Beamforming and Power Allocation for Physical-Layer Security in Hybrid RF/VLC Wireless Networks Mohamed F. Marzban† , Mohamed Kashef ‡ , Mohamed Abdallah† § , Mohamed Khairy† †
Electronics and Electrical Communications Engineering, Cairo University, Giza, Egypt Email:
[email protected],
[email protected] ‡ Electrical and Computer Engineering, Texas A&M University at Qatar, Doha, Qatar Email:
[email protected] § Division of Information and Computing Technology, College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar Email:
[email protected] Abstract—Visible light communication (VLC) has emerged as a promising candidate to complement and enhance the performance of the existing radio frequency (RF) networks in indoor environments. Due to the broadcast nature of both RF and VLC channels, improving the transmission confidentiality is a requirement in practical wireless networks. Physical-layer security has emerged to provide a first line of defense against eavesdropping attacks. In this paper, we study the physical layer security problem of a hybrid RF/VLC system. First, we formulate the minimization problem of the consumed electrical power in the hybrid RF/VLC network while satisfying the user’s required secrecy rate. Then, we propose a zero forcing beamforming strategy and a minimum power allocation algorithm. Simulations results show that the proposed power allocation and beamforming algorithms outperform the benchmark algorithms in terms of the average consumed electrical power in various indoor scenarios. Index Terms—Physical Layer Security ; Beamforming; VLC.
I. I NTRODUCTION White light emitting diodes (LEDs) have high energy efficiency compared to conventional incandescent and fluorescent light bulbs [1]. Moreover, the light intensity of the LEDs can be varied at high rates to allow data modulation without affecting the illumination level or bothering the human eye [2]. That’s why white LEDs have paved the way for visible light communication (VLC). At a VLC transmitter, intensity modulation is performed to encode the data signal over the light waves. At the receiver side, photodiode is used to transform the incident optical power to an electrical signal, after which demodulation occurs. As a result, VLC can be considered as an energy efficient solution that provides data communication on the visible spectrum along with illumination. Heterogeneous networks (Het-Nets) are developed as a promising network architecture that provides collaboration between multiple radio access networks (RANs) to serve the intended users. The diversity introduced from RANs having different operating capabilities can significantly enhance the network performance. Radio resource allocation in Het-Nets is considered a major challenge due to the complexity of managing networks with different service requirements [3], [4]. Aside from the network diversity gains obtained from combining two different networks, hybrid RF/VLC networks have other advantages due to the different propagation characteristics of the radio and light waves. Light waves do not
penetrate the walls which protect the signal considerably from interference. However, line of sight (LOS) is essential for high data rate VLC transmissions. In contrast, the RF spectrum is very congested and therefore, the RF signal is susceptible to interference from existing nearby RF transmitters. The main advantage of RF networks over VLC ones is their high non line of sight (NLOS) reliability. The various network gains obtained from RF/VLC collaborations have been considered in many papers [5]–[8]. The huge increase in the offered wireless services makes data privacy and confidentiality major concerns for users. Upper layers security techniques including access control mechanisms and encryption are typically implemented. These techniques require extra computational and storage capabilities at users which may be not always enough to achieve the required security level. Hence, physical-layer security has emerged to complement the existing security techniques and to add another level of security that may be required for specific applications. Physical-layer security techniques exploit channel characteristics in securing information from eavesdroppers without the help of upper layers [9]. This can be achieved by sacrificing a fraction of the authorized user’s communication rate to confuse the eavesdroppers. Although VLC depends on LOS propagations, its channel is still a broadcast channel. VLC transmissions are susceptible to be overheard by unauthorized users located at the area illuminated by the data transmitters. The security aspects of VLC networks have been considered in few papers. In [10], lower and upper bounds on the achievable VLC secrecy rates are obtained. Key-extraction security approach for VLC systems is considered in [11] while secrecy using massive LED arrays is considered in [12]. In [13], The authors obtained an optimal transmit beamforming and jamming precoding strategies for a VLC network in the presence of multiple eavesdroppers. In this paper, we consider the physical layer security in a hybrid RF/VLC network comprising of a single VLC access point (AP) and a single RF AP. Following the increasing demands for minimizing the transmission power in wireless networks, we formulate the minimization problem of the weighted sum of consumed power in both networks. The problem is constrained to satisfy the users secrecy require-
ments. Efficient beamforming and power allocation algorithms are proposed. We evaluate the performance of our proposed algorithms in various indoor scenarios. To the best of our knowledge, none of the previous research has considered the physical layer security in a hybrid RF/VLC setting. II. S YSTEM M ODEL We consider an indoor downlink scenario consisting of an RF AP and a VLC AP. Both APs are required to cooperate in sharing confidential information to a receiver in the presence of an eavesdropper that lies within the coverage of both APs. We follow the notations used in security research by referring to the intended receiver as Bob and the eavesdropper as Eve. Both Bob and Eve are equipped with multi-homing capability that provides concurrent association to both networks [3]. For the RF communications, let hRF and gRF denote the channel gains connecting the RF AP with Bob and Eve, respectively. We consider the WINNER II (A1) channel model for residential/indoor office propagation scenarios [14]. In this model, the pathloss is expressed as, fc + X, (1) P L[dB] = Alog10 (dRF ) + B + Clog10 5 where fc is the carrier frequency in GHz. A, B and C are constants that depend on the propagation model, dRF represents the distance between the RF AP and the receiver, X represents the wall attenuation in an indoor NLOS scenario. For LOS scenario, A = 18.7, B = 46.8 and C = 20. In NLOS scenario, A = 36.8, B = 43.8, C = 20 and X = 5(nw − 1) in case of light walls while X = 12(nw − 1) in case of heavy walls where nw is the number of walls between the RF AP and the receiver. The RF channel average power gain can be defined −P L[dB] as, γRF = 10 10 . The instantaneous channel gain for the RF channel follows Rayleigh distribution and is denoted by hRF . Considering a MISO setting where the RF AP contains MRF antennas, we exploit the multiple antennas at the AP to beamform the signal and maintain security. let sRF denote the (MRF × 1) beamformed RF signal transmitted to Bob. Let nb,RF and ne,RF denote the scaler Additive White Gaussian Noise (AWGN) at Bob and Eve, respectively. Without loss of generality, we assume that Bob and Eve have equal thermal noise spectral density denoted by N0,RF . Thus, the received signal at Bob and Eve can be represented respectively by, yRF = hTRF sRF + nb,RF , and
T zRF = gRF sRF + ne,RF .
The beamformed signal (sRF ) can be expressed as, p sRF = PRF wRF xRF .
(2) (3)
(4)
where wRF is the normalized MRF × 1 beamformer vector, xRF denotes the scaler data symbol, and PRF is the power transmitted by the RF AP. For the VLC communication, we consider a VLC AP consisting of a number of light fixtures. Each fixture is comprised of a group of LEDs. Let these LEDs be driven by a constant DC bias current Ivlc . The VLC AP contains a data
encoder that encodes raw bits to produce xvlc which is a zeromean pulse amplitude modulated (PAM) current data signal. xvlc is superimposed on Ivlc to form the composite current signal xvlc + Ivlc which is then transmitted over the wireless medium. In contrast to RF networks, VLC communication is constrained by an amplitude constraint to allow linear current-light conversion at the transmitter [10]. This amplitude constraint can be expressed as follows, |xvlc | ≤ Ivlc ,
(5)
where ∈ [0, 1]. The instantaneous produced optical power by the VLC AP can be expressed as, Popt,vlc = kvlc (Ivlc + xvlc ), where kvlc (watt/Amp) is a proportionality factor that depends on the LED characteristics and represents the efficiency of transforming the electrical signal to optical one at the VLC transmitter. Since xvlc is a zero-mean signal, we can deduce that the mean transmitted optical power is constant with kvlc Ivlc which controls the room illumination. Therefore, the room illumination level is independent on the modulated signal xvlc . The optical signal is then transmitted through a channel of gain hvlc . We consider a VLC LOS model whose channel gain is given by [15], ( ARX 1 m ; |ψ| ≤ ψFoV 2π (m + 1)cos (φ) d2vlc cosψ hvlc = 0 ; |ψ| > ψFoV (6) where m = log −log2 represents the order of Lambertian (cosφ 1 ) 2
emission with half irradiance semi-angle of φ 21 , the variable dvlc represents the LOS distance between the light fixture and the receiver, ψFOV denotes the field of view (FoV) semiangle, ψ represents the angle of incidence while φ is the angle of irradiance. All these angles characterize the VLC channel gain. The receiver collection area can be described 2 as, ARX = sin2 n(ψFoV ) APD , where APD is the detector physical area and n is the refractive index. At the VLC receiver, the photo-detector collects the incident optical power, transforms it to an electrical signal and then the DC bias is removed. Hence, the received signal at Bob and Eve are given respectively by, yvlc = ρvlc kvlc hvlc xvlc + nb,vlc and
zvlc = ρvlc kvlc gvlc xvlc + ne,vlc ,
(7) (8)
where ρvlc (Amp/watt) is the responsivity of the photo-detector at the VLC receiver which transforms the optical signal to an electrical one, hvlc and gvlc represent the channel gains for Bob and Eve, respectively nb,vlc and ne,vlc are the AWGN at Bob and Eve, respectively. Without loss of generality, we assume that both noise signals have equal shot noise of N0,vlc . We account for a VLC AP consisting of Mvlc light fixtures, each of which experience different channel gains. Each fixture is comprised of Nvlc LEDs, all of which lie in proximity close enough that their channel gains to a single receiver are identical. The channel amplitude gains hvlc and gvlc are therefore represented by an Mvlc × 1 vector. Hence, the signal received at Bob and Eve can be represented respectively by, yvlc = ρvlc kvlc hTvlc wvlc Nvlc xvlc + nb,vlc ,
(9)
and
T zvlc = ρvlc kvlc gvlc wvlc Nvlc xvlc + ne,vlc ,
(10)
where wvlc is the Mvlc × 1 VLC beamformer vector. The transmitted signal is constrained by the amplitude constraint defined in equation 5. However on having multiple antennas, the beamformer weights can violate such constraint. Therefore, the amplitude constraint is extended to cope with the MISO setting and the beamformer VLC constraint is expressed as, |wvlc | 1,
(11)
where is the element-wise inequality, |.| denotes the element-wise absolute value, and 1 denotes the all-ones vector. The total consumed power is very critical as it determines the operational cost of using the VLC network. It can be obtained by calculating the variance of the transmitted signal as follows,
where Bvlc denotes the VLC channel BW. Our ultimate goal is to exploit the diversity obtained from the hybrid RF/VLC network in ensuring the secrecy of Bob’s data while lowering the system consumed power. Moreover, in order to cope with the current state-of-the-art radio resource allocation strategies, we focus on minimizing the weighted sum of consumed electrical power for economic and environmental reasons as follows, Minimize
PVLC , PRF , wRF , wvlc
2 T T αNvlc wvlc wvlc Pvlc + (1 − α)wRF wRF PRF
(17) s.t. RRF + Rvlc ≥ γ,
(a)
PRF ≤ PRF,max ,
(b)
Pvlc ≤ Pvlc,max ,
(c)
(12)
T gRF wRF = 0
(d)
where Pvlc denotes the average consumed electrical power for data transmission per LED which is the variance of xvlc . At the receiver, the total received power (Pvlc,rx ) which affects the achieved data rate can be given by,
T gvlc wvlc = 0 T wRF wRF ≤ 1
(e) (f )
|wvlc | 1
(g)
2 T Pvlc,tx = Nvlc wvlc wvlc Pvlc ,
Pvlc,rx = (ρvlc kvlc hTvlc wvlc Nvlc )2 Pvlc .
(13)
III. P ROBLEM F ORMULATION The RF MISO secrecy capacity has been considered in [16]. It is shown that the secrecy rate achieved using zero forcing (ZF) beamforming is very close to optimal when there is low correlation between Eve’s and Bob’s channels which is the case in most wireless channels where fading exists. ZF beamforming is ensured when the beamformer weight (wRF ) T is in the null space of Eve’s channel as follows, gRF wRF = 0. In this scenario, the RF secrecy rate can be represented using Shannon’s capacity formula as follows, PRF (hTRF wRF )2 BRF log2 1 + , (14) RRF = 2 N0,RF BRF where BRF represents the RF channel BW. Under the typical scenario where the WLAN operation is carried out in an unlicensed band, we consider the effect of neighbouring NLOS RF APs transmitting on similar channels and interfering on the reception of Bob. Hence, the RF secrecy rate can be represented by, PRF (hTRF wRF )2 BRF P log2 1 + , (15) RRF = 2 N0,RF BRF + i Pi h2i where Pi represents the power of interfering AP i and hi represents the NLOS channel gain between interfering AP i and Bob. For VLC, the MISO secrecy capacity is investigated in [10]. Similar to the RF case, zero forcing beamforming in VLC networks is a sub-optimal beamforming strategy with much lower complexity. The ZF strategy ensures nulling the data T rate at Eve, i.e. gvlc wvlc = 0. In such case, the MISO VLC secrecy rate can be expressed as, Bvlc 2Pvlc,rx RVLC = log2 1 + , (16) 2 πeN0,vlc Bvlc
where α < 1 is a weighting factor that focuses the power minimization on any of the two networks, γ denotes Bob’s total required secrecy rate. Constraint (a) ensures meeting Bob’s secrecy rate requirements. Upper bounds are set on the allowable transmission power in RF and VLC networks through constraints (b) and (c), respectively. The RF unity power is maintained through constraint (f ). The above problem can be solved using a two-stage approach. In the first stage we obtain the best ZF beamformer weights and in the second stage we obtain the minimum power allocation strategy. IV. B EAMFORMER V ECTORS A. RF Beamformer Vectors The problem that aims to obtain the best RF beamformer weights that maximizes Bob’s channel gain while maintaining it secure from Eve can be expressed as, Maximize hTRF wRF wRF
(18)
s.t. T wRF wRF T gRF wRF
≤1
(a)
=0
(b).
In problem (18), the objective function is linear and both constraint functions are convex. Therefore, it is a convex optimization problem and can be solved using the Lagrangian duality [17]. The Lagranian function augments the objective function with the constraint functions and can be expressed as, T T L = −hTRF wRF + λRF (wRF wRF − 1) + νRF (gRF wRF ),
(19)
where, λRF and νRF are Lagrangian multipliers for the inequality and equality constraints, respectively. By applying Karush Kuhn Tucker (KKT) conditions ( ∇L = 0 ) we obtain the optimum RF beamformer vectors as, ∗ wRF =
hRF − νRF gRF . 2λ
(20)
Using the Lagrangian duality, we can transform problem (18) into a secondary optimization problem with the same solution [17]. The Dual function (G) is the minimum value of the Lagrangian function over wRF which can be given by, T −hTRF hRF νg T hRF ν 2 gRF gRF + RF − − λ (21) wRF 4λ 2λ 4λ The dual problem is then expressed as,
G = inf L =
max
λRF ≥0,νRF
T −hTRF hRF νg T hRF ν 2 gRF gRF + RF − −λ 4λ 2λ 4λ
(22)
By applying the KKT conditions over the dual problem, we can find the optimum values of the Lagrangian multipliers ∗ (νRF , λ∗RF ) as follows, ∗ νRF =
"r λ∗RF =
hTRF gRF T g gRF RF
(23)
2 T T h hTRF hRF − 2νRF gRF RF + νRF gRF gRF 4
#+ (24)
B. VLC Beamformer Vectors Similarly, the VLC beamformer problem is formulated with the target of maximizing Bob’s VLC channel gain [10]. The problem is constrained with the VLC amplitude constraints and the zero forcing beamforming constraint as follows, Maximize hTvlc wvlc
Fig. 1: Location of RF AP and VLC light fixtures TABLE I: RF network simulation parameters Parameter Carrier Frequency (fc ) Number of transmit antennas (MRF ) Thermal Noise Spectral density (N0,RF ) Bandwidth (BRF ) Maximum Allowable RF power (PRF,max )
where, λ, ν and ξ are Lagrangian multipliers, ζvlc and ζRF are given respectively by, ζvlc =
(25)
wvlc
s.t. wvlc 1
(a)
wvlc −1
(b)
T gvlc wvlc
(c)
=0
Value 3 GHz 4 10−21 watts/Hz 10 MHz 1 watt
2(Nvlc ρvlc kvlc hTvlc wvlc )2 πeN0,vlc Bvlc
(28)
(hTRF wRF )2 . N0,RF BRF
(29)
ζRF =
By applying the KKT conditions, we can obtain optimal RF ∗ ∗ and VLC powers (PRF , Pvlc ) as,
Amplitude constraints (a) and (b) are used instead of constraint 17 (g) to obtain linear functions. Problem (25) has a linear objective function in addition to linear equality and inequality constrains. Hence it can be solved using any linear programming optimizer. V. P OWER M INIMIZATION After obtaining the beamformer vectors, the power minimization problem formulated in problem (17) can be represented by, 2 T T Minimize αNvlc wvlc wvlc Pvlc + (1 − α)wRF wRF PRF Pvlc , PRF
(26)
s.t. RRF + Rvlc ≥ γ,
(a)
PRF ≤ PRF,max ,
(b)
Pvlc ≤ Pvlc,max ,
(c)
Problem (26) is a convex optimization problem and can be solved using the Lagrangian duality. Hence, the Lagrangian function can be expressed as, 2 T T L = αNvlc wvlc wvlc Pvlc + (1 − α)wRF wRF PRF BRF Bvlc +λ γ− log2 (1 + ζRF PRF ) − log2 (1 + ζvlc Pvlc ) 2 2 + ξ(PRF − PRF,max ) + ν(Pvlc − Pvlc,max )) (27)
∗ PRF =
∗ Pvlc =
λ∗ BRF −1 + T w ) ζRF 2ln(2)(ξ ∗ + (1 − α)wRF RF
(30)
−1 λ∗ Bvlc + 2 wT w ∗ ζvlc 2ln(2)(αNvlc vlc vlc + ν )
(31)
By applying the complementary slackness conditions, we can obtain the optimal values of the Lagrangian multipliers. i.e. λ∗ (γ − RRF − Rvlc ) = 0
(32)
∗ ξ ∗ (PRF − PRF,max ) = 0
(33)
∗ ν ∗ (Pvlc − Pvlc,max ) = 0
(34)
VI. R ESULTS AND D ISCUSSIONS In this section, we assess the performance of the hybrid RF/VLC system from physical-layer security point of view. We observe the consumed electrical power to achieve Bob’s required secrecy rate. An indoor environment having dimensions of 5×5×3 m3 is considered where the RF AP is located at the center of the room at one meter height. We consider a VLC AP comprising of four light fixtures fixed in the room’s ceiling and directed vertically downwards. The coordinates of these fixtures are (5/3,5/3,3), (5/3,10/3,3), (10/3,5/3,3) and (10/3,10/3,3) as depicted in Fig. 1. We consider the tilt in Bob’s and Eve’s orientation compared to the fixtures by
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Fig. 2: Consumed electrical power by the RF/VLC APs with respect to Bob’s location in the room 20
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Fig. 3: Achieved secrecy rate by the RF/VLC APs with respect to Bob’s location in the room allowing ψ = uniform [ φ − π6 , φ + π6 ]. The RF network parameters are depicted in Table I while the VLC network parameters are obtained from [18] as depicted in Table II. We set α = 0.5 to balance the power minimization between the two networks. The required secrecy rate by Bob (γ) is set to 50 Mbps. It is assumed that Eve’s location is fixed at (1.9,3.7,0.85).
depends on Bob and Eve’s orientation as well as the distance between the light fixtures and Bob/Eve. So, as Bob gets closer to Eve, their VLC channels becomes more dependent and Bob’s null space becomes very close to Eve’s null space. In contrast, the RF has a probabilistic channel model and the effect on the correlation between Bob and Eve channels as Bob gets closer to Eve is much less than the VLC case.
We consider four RF interferers in neighbouring rooms with one light wall between each of them and Bob. Each interferer has a transmission power of Pi = 17 dbm and is located ten meters away from Bob. Fig. 2 depicts the consumed electrical power and the achieved secrecy rate by the RF AP using the proposed power allocation and beamforming schemes. The figures are drawn with reference to Bob’s location in the room. It is assumed that Bob’s height is always fixed at desktop height (0.85 m). Fig. 3 depict the consumed power and the achieved secrecy rate by Bob using the proposed scheme for power allocation and ZF beamforming.
In Fig. 4, we compare the performance of our proposed power allocation strategy in hybrid RF/VLC networks with the secrecy rate achieved using ZF beamforming in RF-only and VLC-only networks. It is assumed that Bob’s location is fixed at (1,1,0.85). As expected, the proposed beamforming and power allocation strategy achieves considerable power gains (> 10dbm) over the two benchmarks. In case of zero nearby RF interferers, the whole secrecy rate is achieved through the RF AP due to its better LOS channel. However, by the introduction of the first NLOS RF interferer, cooperation occurs between the two APs to achieve required secrecy rate with minimum power consumption.
We can notice that there is an increase of the RF secrecy rate achieved in the middle of the room where the RF AP is located. Similarly, there is an increase in the achieved VLC secrecy rate as we get closer to the VLC Light fixtures. However, at one corner of the room at (x=0:2, y=3:5), more power is consumed to achieve the required secrecy rate. Compared to the other three corners, this corner specifically witness an increase in the RF share of the achieved secrecy rate as Eve is located in this corner. The VLC has a deterministic channel model which
In Fig. 5, we consider a scenario where the RF AP is located outside the room at coordinates (12,6,1) with no RF interferers. RF NLOS channel model is considered with three heavy walls laying between the RF AP and Bob/Eve. We compare the performance of the proposed algorithm with respect to the two benchmarks (RF-only and VLC-only) and we draw the consumed electrical power to achieve Bob’s required secrecy rate. At low number of RF antennas, the RF beamforming
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This publication was made possible by the NPRP award [NPRP 9-077-2-036] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the author[s].
R EFERENCES
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tion radio resource allocation algorithm. The hybrid use of RF and VLC systems achieved the required secrecy rate with much improvement in the consumed electrical power compared with the RF-only and the VLC-only systems. In case of no RF interferers and LOS availability, minimum power physical layer security can be achieved from counting only on the RF AP. However, in more practical scenarios where NLOS RF interferers exisits, minimum power consumption can only be attained in the hybrid RF/VLC network. In case of absence of LOS between the RF AP and the receiver, power savings occurred as well in the hybrid RF/VLC systems compared with the two benchmarks. ACKNOWLEDGMENT
16
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number of RF Antennas
Fig. 5: Achieved secrecy rate by the VLC and RF APs with respect to the number of RF interferers could not maintain strong channel gains to Bob while zeroforcing Eve’s channel gain. Therefore high power consumption occurred in case of RF-only networks. The RF beamforming ability improves as the number of RF antennas increases and subsequently, the consumed electrical power decreases. The hybrid RF/VLC combined the benefits of the RF-only and the VLC-only systems and met Bob’s secrecy rate requirements with much power savings due to the diversity gain included. VII. C ONCLUSION The research in the area of physical-layer security in wireless communications has been motivated by the privacy and confidentiality requirements. We proposed a zero-forcing beamforming strategy along with minimum power consumpTABLE II: VLC network simulation parameters Parameter Number of Light Fixtures Number of LEDs in each fixture Maximum power per LED (Pvlc,max ) Bandwidth (Bvlc ) half irradiance semi-angle (φ 12 ) Shot Noise (N0,vlc ) Receiver field of view (ψFoV ) Lens refractive index (n) Detector Physical Area (APD ) Responsivity at VLC AP (kVLC ) Receiver photodetector responsivity (ρVLC )
Value 4 72 0.3 Watt 20 MHz 60◦ −21 2 10 A /Hz 85◦ 1.5 1cm2 0.54 watt/A 0.8 A/watt
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