Effective Channel Perturbation based on CyclicDelay for Physical Layer Security in OFDM Systems

Yuh-Ren TsaiInstitute of Communications Engineering

National Tsing-Hua UniversityHsinchu, 30013, Taiwanyrtsai@ee.nthu.edu.tw

Chia-Wei TaiMediaTek Inc.

Hsinchu, 30013, Taiwanfred770908@hotmail.com

Kai-Jie YangRealtek Semiconductor Corp.

Hsinchu, 30013, Taiwand919608@oz.nthu.edu.tw

Abstract—Orthogonal frequency division multiplexing(OFDM) offers a promising solution for emerging high-data-rateservices. Moreover, physical layer security was proposed asan alternative way to provide information security in wirelesscommunications. In this work, we focus on improving physicallayer security in OFDM systems. Our approach perturbs theeffective channels observed at eavesdroppers by nonlineardistortion, while maintaining the same effective channelexperienced at the intended receiver. At the transmitter, theperturbation on eavesdropper’s effective channel is randomand can be changed on a symbol-by-symbol basis based onthe known original channel state information (CSI). At theintended receiver, no additional information or informationexchange with the transmitter is required for data detection. Wederive the results of the proposed scheme for the multiple-inputsingle-output single-antenna-eavesdropper (MISOSE) wiretapchannel. According to simulations, the proposed scheme canseverely degrade the receiving performance at eavesdroppersand outperform the artificial-noise-based approaches in theperformance measure of BER.

Keywords—Physical layer security; orthogonal frequency divi-sion multiplexing (OFDM); channel perturbation; artificial noise(AN).

I. INTRODUCTION

In radio communications, data transmission between atransmitter and an intended receiver is vulnerable to maliciouseavesdroppers because of the broadcasting nature of wirelesspropagation. The technologies to ensure information securitybased on physical layer manners have been studied and pro-posed as an alternative way to retain or even improve thesecurity of wireless communications. In a pioneering work[1], Wyner investigated secure communication over a discretememoryless wiretap channel, where secrecy capacity was firstproposed as a metric used to evaluate the level of physical layersecurity. When the channel capacity between a transmitter andthe intended receiver is larger than that between the transmitterand an eavesdropper, the value of secrecy capacity is positiveand a secure transmission from the transmitter to the intendedreceiver is available; otherwise, secrecy capacity is equal tozero and a secure transmission between the transmitter andthe intended receiver is impossible. Following Wyner’s work,the secrecy capacity of a Gaussian wiretap channel was derivedin [2]. Recently, some studies investigated the secrecy capacityof fading wiretap channels [3]-[5].

†This work was supported in part by the Ministry of Science and Technol-ogy, Taiwan, R.O.C., under Grant NSC 101-2628-E-007-014-MY2.

Considering that multiple antennas will become a stan-dard functionality of wireless equipment in the future, securecommunication over multiple-input multiple-output (MIMO)or multiple-input single-output (MISO) channels has attractedincreasing attention recently [6]-[11]. In [6]-[8], the se-crecy capacity of MISO/MIMO channels with perfect chan-nel state information (CSI) was studied. In addition toinformation-theoretic analysis, many recent works target thedesign and optimization of secure transmission techniques overMISO/MIMO channels. In [9]-[11], the artificial noise (AN)-embedded beamforming schemes were proposed to improvethe secrecy capacity of a MIMO system. The basic concept ofAN methods is to use a fraction of the transmission power togenerate an additional AN signal projected to the null spaceof the desired channel at the intended receiver. Hence, onlythe eavesdropper is impacted by the generated AN, and theintended receiver is not affected. By slightly sacrificing thereceived signal-to-noise power ratio (SNR) at the intendedreceiver, AN methods can degrade the received SNR at aneavesdropper at the same time, thereby increasing the secrecycapacity.

In this work, we focus on improving physical layer securityin OFDM systems. For the investigation of physical layersecurity, it is generally assumed that both the transmitter andthe intended receiver have full CSI of the desired channelbetween them; while an eavesdropper has not only the fullCSI of the eavesdropping channel but also the full CSI ofthe desired channel. Different from the AN methods, whichtry to contaminate the signal received at eavesdroppers byadding artificial noise, we aim to perturb the effective channelsobserved by eavesdroppers based on introducing cyclic delayin OFDM systems, but still maintain the same effective channelexperienced at the intended receiver, which is equivalent tocontaminating the signal received at eavesdroppers by non-linear distortion. We refer to the proposed scheme as theCyclic Delay Perturbation on Effective Channel (CDPEC)scheme. At the transmitter, the perturbation is random and canbe changed on a symbol-by-symbol basis and no additionalinformation about the eavesdropper’s channel is required. Atthe intended receiver, no additional information or informationexchange with the transmitter is necessary for data detection.We derive the results of the proposed CDPEC scheme for theMISO single-antenna-eavesdropper (MISOSE) wiretap chan-nel, which can be extended to the MIMO multiple-antenna-eavesdropper (MIMOME) wiretap channel.

____________________________________978-1-4799-3197-2/14/$31.00 ©2014 IEEE

H

…

Alice

…

Bob

…

Eve

Nrantennas

Neantennas

H

G

G~

CDPEC schemeδδδδ, W, pn

Eavesdropper

Transmitter

Intendedreceiver

Ntantennas

H: original channel gain matrix (Alice to Bob)G: original channel gain matrix (Alice to Eve)G: channel gain matrix after the CDPEC scheme (Alice to Eve)~

Fig. 1. The considered system model

The remainder of this paper is organized as follows. SectionII illustrates the system model and the transmit beamformingtechnique. In Section III, we propose the CDPEC scheme forthe MISOSE wiretap channel and analyze the channel errordue to perturbation at eavesdroppers. Simulation results areprovided in Section IV. Finally, the conclusion is drawn inSection V.

II. PRELIMINARIES

A. System Model

The considered system model consists of a transmitter (Al-ice), an intended receiver (Bob), and a malicious eavesdropper(Eve), which are respectively equipped with Nt, Nb, and Ne

antennas, as shown in Fig. 1. Specifically, if the numbers ofequipped antennas are Nt > 1, Nb = 1, and Ne = 1, theenvironment is an MISOSE wiretap channel. On the otherhand, if Nt > 1, Nb > 1, and Ne > 1, the environment isan MIMOME wiretap channel. The data transmission systemis assumed to be an OFDM system comprising N subcarriers.Before the data transmission phase, channel training/estimationis performed between Alice and Bob via the transmissionof training symbols. After the channel training/estimationprocess, we assume that both Alice and Bob can obtain theperfect CSI of the desired channels between them. Similarly,Eve can obtain the perfect CSI of the eavesdropping channelsfrom Alice to her by wiretapping. Moreover, Eve can steal theCSI between Alice and Bob by eavesdropping when Bob triesto report the estimated CSI to Alice.

Because OFDM is a wideband transmission technique, weassume that the propagation channels are frequency-selectiveslow-fading and the CSI remains constant during a data trans-mission interval. We denote the overall channel gain matricesof the propagation channels from Alice to Bob and to Eve as

H =

⎡⎢⎢⎣

h(1)0 h

(1)1 · · · h

(1)N−1

......

. . ....

h(Nb)0 h

(Nb)1 · · · h

(Nb)N−1

⎤⎥⎥⎦ ∈ C(NbNt)×N

and

G =

⎡⎢⎢⎣

g(1)0 g

(1)1 · · · g

(1)N−1

......

. . ....

g(Ne)0 g

(Ne)1 · · · g

(Ne)N−1

⎤⎥⎥⎦ ∈ C(NeNt)×N

where h(r)n =

[h(r)1,n h

(r)2,n · · · h(r)

Nt,n

]Tis the channel vector

experienced at Bob’s r-th receive antenna, for r = 1, · · · , Nb,

and g(r)n =

[g(r)1,n g

(r)2,n · · · g(r)Nt,n

]Tis the channel vector at

Eve’s r-th receive antenna, for r = 1, · · · , Ne, all correspond-ing to the n-th subcarrier, for n = 0, · · · , N−1. The elementsh(r)k,n and g

(r)k,n are the complex-valued channel gains on the n-

th subcarrier from the k-th transmit antenna to Bob and Eve,respectively. Specifically, for the MISOSE wiretap channel,we can omit the receive antenna index r. Hence, the channelgain matrices becomes H = [h0 h1 · · · hN−1] ∈ CNt×N

and G = [g0 g1 · · · gN−1] ∈ CNt×N , where hn =[h1,n h2,n · · · hNt,n]

T and gn = [g1,n g2,n · · · gNt,n]T.

B. MISO-OFDM with Transmit Beamforming

To maximize the received signal-to-noise power ratio(SNR) at Bob by transmit beamforming, the signal on the n-th subcarrier is beamformed through all transmit antennas ofAlice according to a 1×Nt beamforming vector

bn = [b1,n b2,n · · · bNt,n] = h†n/‖hn‖, for 0 ≤ n ≤ N − 1

(1)where h†n denotes the conjugate transposition of the channelgain vector hn and ‖·‖ denotes the Euclidean norm. Note thatthe overall power gain of the beamforming vector is equal to 1for each subcarrier; that is,

∑Nt

k=1 b2k,n = 1, for 0 ≤ n ≤ N−1.

Assuming that the frequency-domain data sequence transmittedin an OFDM symbol is S = [S0 S1 · · · SN−1]

T, thefrequency-domain signal vector transmitted on the k-th antennais Xk = [Xk,0 Xk,1 · · · Xk,N−1]

T for k = 1, · · · , Nt,where Xk,n = Snh

∗k,n

/‖hn‖ is the signal transmitted on the

n-th subcarrier. After passing through the propagation channelsdefined by H and G, the signals received on the n-th subcarrierat Bob and Eve can be represented, respectively, as

Y (b)n = bnhnSn + v(b)n = Sn ‖hn‖+ v(b)n , (2)

and

Y (e)n = bngnSn + v(e)n = Sn

Nt∑k=1

gk,nh∗k,n

/‖hn‖+ v(e)n , (3)

for 0 ≤ n ≤ N − 1, where v(b)n and v

(e)n ∼ CN (0, σ2)

are i.i.d. additive white Gaussian noise (AWGN) with zeromean and variance σ2. Note that the signal is beamformedaccording to the CSI between Alice and Bob. Therefore, thereception at Eve will not have the maximum SNR. However,because Eve has full CSI knowledge, she still can calculate theeffective channel gains at her receiver based on the transmitbeamforming process.

III. CYCLIC DELAY PERTURBATION ON EFFECTIVECHANNEL SCHEME FOR PHYSICAL LAYER SECURITY

In this section, we propose the CDPEC scheme to improvephysical layer security through randomly perturbing the ef-fective channel experienced by the eavesdropper. Randomlyperturbing the effective channel of a receiver can be achievedeasily at the transmitter; however, the effective channel experi-enced by Bob must be maintained to be the same as the originalone to facilitate signal detection at Bob. If only the effective

channel of Eve is perturbed, the receiving performance at Evewill be degraded, and thus physical layer security betweenAlice and Bob can be improved.

A. Channel Perturbation by Cyclic Delay

In OFDM transmission, cyclic delay diversity (CDD) [12]-[13] was proposed to increase frequency diversity of theeffective channel. In other words, the effective channel canbe changed by introducing cyclic delays into the transmitsignal. For the frequency-domain signal vector transmitted onthe k-th antenna Xk = [Xk,0 Xk,1 · · · Xk,N−1]

T, the time-domain signal after inverse fast Fourier transform (IFFT) canbe represented as

xk[l]=1√N

∑N−1

n=0Xk,ne

(j2πnl/N), for 0 ≤ l ≤ N−1, (4)

where l is the time domain index. Before appending the cyclicprefix (CP), the time-domain signal transmitted on the k-thantenna is cyclically shifted by a delay δk, represented asxcyck [l] = xk[(l − δk) mod N ]. Without loss of generality, we

assume that the circular-shift on the first antenna is δ1 = 0.After passing through the propagation channels, the signalsreceived on the n-th subcarrier at Bob and Eve can berepresented, respectively, as

Y ′(b)n =∑Nt

k=1hk,nXk,n × e(−j2πnδk/N) + v(b)n (5)

and

Y ′(e)n =∑Nt

k=1gk,nXk,n × e(−j2πnδk/N) + v(e)n . (6)

As we observe, both the effective channels experienced by Boband Eve are changed into linear combinations of phase-rotatedchannel gains. Consequently, neither Bob nor Eve can figureout the new effective channels from the original CSI if Aliceuses a set of random circular-shifts δ = [δ1 δ2 · · · δNt ].

B. Recovering Weighting Factor

Because our purpose is to randomly perturb the effectivechannel at Eve without affecting Bob’s original channel, wemust recover the effective channel at Bob after introducingcyclic shifts into the OFDM system. In the frequency-domain,the cyclic shifted signal is multiplied by a weighting factor,which is intended to recover Bob’s effective channel only,while leaving the perturbation on Eve’s effective channel op-erative. To recover the effective channel at Bob, the weightingfactor for the signal on the n-th subcarrier is set as

wn =

√ρ ‖hn‖∑Nt

k=1 hk,n exp (−j2πnδk/N), (7)

where ρ is a power normalization factor. For each subcarrier,there is a unique weighting factor depending on the corre-sponding CSI and the circular-shifts δk, for k = 1, · · · , Nt.Based on the total transmit power constraint, the weightingfactor wn satisfies that Nt

∑N−1n=0 |wn|2

/N = 1. By averaging

over all the subcarriers, the power normalization factor is

ρ =N

∑N−1n=0 Nt‖hn‖2

/∣∣∣∑Nt

k=1 hk,n exp (−j2πnδk/N)∣∣∣2.

(8)

Note that, based on Cauchy-Schwarz inequality, the powernormalization factor ρ is a real number less than or equal to1 (i.e., ρ ≤ 1) to maintain the total transmit power constraintin each OFDM symbol.

Substituting (8) into (7), the weighting matrix W =diag (w0, w1, · · · , wN−1) can be obtained. Before IFFT, thetransmit frequency-domain signals are obtained as

Xk = WS, for k = 1, · · · , Nt. (9)

After passing through the propagation channels, the signalsreceived on the n-th subcarrier at Bob and Eve, based on (5)and (6), can be represented, respectively, as

Y (b)n =

∑Nt

k=1hk,nwnSn × exp (−j2πnδk/N) + v(b)n (10)

and

Y (e)n =

∑Nt

k=1gk,nwnSn × exp (−j2πnδk/N) + v(e)n , (11)

for 0 ≤ n ≤ N − 1. Substituting (7) into (10), we obtain

Y(b)n =

√ρSn ‖hn‖+ v

(b)n . (12)

Note that the received signal in (12) is the same as that in(2), excepting the scaling factor

√ρ, this implies that the

same effective channel can be obtained at Bob. However, bysubstituting (7) into (11), the received signal of Eve becomes

Y(e)n =

√ρSn‖hn‖[

∑Ntk=1 gk,n exp(−j2πnδk/N)]

[∑Nt

k=1 hk,n exp(−j2πnδk/N)]+ v

(e)n , (13)

which is completely different from that in (3). This implies thatthe effective channel at Eve is perturbed randomly for a set ofrandomly selected circular-shifts δk, for k = 2, · · · , Nt.

For Eve, even if she has both Bob’s and her CSI, it isstill impossible for her to figure out the effective channelfrom Alice to her because the new effective channel has beenperturbed by the selected circular-shifts δk, as shown in (13).On the other hand, Bob can equalize the channel effect byusing the trained CSI, and the power normalization factor canbe estimated easily based on the average received signal powerin the frequency-domain. Hence, the data detection processcan be properly performed without the requirement of anyadditional information. However, the average received signalpower is degraded because the power normalization factor isρ ≤ 1.

C. Control on Power Loss Factor

Based on the power normalization factor ρ, we definethe power loss factor as ζ = 1 − ρ, which is the per-centage of power loss in the information signal receivedby Bob when compared to the conventional beamformingscenario. Intuitively, the resultant power loss factor stronglydepends on the set of selected circular-shifts δ. To furtherreduce the power loss factor, we design a pre-filtering vectorpn = [p1,n p2,n · · · pNt,n]

T, which corresponds to the n-th subcarrier, to introduce additional phase-shifts into the datasignals transmitted on all antennas, where pk,n = exp (jφk,n)with φk,n a randomly selected phase. The block diagram ofthe proposed CDPEC scheme is shown in Fig. 2. Similar to

Informationbits

SubcarrierAllocation

andModulation

IFFT CyclicDelay δ2

AddCP Antenna

2

IFFT AddCP Antenna

1

IFFT CyclicDelay δK

AddCP Antenna

K

W

p2

pK

TransmitAntennas

ParallelData

Fig. 2. The block diagram of the proposed CDPEC scheme

(7), the weighting factor for the n-th subcarrier to recover theeffective channel at Bob is set as

w′n=√ρ′ ‖hn‖

/[∑Nt

k=1hk,ne

(−j2πnδk/N)×e(jφk,n)

](14)

for 0 ≤ n ≤ N − 1, where

ρ′ = N∑N−1n=0 Nt‖hn‖2

/∣∣∣∣∑Ntk=1 hk,ne

(−j2πnδk/N+jφk,n)∣∣∣∣2 (15)

is the new power normalization factor after the introduction ofpn. Based on the pre-filtering vector pn, the signal on the n-thsubcarrier transmitted by the k-th antenna is Sn exp (jφk,n).Accordingly, after passing through the propagation channels,the signals received on the n-th subcarrier at Bob can beobtained, based on (10) and (14), as

�

Y(b)

n = w′n∑Nt

k=1 Sne(jφk,n)hk,ne

(−j2πnδk

N ) + v(b)n

=√ρ′Sn ‖hn‖+ v

(b)n ,

(16)

which is the same as (12) except for the new power normal-ization factor, implying the same channel gain at Bob. Notethat Bob does not require any information about pn. Similarly,the signals received on the n-th subcarrier at Eve is

�

Y(e)

n =

√ρ′Sn ‖hn‖

[Nt∑k=1

gk,ne

(jφk,n− j2πnδk

N

)][

Nt∑k=1

hk,ne

(jφk,n− j2πnδk

N

)] +v(e)n , (17)

yielding a randomly distributed effective channel at Eve.

Selecting the pre-filtering vector pn is intended to achieve alarge enough power normalization factor (e.g., a desired powernormalization factor ρ). Note that, according to simulations,there are multiple candidates of pn yielding the same powerloss factor ρ on a subcarrier, even for the same δ. As a result,the pre-filtering vector pn provides not only the control onpower loss factor, but also the randomness of perturbationon Eve’s effective channel. By properly choosing pn withrandomness, the power loss factor can be effectively controlled,and Eve cannot estimate the selection of δ and pn based onthe received signal.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Real

Imag

inar

y

Without channel perturbationCDPEC: ρ = 0.5

Fig. 3. Distribution of the exact effective channel gain Gn normalized tothe original channel estimate Gn for Nt = 2, Nb = Ne = 1, and ρ = 0.5

D. Channel Error at Eve

By applying the proposed scheme, Bob can use the CSIobtained in the training process to reconstruct the effectivechannel. On the other hand, although Eve knows all thecorresponding CSI, she cannot acquire the information ofthe cyclic shifts δ and the extra phase-shifts pn, for 0 ≤n ≤ N − 1. Equalizing the received signal based on thetransmit beamforming process may be the best strategy foran eavesdropper. Accordingly, Eve performs the equalizationof the signal received on the n-th subcarrier by using theequivalent channel estimate

Gn =∑Nt

k=1gk,nh

∗k,n

/‖hn‖. (18)

Actually, by applying the proposed method, the channel gainof the n-th subcarrier at Eve is

Gn =

√ρ′ ‖hn‖

[∑Nt

k=1 gk,n exp(jφk,n − j2πnδk

N

)][∑Nt

k=1 hk,n exp(jφk,n − j2πnδk

N

)] . (19)

Defining the channel estimation error ΔGn = Gn − Gn, werepresent the mean square error (MSE) of the channel gainestimation at Eve as

Eδ,pn,gn,hn

[|ΔGn|2

]=∫ ∫ ∫ ∫ ∣∣∣Gn − Gn

∣∣∣2 fδ(δ)fpn(p)fgn(g)fhn(h) dδ dp dg dh,

(20)for a specific value of Ω, where fδ(δ), fpn(p), fgn(g), andfhn(h) are the probability density functions of the cyclicshifts, pre-filtering vector, Eve’s channel vector, and Bob’schannel vector, respectively.

IV. SIMULATION RESULTS

In the simulations, the applied channel model is the EVAmodel with 9 Rayleigh distributed taps generated by using theJack’s method. The channel gains remain unchanged duringan OFDM symbol. We assume the number of subcarriers isN = 512, with subcarrier spacing equal to 15kHz and the CPlength N/4 = 64. The average total SNRs received at Boband Eve are assumed to be the same.

100

10-1

10-4

10-2

10-3

0 5 10 15 20 25Eb/N0 (dB)

Bit

Erro

r Rat

e

Bob’s BER: CDPEC schemeBob’s BER: AN schemeEve’s BER: CDPEC schemeEve’s BER: AN schemeBPSK BER: Rayleigh fading

Fig. 4. Uncoded BER performance comparison between the proposed CDPECand AN schemes for BPSK modulation with Nt = 2, and Nb = Ne = 1

Fig. 3 shows the distribution of the exact effective channelgain Gn normalized to the original channel estimate Gn (i.e.,Gn/Gn) for Nt = 2, Nb = Ne = 1, and ρ = 0.5. The resultsare accumulated from the channel gains of all subcarriers intwo sampled OFDM symbols. If the CDPEC scheme is notapplied, the value of Gn/Gn shall be a constant equal to 1. Ifthe CDPEC scheme is applied, the values of Gn/Gn spreadout in the complex plane, implying that the perturbation ofthe effective channel at Eve is very efficient, including thedistortion in the magnitude and phase.

Fig. 4 and Fig. 5 show the BER performance comparisonbetween the proposed CDPEC and AN schemes for BPSK andQPSK modulation with Nt = 2, Nb = Ne = 1, and ρ set to theoptimal power allocation for AN. Because the fraction of totalpower allocated to the information signal for Bob is the samein the CDPEC and AN schemes, the BER performance at Bobis the same for both schemes. For the BER performance at Eve,a worse BER performance is achieved for CDPEC, implyingthat the proposed CDPEC scheme can provide better secrecyperformance than the AN scheme. In fact, the use of differentpower allocations to the information signal only results indifferent gapes between the BER performance at Bob and Eve.The CDPEC scheme still outperforms the AN scheme in themeasure of BER because of the nonlinear channel perturbation.

V. CONCLUSION

In this work, we have proposed the CDPEC scheme toimprove physical layer security in OFDM systems. The pro-posed scheme needs only the known original CSI of the desiredchannel to perform the channel perturbation process. For thedata detection at the intended receiver, no additional informa-tion or information exchange with the transmitter is necessary.Moreover, the proposed scheme is applicable to MIMO andMISO OFDM systems. The proposed CDPEC scheme canperturb the effective channels at eavesdroppers efficiently,including distortion in magnitude and phase. According to thesimulation results, when the receiving performance at Bob ismaintained to be the same, the BER of the CDPEC schemeis much worse than that of the AN method for both theMISOSE scenario, showing that our scheme outperforms theAN method in secrecy performance. Note that the perturbation

0 5 10 15 20 25

100

10-1

10-4

10-2

10-3

Eb/N0 (dB)

Bit

Erro

r Rat

e

Bob’s BER: CDPEC schemeBob’s BER: AN schemeEve’s BER: CDPEC schemeEve’s BER: AN schemeQPSK BER: Rayleigh fading

Fig. 5. Uncoded BER performance comparison between the proposed CDPECand AN schemes for QPSK modulation with Nt = 2, and Nb = Ne = 1

on eavesdroppers’ effective channels is random and can bechanged on a symbol-by-symbol basis to improve physicallayer security.

REFERENCES

[1] A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J., vol. 54, no. 8,pp. 1355–1387, 1975.

[2] S. K. Leung-Yan-Cheong and M. E. Hellman, “The Gaussian wire-tapchannel,” IEEE Trans. Inf. Theory, vol. IT-24, no. 4, pp. 451-456, Jul.1978.

[3] J. Barros and M. R. D. Rodrigues, “Secrecy capacity of wirelesschannels,” in Proc. IEEE Int. Symp. Information Theory (ISIT), Seattle,WA, Jul. 2006, pp. 356-360.

[4] Y. Liang, H. V. Poor, and S. Shamai, “Secure communication over fadingchannels,” IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2470-2492, Jun.2008.

[5] P. K. Gopala, L. Lai, and H. El Gamal, “On the secrecy capacity of fadingchannels,” IEEE Trans. Inf. Theory, vol. 54, no. 10, pp. 4687-4698, Oct.2008.

[6] T. Liu and S. Shamai, “A note on the secrecy capacity of the multiantennawiretap channel,” IEEE Trans. Inf. Theory, vol. 55, no. 6, pp. 2547-2553,Jun. 2009.

[7] A. Khisti and G. W. Wornell, “Secure transmission with multipleantennas-I: the MISOME wiretap channel,” IEEE Trans. Inf. Theory,vol. 56, no. 7, pp. 3088-3104, Jul. 2010.

[8] A. Khisti and G. W. Wornell, “Secure transmission with multipleantennas-II: the MIMOME wiretap channel,” IEEE Trans. Inf. Theory,vol. 56, no. 11, pp. 5515-5532, Nov. 2010.

[9] S. Goel and R. Negi, “Guaranteeing secrecy using artificial noise,” IEEE.Trans. Wireless Commun., vol. 7, no. 6, pp. 2180-2189, Jun. 2008.

[10] X. Zhou and M. R. McKay, “Secure transmission with artificial noiseover fading channels: achievable rate and optimal power allocation,”IEEE Trans. Veh. Technol., vol. 59, no. 8, pp. 3831-3842, Oct. 2010.

[11] W.-C. Liao, T.-H. Chang, W.-K. Ma, and C.-Y. Chi, “QoS-basedtransmit beamforming in the presence of eavesdroppers: An optimizedartificial-noise-aided approach,” IEEE Trans. Signal Process., vol. 59, no.3, pp. 1202–1216, Mar. 2011.

[12] P. Larsson, “Cyclic Delay Diversity for Mitigating Intersymbol Inter-ference in OFDM Systems,” United States Patent: US-6842487 B1, Jan.2005.

[13] 3rd Generation Partnership Project; Technical Specification Group Ra-dio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and ModulationRelease 11, 3GPP TS 36.211V11.1.0, Dec. 2012.