Title: Associating MIMO beamforming with security codes to achieve unconditional communication security
Abstract: IET CommunicationsVolume 10, Issue 12 p. 1522-1531 Research ArticlesFree Access Associating MIMO beamforming with security codes to achieve unconditional communication security Jie Tang, Jie Tang National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorHong Wen, Corresponding Author Hong Wen [email protected] National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorLin Hu, Lin Hu National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorHuanhuan Song, Huanhuan Song National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorGaoyuan Zhang, Gaoyuan Zhang National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of China School of Electronic and Information Engineering, Henan University of Science and Technology, Luoyang, People's Republic of ChinaSearch for more papers by this authorFei Pan, Fei Pan National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorHongbin Liang, Hongbin Liang School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, 610031 People's Republic of ChinaSearch for more papers by this author Jie Tang, Jie Tang National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorHong Wen, Corresponding Author Hong Wen [email protected] National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorLin Hu, Lin Hu National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorHuanhuan Song, Huanhuan Song National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorGaoyuan Zhang, Gaoyuan Zhang National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of China School of Electronic and Information Engineering, Henan University of Science and Technology, Luoyang, People's Republic of ChinaSearch for more papers by this authorFei Pan, Fei Pan National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, People's Republic of ChinaSearch for more papers by this authorHongbin Liang, Hongbin Liang School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, 610031 People's Republic of ChinaSearch for more papers by this author First published: 01 August 2016 https://doi.org/10.1049/iet-com.2016.0039Citations: 15AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study investigates the framework of associating multiple-input–multiple-output (MIMO) beamforming with secure code to achieve unconditional secure communications in the wireless passive eavesdropping environment. The schemes are based on a two-step method under Wyner's wiretap channel model. First, with MIMO transmit beamforming, one can utilise the spatial degree of freedom to cripple eavesdroppers' interceptions even when he does not know the eavesdropper's channel state information. Consequently, by taking the threshold characteristics of the secure code, the legitimate receivers will continue to extend an average bit error rate advantage over eavesdroppers when they share similar conditions (background noise power and channel gains). By this way, the proposed system could achieve almost zero information obtained by the eavesdroppers while still keeping rather lower error transmissions for the main channel. A profound theoretical analysis for the MIMO advantage channel and the exact closed-form expressions of secrecy outage probability for the secure code joint system are presented. The authors launch extensive experiments to verify the proposed security systems and demonstrate its feasibility and implement ability. 1 Introduction For the broadcasting nature of wireless communication, a passive eavesdropper can overhear the transmission. Cryptographic techniques do not directly leverage the unique property of the wireless domain to address security threats. Thus, this unique physical-layer weakness calls for innovative physical-layer security designs in future mobile communication system, which aroused a lot of attention in recent years. Using physical-layer techniques in wireless communications is based on the perfect secrecy model by Shannon [1], which is the strongest possible notion of security of a cryptosystem in effective resolving the boundary, efficiency, and link reliability issues. Wyner [2] first proposed the wiretap channel as an information-theoretic model, in which a fact was proved that the perfect secrecy (also called as unconditional security) can be realised by taking advantages of the security codes (SCs) when the eavesdropper's channel is a degraded version of the legitimate channel [2]. However, the method for establishing such channel model and combining with the practice secret code [3-7] is not so obvious. Motivated by emerging wireless communication applications with multiple antenna system, there has been a great interest on the information-theoretic secrecy capacity of multiple-input–multiple-output (MIMO) communication. Khisti and Wornell [8, 9] have discussed the achievable secrecy rate with beamforming in a multiple-input–single-output multiple-eavesdropper wiretap channel. The transmitter could directionally launch the optimal beamforming to create the biggest channel advantage for legitimate user. Khisti and Wornell [9] given an upper bound of achievable secrecy rate for the multiple-input-multiple-output and multiple-antenna eavesdropper (MIMOME) case in the asymptotic regime via signal-to-noise ratio (SNR) under such environment. The investigations on MIMO secrecy capacity were extended to various secure communication scenes such as the MIMO broadcast wiretap channel [10], some relay, and cooperate communication [11, 12]. Meanwhile, many scholars have also discussed the secrecy capacity on the situation when the transmitter is unknown about the eavesdropper's channel. Bloch and Barros defined the secrecy outage probability for the single-input–single-output wiretap channel under Rayleigh fading, where only the main channel channel state information (CSI) is known to the source [13]. For MIMO quasi-static wiretap fading channel, the studies [13-16] showed that even if the eavesdropper has an instantaneous advantage regarding the SNR, a positive secrecy rate could still be provided in average. Ammari and Fortier [16] compared the secrecy of MIMO system employing transmit beamforming with maximum ratio combining (MRC) at legitimate receiver and either MRC or select combining (SLC) at the eavesdropper. While many works are interested in the MIMO information-theoretic secrecy and analysis of the achievable secrecy capacity, there have been some research from the signal processing perspective to provide practical security algorithm to minimise the likelihood that the transmitted confidence message is intercepted by an eavesdropper [17-20]. By combining the CSI of both legitimates and eavesdropper, the secure MIMO beamforming (MB) designs [8, 17] can calculate the optimum beamforming to weaken eavesdropper's interception signal as much as possible meanwhile keeping the intended receiver's signal at a special required quality level. In this way, the legitimate receiver that may correspond to an acceptable bit error rate (BER), while eavesdropper can only have far inferior BER reception performance. Since the eavesdroppers' CSI is impossible to be available in many passing eavesdropping scenario, the artificial noise (AN) methods [19] are considered mostly for this case by transmitting AN in the null space of the legitimate channel to obstruct the illegal receivers. On the basis of this, the quality of service (QoS)-based physical-layer security system [17, 18, 20] are usually considered focused on using only enough power to guarantee a certain QoS for Bob, and then use the remaining power to generate the artificial interference [20]. However, in some power limited system, the transmitter has to allocate part of power to send the AN, that may reduce the transmit efficiency and increase the computational complexity. Generally in the AN system, the legitimates could hardly guarantee the eavesdropper's BER close to 0.5 when the power of AN is limited, and some secret information may leak to the eavesdropper. Moreover, that the eavesdropper could also conduct some blind algorithm and adaptive interference elimination algorithm [21-24] to improve his BER performance. According to Wyner [2], the unconditional secure communications could be achieved by taking the role of SCs. Owing to lack of the eavesdropper's CSI, all of those research [17-20] did not investigate associating the secure code to support for the security. Up to now, there is still less study about the specific way of combining the MIMO system with an implementable SCs to fulfil the security when the legitimate partners are unknown about the eavesdropper. In this present paper, we approach to the unconditional security by taking full advantage of the secure code's decision threshold properties with the MB. We assume the legitimate partners are unknown about the eavesdropper's CSI but the eavesdropper could achieve precise equivalent CSI. In this case, we analyse the eavesdropper's optimal MIMO reception BER performance by assuming that he could process the signal by perfect MRC. The eavesdropper's optimal MIMO reception BER could help the transmitter to analyse the advantage channel for legitimate receivers and provide the connection to secure code. Under this situation, we observe that the legitimate receivers can still acquire relative better average BER performance than the eavesdroppers after the MIMO reception, when they share similar conditions (number of antennas, background noise power, and channel gains). Consequently, by adjusting the MIMO reception BER of legitimate receiver and eavesdropper cooperatively with the secure code's transport threshold at suitable rate, the proposed system could achieve nearly zero information obtained by the eavesdroppers while still keeping rather lower error transmissions for the main channel. The profound theory analysis for the two-step joint framework is present in this paper. In addition, we also derived the exact closed-form expression of the secrecy outage probability at target secret rate to analyse for the system. What is different from the model in [16], the proposed framework consist of the secrecy code under a rate in cooperating with the front MB process; therefore, we focus more on the analysis of the secrecy outage probability at a normalised target secrecy rate. Besides, our derivative process about the secrecy outage probability is different from [16] and the final closed-form expression does not contain confluent hypergeometric function [16]. The rest of this paper is organised as follows. The structure of unconditional secure communication model and the detail about associating MB with the SCs are proposed in Section 2. In Section 3, we provide theory analysis for MIMO channel advantage for the legitimate receiver. Besides, the secrecy outage probability analysis for the secure code joint system is also proposed. Section 4 illustrates the elaborate experiment results on the proposed security system. Section 5 concludes this paper. 2 System model and secure code joint framework 2.1 Unconditional secure communication system The unconditionally secure communications model targeted in this paper is shown in Fig. 1, in which Alice first encodes bits message by suitable secret coding as . After the binary phase shift keying (BPSK) modulation, the MB process is performed. The typical MIMO wiretap channel model is illustrated in Fig. 1 dash line box part. In our model, all three sides are assumed possessing multiple antennas, the number of which was denoted by NT, NR, and NE. After the communication between the legitimate partners Alice and Bob, the sequence received by Bob is the noisy version of sequence s. Meanwhile, the eavesdropper Eve can also observe the noisy sequence . Then, Bob and Eve perform security decoding. The destination and eavesdropper can decode and from their respective receive signal. Fig. 1Open in figure viewerPowerPoint Unconditional secure communication system model The Shannon's unconditional security [1] includes both reliability and security conditions, which ensure the legitimate parties can have reliable communication while the eavesdroppers unable to receive any useful information without a shared secret key. In a binary system, the reliability and security conditions are (1) (2)As for the MIMO transmission in most passive eavesdropping environments, the eavesdroppers' CSI is usually unavailable for the legitimate partners. Therefore, it is hard to get the secrecy optimised beamforming design in [8, 17]. The goal in (1) and (2) is far from achieving. According to Wyner [2], conditions (1) and (2) can be realised only if the eavesdropper's channel is a degraded version of the main channel. Thus motivate us to achieve unconditional communications through two-step way. The first step is to build a superiority channel by keeping better channel quality between the legitimate communication peers than that of the eavesdropper. The second step is to approach the secure communications by ensuring about 0.5 bits error probability seen at the eavesdropper. This must be done with a reliable yet practically implementable SCs. The transmit beamforming [25] is widely investigated and applied in the MIMO systems. In such a way, the signals could transmit in a particular direction to the destination without additional power cost. Considering that the passive eavesdropper generally lie in different directions relative to Bob, the received signal at him will be weaker than the destination node. Therefore, the MIMO transmit beamforming are very potential to build the advantage channel for Bob. In the front MB processing, Alice transmits modulated symbol streams s(n) with multiplied by the vector , where and denotes the norm operation. Assuming a flat-fading scenario and transmit power is Pf, the signals received by Bob and Eve can be represented as follows (3) and are the white noise corresponding to the receiving signals of Bob and Eve. With possibly different power levels , . The operator ɛ{·} denotes expectation, ( · )H denotes the Hermitian transpose, and I is an identity matrix of appropriate dimension. The and are NR × NT, NE × NT dimension of channel matrix, respectively, whose coefficients hij are independent complex circular symmetric Gaussian distributed with zero-mean and unit variance. In particular, let and denote NR × 1, NE × 1 beamformers, respectively. After processing with the combining vector, we have (4)The optimum combining vector at the receiver [26] is well known to be given by (5)If the transmitter fully known to eavesdropper's CSI, he could approach optimal secrecy rate by making beamforming f to be the eigenvector corresponding to the largest eigenvalue of [8, 17]. However, generally the legitimate partners are unknown about the accurate information about in the passive eavesdropping environments. In our proposed model, without knowing about , Alice could choose transmit beamformer f as the eigenvector corresponding to the largest eigenvalue of and the optimal combining vector then is equivalent to be the left singular vector of corresponding to its dominant singular value [25]. As mentioned above, Eve will be hard to peep the information about and . However, the optimal beamformer for Eve to maximise his receive SNR (referred to as MRC in [26]), which needs he implement special blind algorithm [21, 22] to estimate the equivalent channel information . Here, we are focusing on the worst case for legitimates that Eve could acquire the precise and then he can achieve the optimal MIMO average BER performance by MRC processing. However, as for the directional characteristic of the MB [26], Alice choose transmit beamformer corresponding to create largest diversity gain at the direction of . Thus in any other direction, the passive eavesdropper benefits nothing from the multiple transmit antennas at Alice. Therefore, Bob will continue to enjoy an average BER advantage than Eve when they share similar receiving conditions (number of antennas, background noise power, and channel gains). This BER performance disparity between Bob and Eve motivates us to associate the SCs by taking fully advantage of its threshold property. The detail of it will be discussed in Section 2.2. Besides, the more specific theory analysis about the MIMO channel advantages for Bob and the secrecy outage probability at target secure rate for the system is investigated in Section 3. 2.2 Secure code associating framework We assume that both the Bob and Eve adopt optimal hard decision decode in the scheme. The low complexity secure code with decodable in linear time, applicable at finite block length are suited to employ in the schemes. In particular, the proposed SCs [4] used in our model which is the best reported result with short enough code lengths for practical implementation in binary symmetric channel (BSC). It constructs from the resilient function and possesses natural threshold attributes [4]. For (n, m) SC with rate RS, when the input equivalent BSC channel with transition probability ρc [4] at the decoder satisfy (6)the output BER will be very close to 0.5, where n is the length of the code and m is the number of secret information bits. The equality in (6) holds when the dual code of the secure code is maximum distance separable code [4]. This property is depicted in Fig. 2, which shows the output BER performance of (7, 3) (dashed line) and (63, 6) (solid line) secure code constructed by Hamming code via input transport probability. It could be clearly seen if the transport probability before decoding is slightly higher than ρc, the output BER at the decoder is close to 0.5. Also, the ρc can be decreasing with the code length increasing. This can be obviously seen from Fig. 2, is about 0.2142 and is decreasing to 0.047. Fig. 2Open in figure viewerPowerPoint Performance of BSC secure code construct by Hamming code We hope to adjust Alice-to-Bob transmitting ('whispering') power to achieve the security by making the minimum BER achieved by Eve always larger than the ρc, meanwhile keep the BER of Bob as very small. This principle could be illustrated in Fig. 3. The ρc + ɛ2 is the minimum input BER which the decoder required for Eve. The BER gap is the BER difference between ρc + ɛ2 − ɛ1, that should maintain between Bob and Eve before the secure decoding, in order to approach both reliability and security conditions in (1) and (2). We could define the reliable parameter ɛ1 and secure parameter ɛ2 which satisfy (7)where ɛ1, ɛ2 ≥ 0 and they are both very small positive numbers which are close to zero. PEB,max is the maximum BER allowed for Bob at the input of the secure decoder and PEE,min is the minimum input BER required for Eve at the decoder. We assume the (ρB, ρE)SNR denotes the average BER of Bob and Eve at specific SNR before the secure decoding, if (8)The property of MIMO channel advantage mentioned above which can be illustrated in Fig. 4 by Monte Carlo simulation. It shows the average BER performance of the proposed MB with BPSK modulation in dash line box part of Fig. 1. The Alice has four antennas, both Bob and Eve have four receive antennas. The channel is assumed to be block Rayleigh fading and both Bob and Eve with one power background additive additive white Gaussian noise. The horizontal ordinate denotes the average SNR per receive antenna. The blue line denoted the optimal BER performance for Eve when he gets precise and processing MRC after MIMO receiving. From Fig. 4, it could be clearly seen that Bob can always achieve a relatively better BER performance than Eve against SNR. However, the BER of Eve is far lower than 0.5. Thus the SC is followed cooperatively in the system to enlarge such advantages. Eve gets the bits stream with error probability larger than that of Bob against SNR after MIMO receive processing. If fixed the SNR, the eavesdropper sees a BSC with error probability ρE while the main channel could experience with error probability ρB. We suppose the secure code with threshold ρc is employed in the system. Referred from Fig. 4, by common intuition, we hope to adjust Alice-to-Bob transmitting ('whispering') power to achieve the security by making the minimum BER achieved by Eve always larger than the ρc, meanwhile keep the BER of Bob as very small. Fig. 3Open in figure viewerPowerPoint Typical BER performance curve of a BSC secure code Fig. 4Open in figure viewerPowerPoint Average BER performance of the proposed MB with BPSK modulation For example in Fig. 4, if we choose ɛ1 = 10−3, and adopt secure code rate in the system which are satisfied (RS/2) + ɛ2 ≤ 0.01, then, at SNR −2 dB the eavesdropper experiences a BER beyond 0.027 while the Bob with much more reasonable BER 0.0008 which is lower than ɛ1. Similarly, the SNR from −1 to 0 dB all meet the same conditions. After MIMO receive processing, the BER of Bob and Eve at specific SNR which should satisfy (9)Obviously, from (9) we can launch that ρE must be greater than ρB, in order to guarantee the positive secure rate. On the other side, if the left side on (9) is fixed, we hope smaller the value ɛ2 − ɛ1 on the right side of the inequality which will leave more space for the higher rate option of secure code. To narrow the gap, we can let ɛ2 approach to 0, which is still keeping Eve's output BER very close to 0.5 for long length code [4]. It is obvious that we hope the larger ɛ1, whereas the larger ɛ1 will make the higher output BER of Bob. What is more, (9) is also verified that the more ρE is greater than ρB, the higher RS of SC is permitted to employ in the system. In the quasi-static flat-fading channel, we could assume Alice transmits k frames data and each frame contains N blocks of (n, m) code. The channel will not change in a frame time. The average BER ρE for Eve before secure decoding can write as (10)where presents the instantaneous BER for the Eve in his kth received frame data. For an n length block secure code, according to Wen et al. [4], if the error bits number in a block exceed the nρc before the decoding, the result will make the decode output BER close to 0.5. However, when (8) and (9) are satisfiable, there are still minority blocks may happen producing error bits less than expected nρc before the decoder. The probability of such event occurring could be measured by 3σ error range parameter t3σ that reflects the degree of error number in an n length blocks deviation from the average three times of the standard deviation. It is well known that if the channel with transmit probability ρ, for n bit block transmission, the average error bits number is (11)The standard deviation σ reflects the extent of the deviation from the average (12)Assuming the system adopts a secure code with threshold ρc, the parameter t3σ could defined as (13)where (14)and . For the n bit length block code, the probability of Eve's error bits number that is lower than the t3σ before decoding in BSC is (15)Moreover, the average probability for all k frames data could be calculated as (16)It is easy to prove that when the code rate is fixed in the system, the outage probability P(t ≤ t3σ) is convex function of ρE,i(0 ≤ ρE, i ≤ 0.5). Therefore, we define the function (17)In the quasi-static flat-fading channel, the average probability for all k frames data in (16) can be written as (18)and (19)For the property of convex function we can launch (20)when ρE,i = ρE(i = 0, 1, …, k), the outk gets the minimum value out (ρE). Therefore, if the channel is not changed very much during the communication period, the are very close to each other, then we can use out (ρE) to estimate the lower bound of the probability outk of Eve. Of course that we hope the probability as very small. For example, if Eve's input BER is 0.07 at the secure decoder with code length n = 127, then and t3σ ≃ 5.535, and the P(t ≤ t3σ) is about 9.93 × 10−5 which means that for every 100,000 blocks, there are about 9.94 blocks with the error bits number lower than 5.535. The more intuition interpretation on probability is understandable. For any 127 bit block, if the error bits number is lower than 5.535, then the probability is 9.93 × 10−5. 3 Framework secure analysis 3.1 Channel advantage for Bob analysis In this section, we present the theory analysis for the MIMO channel advantage for Bob. Under Rayleigh channel the equivalent channel for Eve is NE × 1 which can be given as (21)We assume Eve fully knows the and combines optimal vector to maximise his instantaneous received SNR, the average output SNR [26] for him is (22)where |s|2 = 1 presents the power of modulated symbols and we let ηs = (Pf|s|2/σ2) which denotes the average SNR per receive antenna. For simplified analysis, we assume Bob and Eve share the same powered background noise with . From (22), the largest array gain [26] for Eve will be no more than NE even if he got the accurate . Now, we are interested in the BER performance of Eve and Bob. For coherent reception of BPSK signals, the BER corresponding to SNR η is given by (23)where Q(·) denotes the Q-function which is decreasing function of η (24)Then, the average BER could be computed as (25)where the p(η) is the probability distribution function of SNR η. The maximum instantaneous SNR of Eve could be denoted as (26)As is known that , for BPSK signal, the corresponding optimal achievable average BER [26] for Eve can be given by (27)where p(h) is the probability density distribution of h. For Bob, the instantaneous beamforming [25] receive SNR can rewritten as (28)where λmax corresponding to the largest eigenvalue of . The matrix has a Wishart distribution [25, 27]. When NT > NR, the probability density distribution of λmax is [25] (29)where (30)The ci,m are the coefficients. Bob's average BER [25] can be given as (31)The exact closed-form BER expressions are very helpful for legitimates to estimate the channel advantage over the eavesdropper, which set up a convenient bridge to associate with the secure code on the global system level. In high SNR regime, the and Eve's average BER is very close to the curve [26, 28] (32) (33)Therefore, in the high SNR regime, when NE < NTNR, we have (34)where is a finite constant based on NR, NT, NE (35)From analysis above, Even when Eve achieves his optimal BER performance, the channel advantage for legitimate receiver could still be guaranteed for all SNR scope. Actually, both the legitimate partners and the eavesdropper could increase the antenna numbers to improve the BER performance. When NR, NT is very large [26], we have (36)Noting from (22) the Eve's array gain will never exceed NE. If the transmitted power is limited by Pf ≤ Pmax, in this case the average achievable secrecy rate can be written as (37)When NR = NT the maximum average secrecy rate can be achieved as (38) 3.2 Secrecy outage probability analysis According to papers [13-16], when the legitimate partners unknown about the eavesdropper, the system could produce an average secure rate for legitimates with comparatively small secrecy outage probability to support the secure transmit. Therefore, we extend the secrecy outage probability in [13] to analyse our MIMO united with secure code joint system, which could help us to analyse and choose the appropriate rate of code at a target secrecy outage probability. Let
Publication Year: 2016
Publication Date: 2016-05-09
Language: en
Type: article
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