-lular bands, has been considered as a key technology for future5G wireless networks [1]. The smaller wavelength of mmWavesignals enables a large antenna array to be packed in a smallphysical dimension at the transceiver ends. However, conven-tional full-digital precoder and combiner are realized using alarge number of expensive radio frequency (RF) chains andenergy-intensive analog-to-digital converters (ADCs), whichare impractical in the mmWave communication systems. Re-cently, economic and energy-efficient analog/digital hybridprecoding and combining transceiver architecture has emergedas a promising solution in mmWave multiple-input multiple-output (MIMO) systems. The hybrid beamforming structure applies a large numberof analog phase shifters (PSs) to implement high-dimensionalanalog beamformer and a small number of RF chains for low-dimensional digital beamformer to provide the necessary flex-ibility to perform multiplexing/multiuser transmission [2]. Theexisting hybrid beamforming designs can be categorized into i ) codebook-based scheme in which the analog beamformer isselected from certain candidate vectors, such as array responsevectors of the channel and discrete fourier transform (DFT)beamformers [3]-[5]; ii ) codebook-free scheme in which theinfinite resolution of PSs is assumed [6], [7]. Currently,the codebook-based beamforming designs are more popularbecause of the less complexity and satisfactory performancedue to the special structure of hybrid beamformer and thecharacteristic of mmWave MIMO channels.While existing hybrid beamforming designs focus on im-proving spectral efficiency of a point-to-point mmWave MIMOchannel, however, the secrecy in a mmWave MIMO wiretapchannel and the beamforming design for the secure transmis-sion have not been well investigated. In recent years, physicallayer security (PLS) has been identified as a promising strategyfor secure wireless communications. Especially, beamformingtechnology becomes a powerful tool for enhancing the physicallayer security in conventional MIMO systems [8], [9]. Withthe spatial degrees of freedom (DoF) provided by multiple an-tennas, the transmitter can adjust its beamforming orientationto reduce/prevent the information leakage to eavesdroppers orgenerate artificial noise (AN) to jam potential eavesdroppers.However, the obtained results cannot be directly applied tommWave MIMO systems due to the different propagationcharacteristics and the special hybrid beamforming archi-tecture. Therefore, secure transmission in mmWave MIMOsystems attracts new research interests [10]-[12].In [10], the network-wide PLS performance of a mmWavecellular network was investigated under a stochastic geom-etry framework. In [11], the authors considered a mmWavesystem with the multi-input single-output (MISO) channeland presented two simple beamformer designs for the securetransmission. Based on this system model, in [12] the authorsfurther introduced a new form of AN generation method ig. 1. The mmWave MIMO wiretap system with hybrid precoder andcombiners. The channel is modeled as scatterer-sharing model. depending on the propagation characteristics of the mmWavechannel. Unfortunately, all those mentioned works focus onthe comprehensive secrecy performance analysis rather thanthe beamformer design. More importantly, the presented sim-ple beamformer designs are based on the conventional full-digital beamforming architecture, which are not practical inthe mmWave MIMO systems comparing with the hybridbeamforming structure. To the best of our knowledge, thehybrid beamformer design for the secure transmission in themmWave MIMO systems has not been studied yet.In this paper, we investigate hybrid beamformer design forthe secure transmission and propose a novel codebook-basedhybrid precoder and combiner design algorithm in order toprotect the legitimate transmission from eavesdropping. Inthe case that eavesdropper’s channel state information (CSI)is available, we first develop a joint analog precoder andcombiner design algorithm which can prevent the informa-tion leakage to the eavesdropper. Then, the digital precoderand combiner are computed based on the obtained effec-tive baseband channel to further maximize the secrecy rate.Then, when prior knowledge of the eavesdropper’s CSI isunavailable, we introduce an AN-based hybrid beamformingapproach, which can generate disturbance to the eavesdropperwhile maintaining the quality-of-service (QoS) of the intendedreceiver at the pre-specified level. Simulation results demon-strate the significant secrecy performance improvement of ourproposed algorithms compared with other hybrid beamformingalgorithms.II. S YSTEM M ODEL AND P ROBLEM F ORMULATION
A. System Model
We consider a mmWave MIMO wiretap system as illustratedin Fig. 1, in which the legitimate transmitter Alice is equippedwith N a antennas and N RFa
RF chains to simultaneouslytransmit N s data streams to the legitimate receiver Bob, who isequipped with N b antennas and N RFb
RF chains. To ensure theefficiency of the communication with the limited number ofRF chains, we assume N RF = N RFa = N RFb and the numberof data streams is constrained as N s ≤ N RF . There also existsan eavesdropper Eve, who is equipped with N e antennas and N RFe
RF chains, N s ≤ N RFe , and attempt to overhear the datatransmission from Alice to Bob.The transmitted symbols are firstly processed by an N RF × N s baseband digital precoder F BB , then up-converted to theRF domain via N RF RF chains before being precoded withan N a × N RF analog precoder F RF . While the basebandprecoder F BB enables both amplitude and phase modifica-tions, the analog precoder F RF is implemented by analogcomponents like phase shifters and its elements are constrainedto satisfy with constant magnitude. In the codebook-basedprecoder scheme, the analog beamformer is selected from apre-specified codebook F , i.e. a set of N a × vector withconstant-magnitude entries. The normalized power constraintis given by k F RF F BB k F = N s . Therefore, the transmit signalhas a form of x = √ P F RF F BB s (1)where P is the transmitted power and s is the N s × symbolvector such that E { ss H } = N s I N s .Denote H b ∈ C N b × N a as the channel matrix of Alice-to-Bob channel. Let n b ∈ C N b × represent the noise vectorof independent and identically distributed (i.i.d.) CN (0 , σ b ) elements. At Bob, the received signal r b = H b x + n b (2)are first processed by the analog combiner of Bob W RF,b ,then the digital combiner W BB,b ∈ C N RF × N s . Let W b , W RF,b W BB,b and F , F RF F BB for simplicity. Thus, theprocessed receive signal at Bob can be expressed as ˆs b = √ P W Hb H b Fs + W Hb n b , (3)where the subscript “ b ” indicates Bob.The signal processing at Eve have the same procedure.Let H e ∈ C N e × N a denote the Alice-to-Eve eavesdroppingchannel and let n e ∈ C N e × represent the noise vectors ofi.i.d. CN (0 , σ e ) elements. Then, we have the processed receivesignal at Eve ˆs e = √ P W He H e Fs + W He n e , (4)where the subscript “ e ” indicates Eve. B. MmWave MIMO Channel Model
The mmWave MIMO channel can be described with thewidely used limited scattering channel, in which the number ofscatters is L , and each scatter is further assumed to contributea single propagation path between the transmitter and thereceiver. Under this model, the Alice-to-Bob channel matrix H b can be expressed as H b = s N a N b ρ b L b X l b =1 α l b a b ( θ l b ) a Ha ( φ l b ) , (5)where ρ b denotes the average path-loss between Alice andBob, and α l b is the complex gain of the l b -th path andassumed to be Rayleigh distributed. The variables θ l b ∈ [0 , π ] and φ l b ∈ [0 , π ] are the l b -th path’s azimuth angles ofdeparture or arrival (AoDs/AoAs) of the transmitter and thereceiver, respectively. a a ( φ l b ) and a b ( θ l b ) are the antennarray response vectors at the transmitter and the receiver,respectively. In this paper, we assume the transmitter and thereceivers adopt uniform linear arrays (ULA) for simplicity andthen a a ( φ l b ) and a b ( φ l b ) are given by a a ( φ l b ) = 1 N a [1 , e j (2 π/λ ) d sin( φ lb ) , ..., e j ( N a − π/λ ) d sin( φ lb ) ] T , (6) a b ( φ l b ) = 1 N b [1 , e j (2 π/λ ) d sin( θ lb ) , ..., e j ( N b − π/λ ) d sin( θ lb ) ] T , (7) where λ is the signal wavelength and d is the distance betweenantenna elements. The Alice-to-Eve channel matrix can bewritten in a similar fashion as H e = s N a N e ρ e L e X l e =1 α l e a e ( θ l e ) a Ha ( φ l e ) (8)with different AoAs θ l e and AoDs φ l e .Due to the sparse property of mmWave MIMO channel,mmWave communication is usually considered as more securethan conventional MIMO systems since the generated beam-former is too narrow to be eavesdropped if the Eve is not closeto Bob. However, it has been verified that rough surface andtiny building cracks can cause diffuse scattering in mmWavechannel and the diffuse range increases as the wavelengthshrinks [13]. Therefore, it is highly possible that differentreceivers share some common scatterers, as shown in Fig. 1.In other words, when Bob and Eve have similar AoDs withsome common scatterers and Alice use those AoDs to transmitthe secret information to Bob, Eve will have chance to receivevery strong signal from Alice, resulting in severe informationleakage. Therefore, it is easier for Eve to eavesdrop secretinformation in this scatterer-sharing model and we aim toinvestigate the physical layer security for the mmWave MIMOsystems with the scatterer-sharing model. C. Problem Formulation
In the context of physical layer security, the secrecy rate isusually used as the performance metric: R s = [log det( I N s + S b ) − log det( I N s + S e )] + (9)where S b = PN s R − n,b ( W BB,b ) H ( W RF,b ) H H b F RF F BB × F HBB F HRF H Hb W RF,b W BB,b , (10) S e = PN s R − n,e ( W BB,e ) H ( W RF,e ) H H e F RF F BB × F HBB F HRF H He W RF,e W BB,e , (11) R n,b = σ b ( W BB,b ) H ( W RF,b ) H W RF,b W BB,b , (12) R n,e = σ e ( W BB,e ) H ( W RF,e ) H W RF,e W BB,e . (13)In the following, we carry out simulations to illustrate thesecurity threaten in the mmWave MIMO systems. We assumeboth H b and H e are known to Alice and Bob and firstconsider the full-digital precoder and combiner scheme. Fig.2 shows the secrecy rate under beamforming designs with:1) no PLS effort; 2) generalized singular value decomposition(GSVD)-based PLS approach [9]; 3) generalized eigen decom-position (GED)-based PLS approach [8]. It can be verifiedthat the mmWave MIMO systems with ordinary (no PLS −30 −20 −10 0 10 20 30 40 50 60020406080100120 SNR (dB) S e c r e cy R a t e ( b / s / H z ) No PLSGSVDGED
Fig. 2. Secrecy rate versus SNR, full-digital precoder and combiner ( N a = N b = N e = 192 , N RF = 4 ). −30 −20 −10 0 10 20 30 40 50 60020406080100120 SNR (dB) S e c r e cy R a t e ( b / s / H z ) GED full−digitalPE, PLSSSP, PLS
Fig. 3. Secrecy rate versus SNR, hybrid precoder and combiner ( N a = N b = N e = 192 , N RF = 4 ). effort) beamforming design have notable information leakagein the high SNR range. Therefore, the legitimate transceiverneeds to adopt beamforming with PLS efforts. In addition,unlike the conventional MIMO system, the GSVD approachis not as good as the GED approach under mmWave MIMOsystems, which is because of the sparsity of the mmWavechannel. Therefore, we will use GED effort with full-digitalbeamforming as our secrecy performance benchmark in thefollowing simulation studies.In order to spotlight the impact of hybrid precoding andcombining architecture considered in this paper, in Fig. 3we conduct the simulation using two representative hybridbeamforming algorithms: 1) codebook-based Spatially SparsePrecoding (SSP) [3]; 2) codebook-free PE-AltMin (PE) [6].For the PLS effort, we use these two approaches to find securehybrid beamformers by minimizing the Euclidean distancebetween hybrid beamformers and the GED-based full-digitalsecure beamformers. Fig. 3 illustrates that the secrecy ratedecreases dramatically when mmWave MIMO systems employhybrid precoder and combiner, resulting in severe informationleakage to the eavesdropper. Moreover, the gap between thehybrid beamforming algorithms and the full-digital benchmarkis quite large, which awaits researchers’ investigation.Inspired by the phenomenon illustrated in Figs. 2 and 3, inthis paper we aim to develop a PLS-based hybrid precoder andcombiner design for the secure transmission. Specifically, let F and W denote the beamsteering codebooks for the analogprecoder and combiner, respectively. If B RFt ( B RFr ) bits areused to quantize the AoD (AoA), F and W will consist of allpossible analog precoding and combining vectors, which cane presented as F = { a t (2 πi/ B RFt ) : i = 1 , . . . , B RFt } , (14) W = { a r (2 πi/ B RFr ) : i = 1 , . . . , B RFr } . (15)The PLS-based hybrid precoder and combiner design problemcan be formulated as follows: { F ∗ RF , F ∗ BB , W ∗ RF,b , W ∗ BB,b } = arg max R s (16) s . t . F RF (: , l ) ∈ F , ∀ l = 1 , . . . , N RF , (17) W RF,b (: , l ) ∈ W , ∀ l = 1 , . . . , N RF , (18) k F RF F BB k F = N s . (19)In the next section, we divide the problem according tothe availability of the eavesdropper’s CSI. We first considerthe scenario under which Alice and Bob know eavesdropper’schannel H e and develop our codebook-based hybrid beam-former design algorithm. Then, we study the case where theeavesdropper’s CSI is not available and AN-aided methods areadopted in the hybrid beamforming design problem.III. S ECURE J OINT H YBRID B EAMFORMER AND C OMBINER D ESIGN
A. Known Eavesdropper’s Channel
Under this condition, our algorithm starts with performingsingular value decomposition (SVD) of H e as H e = U e Σ e V He (20)where U e and V e are unitary matrices, Σ e is an N e × N a diagonal matrix of singular values arranged in a decreasingorder. Due to the sparsity of the mmWave MIMO channel, H e can be represented as H e = e U e e Σ e e V He (21)where e Σ e is a diagonal matrix whose elements are the first L b nonzero singular values, e U e and e V e contain the most L b left columns of U e and V e , respectively.In an effort to prevent eavesdropping from Eve, Aliceshould elaborately design her precoder to avoid the AoDcomponents of H e in order to minimize Eve’s reception. Thus,to implement the secure transmission, we propose to removethe AoD components of H e from H b by H , H b ( I − e V e e V He ) . (22)By this operation, H contains only the AoD components of H b but almost no AoD component of H e . After this initialprocessing, we successively select the i -th ( i = 1 , . . . , N RF )analog precoder and combiner pair to maximize the cor-responding channel gain while suppressing the co-channelinterference. The joint design problem can be successivelysolved by the following optimization problem: { w ∗ i , f ∗ i } = arg max w i ∈W f i ∈F | w Hi H i f i | , i = 1 , . . . , N RF , (23)and then assign them to the analog procoder and combinermatrices F ∗ RF (: , i ) = f ∗ i , (24) W ∗ RF,b (: , i ) = w ∗ i . (25)Particularly, before executing the next iteration, we need toremove the components of previous determined precoders andcombiners from the other data streams’ channels such thatsimilar analog precoders and combiners will not be selectedby two different data streams. To achieve this goal, we let p i and q i be the components of the determined analog precoderand combiner for the i -th data stream, respectively. When i =1 , p = f ∗ and q = w ∗ ; when i > , the orthogonormalcomponent p i and q i can be obtained by a Gram-Schmidtprocedure: p i = f ∗ i − i − X j =1 p Hj f ∗ i p j , p i = p i / k p i k , i = 2 , . . . , N RF ; (26) q i = w ∗ i − i − X j =1 q Hj w ⋆i q j , q i = q i / k q i k , i = 2 , . . . , N RF . (27)Then H i +1 is updated for the next iteration by: H i +1 = ( I N b − q i q Hi ) H i ( I N a − p i p Hi ) . (28)After determining the analog precoder F ∗ RF and com-biner W ∗ RF,b , we can obtain the effective channel H eff , ( W ∗ RF,b ) H H b F ∗ RF . Then, an SVD-based baseband digitalprecoder is employed to further suppress the interference andmaximize the sum-rate: F ∗ BB = ¯V (: , N s ) , (29) W ∗ BB,b = ¯U (: , N s ) , (30)where H eff = ¯U ¯Σ ¯V H . Finally, we normalize the basebandprecoder F ∗ BB by F ⋆BB = √ N s F ∗ BB k F ∗ RF F ∗ BB k F . (31)This secure hybrid precoder and combiner design algorithm issummarized in Table I. B. Unknown Eavesdropper’s Channel
Under this condition, by common intuition, low-powerAlice-to-Bob transmission can improve the security by makingthe signal interception of Eve more difficult. Assume theAlice-to-Bob transmission needs to satisfy the QoS threshold R γ , i.e. R b ≥ R γ , R b = log det( I N s + S b ) . Thus, we canutilize the proposed algorithm in Table I with initialization H = H b to find the optimal precoder F ∗ RF , F ∗ BB andcombiner W ∗ RF,b , W ∗ BB,b . Then, we can find the minimumtransmit power P s such that R b ≥ R γ can be satisfied.To further increase the security, the residual power P AN , ( P − P s ) + is utilized for generating AN.In this AN-based secure transmission, we assume N RF >N s and the transmit signal becomes x = F RF ( p P s F BB s + p P AN F BB,w w ) , (32) ABLE IS
ECURE H YBRID P RECODER AND C OMBINER D ESIGN A LGORITHM WITH
CSI OF E VE . Input: F , W , H . Output: F ∗ RF , F ∗ BB , W ∗ RF,b , and W ∗ BB,b . for i = 1 : N RF { w ∗ i , f ∗ i } = arg max w i ∈W f i ∈F | w Hi H i f i | ; F ∗ RF (: , i ) = f ∗ i ; W ∗ RF,b (: , i ) = w ∗ i ; if i = 1 p i = f ∗ i , q i = w ∗ i . else p i = f ⋆i − i − P j =1 p Hi f ∗ i p i , p i = p i / k p i k ; q i = w ∗ i − i − P j =1 q Hj w ∗ i q j , q i = q i / k q i k . end if H i +1 = ( I N b − q i q Hi ) H i ( I N a − p i p Hi ) . end for Obtain F ∗ BB and W ∗ BB,b by (29)-(31). where w represents the ( N RF − N s ) × artificial noise vector, E { ww H } = N RF − N s I N RF − N s , F BB,w is the digital precoderassociated with the AN w . The idea behind the AN-based PLSapproach is that the generated AN should not degrade thereception of Bob. To ensure this principle with the obtainedoptimal combiners W ∗ BB,b and W ∗ RF,b , we should have W ∗ HBB,b W ∗ HRF,b H b F ∗ RF F BB,w = (33) ⇒ W ∗ HBB,b H eff F BB,w = (34)where H eff , W ∗ HRF,b H b F ∗ RF and H eff = ¯U ¯Σ ¯V H by SVD. If N s < N RF , with the optimal W ∗ BB,b obtained by W ∗ BB,b = U (: , N s ) as in (30), the digital precoder F BB,w for theAN should have a form of F ∗ BB,w = V (: , N s + 1 : N RF ) . (35)Finally, we normalize the AN digital precoder as F ⋆BB,w = F ∗ BB,w k F ∗ RF F ∗ BB,w k F . (36)This AN-based secure hybrid precoder and combiner designalgorithm is summarized in Table II.IV. S IMULATION S TUDIES
In this section, we illustrate the simulation results ofthe proposed hybrid precoder and combiner design for se-cure transmission in mmWave MIMO systems. Consider ammWave MIMO wiretap system in which Alice, Bob andEve are all equipped with N a = N b = N e = 192 ULAantennas. The antenna spacing of all ULAs is d = λ . TheAoA/AoD is assumed to be uniformly distributed in [0 , π ] .We assume there exists 20 scatterers from which Bob and Everandomly select ∼ scatterers as propagation paths with acertain probability that Bob and Eve may share some commonscatterers. For simplicity, the noise variance σ b and σ e are setto 1. The codebooks consisting of array response vectors as TABLE IIS
ECURE H YBRID P RECODER AND C OMBINER D ESIGN A LGORITHMWITHOUT
CSI OF E VE . Input: F , W , H = H b , P , R γ . Output: F ∗ RF , F ∗ BB , W ∗ RF,b , W ∗ BB,b , F ∗ BB,w , P s , and P AN . Obtain optimal precoder F ∗ RF , F ∗ BB and combiner W ∗ RF,b , W ∗ BB,b using Algorithm in Table I. Determine minimum P s such that R b ≥ R γ . AN power P AN , ( P − P s ) + . AN digital precoder F ∗ BB,w = V (: , N s + 1 : N RF ) . Normalization F ⋆BB,w = F ∗ BB,w k F ∗ RF F ∗ BB,w k F . (6) and (7) with 128 angle resolutions are uniformly quantizedin [0 , π ] .We first consider the case that Eve’s CSI is known andevaluate the proposed secure hybrid beamforming design al-gorithm in Table I. For the comparison purpose, the repre-sentative codebook-based Spatially Sparse Precoding (SSP)algorithm with PLS effort and without PLS effort is alsostudies. For the fairness, we only focus the codebook-basedalgorithm and will not consider the codebook-free algorithms.The full-digital beamforming design is also included as theperformance benchmark. Fig. 4 shows secrecy rate versus SNRfor different beamforming design algorithms. The number ofRF chains is set as N RF = 2 , and the number of data streamsis also N s = 2 . It can be observed from Fig. 4 that ourproposed algorithm can significantly outperform SSP algo-rithm in terms of secrecy rate. This result illustrates that ourproposed algorithm can more efficiently prevent eavesdroppingin the mmWave MIMO systems. However, we also noticethat our algorithm still has a notable gap between full-digitalbenchmark, which inspires us to pursue a more efficient hybridalgorithm in the future. In Fig. 5, a similar simulation is carriedout with larger number of RF chains N RF = 4 and largernumber of data streams N s = 4 . The similar conclusion canbe drawn.Next, we focus on the case that the eavesdropper’s CSI isunknown. The number of RF chains is set as N RF = 8 , and thenumber of data streams is N s = 4 . Fig. 6 shows the spectrumefficiency of Bob R b , spectrum efficiency of Eve R e , and theresulting secrecy rate R s = ( R b − R e ) + with the requiredlegitimate transmission QoS R γ . It can be clearly observed thatour proposed AN-based algorithm can dramatically reduce R e by adding AN in the transmit signaling while maintaining therequired QoS R b . Therefore, our proposed AN-based hybridbeamforming design can implement secure transmission evenwhen the CSI of the passive eavesdropper is unknown. In Fig.7, we repeat the similar simulation by increasing the numberof RF chains to N RF = 16 . The secrecy performance becomesbetter since more spatial DoF can be utilized for generatingAN to interrupt Eve’s reception.V. C ONCLUSION
In this paper, we proposed a hybrid precoder and combinerdesign for secure transmission in a mmWave MIMO wiretapsystem. With the eavesdropper’s CSI, a joint analog precoder
10 −5 0 5 10 15 20 25 30510152025303540
SNR (dB) S e c r e cy r a t e ( b / s / H z ) GED full−digitalSSP, w./o PLSSSP, w. PLSOUR
Fig. 4. Secrecy rate versus SNR ( N a = N b = N e = 192 , N RF = 2 , and N s = 2 ). −10 −5 0 5 10 15 20 25 3001020304050607080 SNR (dB) S e c r e cy r a t e ( b / s / H z ) GED full−digitalSSP, w./o PLSSSP, w. PLSOUR
Fig. 5. Secrecy rate versus SNR ( N a = N b = N e = 192 , N RF = 4 , and N s = 4 ). and combiner design algorithm was proposed to prevent theinformation leakage to the eavesdropper. When eavesdropper’sCSI is unknown, we developed an AN-based hybrid beam-forming approach, which can jam the eavesdropper’s receptionwhile maintaining the required QoS of the intended receiver.Simulation results demonstrated the significant secrecy perfor-mance improvement of our propose algorithms compared withother hybrid beamforming algorithms.R EFERENCES[1] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G.N. Wong, J. K. Schulz, M. Samimi and F. Gutierrez “Millimeter wavemobile communications for 5G cellular: It will work!”
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