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  1. 1. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 3, May 2012 Secured communication technique for MIMO based wireless network using codebook and multiplexing methodology 1 R.RAICHEAL, 2C.ARUNACHALAPERUMAL,Abstract--In this paper we study about the Secure The wire-tap channel, is one of the solution ofcommunication among wireless shared medium using information-theoretic security, was introduced in [1], thesecrecy performance of a codebook based ergodic secrecy capacity is calculated for fading wiretaptransmission beamforming with limited feedback. channels in [2]. In wireless channels, when the numberAnd avoid attacker from stealing the confidential of antenna increases the fading can be reduced, anddata. In the feedback method transmitter is using a transmission rates can be increased . In [3] the secrecypredefined codebook known to transmitter and capacity of the Gaussian multiple-input multiple-outputreceiver knows it after producing index value as (MIMO) wire-tap channel are found, when the source sfeedback during beamforming. The secrecy outage and the destination d have two antennas each and theprobability is analyzed to find whether it is stealed. attacker e has only a single antenna. Outage probabilityThe bound values are provided on the secrecy outage for a target secrecy rate is shown in [4], when s, d and eprobability. The fading in multiple antenna (MIMO) have CSI, and optimal power allocation minimize thewire-tap channel is investigated under short term outage probability are calculated. The DMT is a highpower constraints. The secret diversity multiplexing SNR analysis. The diversity gain decays the rate of thetradeoff (DMT) is found for no transmitter side probability of error, and the multiplexing gain is the ratechannel state information (CSI) and for full CSI. of increase of the transmission rate in the limit of highWhen there is no CSI at the transmitter, while using SNR. In this paper we investigate the code generationGaussian codebooks, it seems that both transmitter and the cryptographic methods[5] in the multiple-and receiver antennas are stealed, and the secret antenna wire-tap channel. Under CSIT, we study theDMT depends on the other degrees of freedom. When effect on secrecy from a codebook based transmissionCSI is available at the transmitter (CSIT), then beamforming with limited receiver feedback. Codebooktransmitter antenna is only stealed. beamforming [6], [7] has become commonly adopted in practice [8], [9] for reducing the amount of feedbackIndex terms — Diversity multiplexing tradeoff overhead. The idea behind this scheme is the use ofMIMO, transmission beamforming, codebook, wiretap code. By using a stochastic encoder to map theinformation-theoretic security, secrecy outage secret message into many codewords according to anprobability appropriate probability distribution, the sender can hide the secret information in the noise on wiretapper‟sI. INTRODUCTION: channel. We see about the secret outage probability in As the wireless medium the communication is II.A, code book generation in III, and feedback methodbeing shared there is much more possibility of stealing in IV.the confidential informations. In any region of thetransmitter the stealer can present and he can be more II. SYSTEM MODEL AND PRELIMINARIES:advantageous than the information producer. The We consider fig1, multiple-antenna wire-tapconfidential information such as user IDs, passwords, or channel, in which s, d and e have 𝑚, 𝑛 and 𝑘 antennas.credit card numbers become vulnerable if he is present Both d and e have CSI about their incoming channels.near to the transmitter antenna. Then, wireless security is For each channel, the received signal is represented asan essential system requirement. In existing wireless follows:systems, protection against stealing is provided at higherlayers of the Open Systems Interconnection (OSI) Yd = HdX + Nd (1)reference model. Therefore, key exchange and renewal Ye = HeX + Ne. (2)may be difficult. In the above equations X is an 𝑚 × 1 vector, which is the transmitted s signal. Yd and Ye are 𝑛×1 and 𝑘×1Manuscript received on April 20121 M.E(Communication systems) S.A Engineering College, Chennai - vectors, shows the received signals at d and e. Then Nd77. and Ne are 𝑛×1, and 𝑘×1 vectors that indicate the 2 Asst. Professor,,Dept of P.G. Studies,S.A Engineering College, independent additive noise at d and e. Both (Nd , Ne)Chennai -77. and (Hd, He) have independent and identically distributed (i.i.d.) complex Gaussian entries with zero All Rights Reserved © 2012 IJARCET 50
  2. 2. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 3, May 2012 mean and unit variance. Hd, He are of size 𝑛× 𝑚, and channel codeword X 𝑛1 . Note that 𝐵 is the number of 𝑘× 𝑚. They indicate the channel gains between s and d dummy code words used to confuse e for each 𝑎 ∈ 𝒜. and the s and e. Since the fading is slow, Hd and He are With full CSI at s and d, 𝑅( 𝑠) is set to 𝑅 𝑠, and R( 𝑑) = fixed for the whole duration of the communication. 𝐼(X;Ye). The total number of code words in the s When there is no secrecy, the error probability is dominated by the outage event. The DMT,d ( 𝑟), codebook is 𝐴 × 𝐵 = 2 𝑁𝐼(X;Yd), and the d can decode establishes a relation between the target transmission W using a. The attacker can decode only the index b and rate 𝑅( 𝑇)(SNR) and probability of error 𝑃 𝑒(SNR), where 𝑟 there will no information about the secret message a. is the multiplexing gain. Therefore the secrecy depends Thus secrecy is achieved. For average power constraint on the remaining degrees of freedom in this system is m-SNR that the transmitter has to satisfy for each min{ 𝑚, 𝑛}, and 𝑟 can increase up to this value. The codeword transmitted. The secret multiplexing gain is maximum diversity gain is 𝑚𝑛, and it decreases as the defined as, multiplexing gain increases. Under secrecy constraints, the source has to send the message 𝑊, So the secrecy rate, 𝑅 𝑠 is achieved lim ≜ 𝑟𝑠. (6) if the secrecy constraint is satisfied; i.e. SNR→∞ 𝑅𝑠 = lim (3) 𝑁→∞ the above equation shows how fast the target secrecy rate scales with increasing SNR. The secret diversity =lim (4) gain, ds, is equal to 𝑁→∞ The probability of decoding error at the d approaches Lim ≜ −ds, (7) zero as 𝑁 approaches infinity. The term lim SNR→∞ 1 𝑁→∞ 𝐻( 𝑊∣𝑌e 𝑁 ) is also known as the equivocation N where Pe(SNR) denotes the probability of error under rate. secrecy constraints. Two events are considered :Either the destination does not receive the secret message reliably, or secrecy is not achieved. Then Pe(SNR) = P (secrecy not achieved, main Destination D channel decoding error) (8) D ≤ (secrecy not achieved)+ (main channel decoding error), (9)Source S Where (secrecy not achieved) 1 ≜ 𝑃 ( lim 𝐻( 𝑊∣𝑌 𝑁 e ) < 𝑅( 𝑇) 𝑠 (SNR)) Attacker E N 𝑁→∞ (10) 𝐵 = 2 𝑁𝑅( 𝑑)(SNR) and 𝐴 × 𝐵 = 2 𝑁 𝑠 𝑅( 𝑇)(SNR) =2 𝑁𝑅( 𝑇) (SNR)+ 𝑁𝑅( 𝑑)(SNR), Fig1: Basic System Model 𝑃(secrecy not achieved) defined in (8) can be calculated as 𝑃(secrecy not achieved) The H( ) denotes the mutual sharing information = 𝑃( 𝑅( 𝑇)(SNR) − 𝐼(X;Ye) < 𝑅( 𝑇) 𝑠(SNR)) = 𝑃 ( 𝐼(X;Ye) > 𝑅( 𝑑)(SNR)). (11) between e. The papers, prove that the secrecy rate. Finally, as the main channel outage event dominates the 𝑅𝑠 = [ 𝐼(X;Yd) − 𝐼(X;Ye)]+ (5) main channel decoding error when the channel block length-N is long enough and good codes are used , is achievable for any input distribution 𝑝(X), where 𝑥+ denotes max{0, 𝑥}. 𝑃(main channel decoding error) =˙ 𝑃(main channel outage) Define 𝐴 = 2𝑁𝑅( 𝑠) , 𝐵=2𝑁𝑅( 𝑑)and the sets 𝒜 = = 𝑃( 𝐼(X;Yd) < 𝑅( 𝑇)(SNR)). (12) {1, ...,} and ℬ = {1, ..., 𝐵}. The source generates 𝐴 × 𝐵 Lower bound is given as follows channel codewords X 𝑁1 i.i.d. with 𝑝(X). In order to send a secret message a ∈ 𝒜, the source chooses 𝑏 uniformly 𝑃 𝑒(SNR) ≥ 𝑃(secrecy not achieved) from the set ℬ, forms 𝑊 = ( 𝑎, 𝑏) and maps 𝑊 into the ≥ 𝑃([ 𝐼(X;Yd) − 𝐼(X;Ye)]+ < 𝑅( 𝑇) 𝑠 (SNR)) All Rights Reserved © 2012 IJARCET 51
  3. 3. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 3, May 2012 ≥ 𝑃( 𝐼(X;Yd) − 𝐼(X;Ye) < 𝑅( 𝑇) 𝑠 (SNR)) ≜ 𝑃(secrecy rate outage), (13)for the chosen achievable scheme with 𝑝(X). If manyantennas are considered power constraint will be larger. Key CB CodeA. Definition Of Secrecy Outage Probability: Generator Generator book To achieve secrecy, s encodes the secretmessage using a scalar Gaussian wiretap code andtransmits in the direction of q. When the input signalingis Gaussian, then the difference of mutual informationbetween s-to-d is Rd and between s-to-e Re is an Characterachievable rate. This implies that when s knows the setchannel information to both d and e, she can design awiretap code such that d can receive data at a rate Re –Rb, whereas d receives no secret information. When no Fig. 2 : Code book generationchannel information is present from e, s can giveinformation to d. Without e‟s channel information, s willset the wiretap code to operate at an arbitrary rate R. If Group Group codeRb − Re ≥ R, then secrecy is achieved. If, Rb − Re < R, AJS Jthen e can eavesdrop at a positive rate so no secrecy is BKT Tthere it is also known as secrecy outage. For any positive CLU CR, the secrecy outage probability characterizes anachievable secrecy rate which is also decodable by d. DMV VFor a target secrecy rate R and transmission power R, ENW Esecrecy outage probability can be expressed as FOX O GPY P𝑃so ( 𝑅, 𝑃) = Prob [ 𝑅d − 𝑅 𝑒 ≤ 𝑅] (14) HQZ Z= P[|H 𝑒q|2 ≥(( 𝜏 ∣⟨hd, q⟩∣2 − 𝛾 𝑒)/2 𝑅) ] (15) IR R Table 1 :Group of element generatedWe denote 𝛾d = 2 𝑅−(1/ 𝑃 𝑏) and 𝛾 𝑒 = 2 𝑅−(1/ 𝑃 𝑒), and weset 𝜏 = 𝑃 𝑏/ 𝑃 𝑒 = 𝛾 𝑒/ 𝛾d. • E is coded as E1, since „E‟ belongs to the group that is having a group code „E‟ and „E‟ is in 1stIII. CODE BOOK GENERATION: position from right. In our system it works by the basis of a Code- • L is coded as C2, since „L‟ belongs to thebook (CB), without the needing of a key to be shared. group that is having a group code „C‟ and „L‟ is in 2ndMaintaining of sessions is done to renew the code-book position from right.from time-to-time. The proposed Methodology works as Likewise the total message is coded as -follows: “Z1E1C2C2O2”. • Generation of CB. This message is coded in such a way that a • Encryption of CB using WEP and exchange of group code is followed by the position of that character CB. in that group.A. Generation of CB: B. Encryption Of CB Using WEP And Exchange Of CB: The code-book is generated as follows: The CB has to be exchanged between the two The Key Generator generates a key, based on communication parties. The WEP is used to encrypt thewhich the Code- Book generator generates a Code-Book code book and is sent to the receiver. Since, initially CBfor the given Character- Set. The key generation process will be only at one side, so there is a need of exchange ofis delaying sensitive, and keys generated this way are CB between both the parties.used to protect the delay-sensitive secret messages.The working is as follows: Each group is identified or denoted by a singlemember (character) of that group. Now, the generatedCB may look like Table-1. Fig. 3 : Packet format for CB Let us suppose that “HELLO” is the message,and then it is coded as: Fig.3.Packet that contains CB and is • H is coded as Z1, since „H‟ belongs to the encapsulated using WEP encryption and sent to the othergroup that is having a group code. „Z‟ and „H‟ is in 1st party. Then the communication begins.position from right. IV BEAM FORMING AND FEEDBACK METHODOLOGY: All Rights Reserved © 2012 IJARCET 52
  4. 4. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 3, May 2012 VI. DISCUSSIONS:A. Effect Of Codebook Size:If the codebook size increases, then the chosen codeword A. Secrecy Outage Probability:q will be closer to the naive beam forming vector. Forlarge 𝑁, the value of 𝛿 is dominated by the term Equal noise power received at both d and e receivers. For codebook beam forming, we use a MISOMax ∣⟨c 𝑖, c 𝑗 ⟩∣2 (16) system with M = 4 transmit antennas. We apply two𝑖, 𝑗, 𝑖≠ 𝑗. different codebooks for this system.. Fig. 5 presents the secrecy outage probability with different number ofFor any given codebook with 𝑁 ≥ 𝑀s, receive antennas at Attacker. The simulation also showsmax ∣⟨c 𝑖, c 𝑗 ⟩∣ can be lower bounded as the performance of another non-security centric𝑖, 𝑗, 𝑖≠ 𝑗 beamforming strategy - equal gain beamforming strategymax ∣⟨c 𝑖, c 𝑗 ⟩∣≥ max{√ ( 𝑁 – 𝑀s)/( 𝑁 -1) 𝑀s, probability with 1 − 2 𝑁− 1/( 𝑀s−1)} (17)𝑖, 𝑗, 𝑖≠ 𝑗 1.2 R=0.5b/sHz, P b=Pe=20dB,where, for large value of 𝑁, the bound is dominated by Mt=4 Secracy outage probabilitythe second term. As 𝑁 →∞, this lower bound becomes 1 8, 1 Equal gainmax ∣⟨c 𝑖, c 𝑗 ⟩∣ ≥ 1 − 2 𝑁− 1/ 𝑀s−1 →1 0.8 beamfor𝑖, 𝑗, 𝑖≠ 𝑗 0.6 ming Therefore, 𝛿 → 1 for large 𝑁 and hence as 𝑁 →∞, That is, for large 𝑁, the secrecy outage probability 𝑃cb 0.4 LB(Naïveso approaches the secrecy outage probability 𝑃nb so from Beamfornaive beam forming. 0.2 ming) 0 UB(N=8) CODE BOOK MESSAGE ALGORITHM 0 5 Me 10 CIPHER (USING Fig .5 Comparison of secrecy outage probability CB) between naive beamforming increasing SNR, where we kept the number of transmit WEP ALGORITHM FINAL CIPHER antenna at User1 fixed to Me = 4. The simulation is performed for target secrecy rate of R = 0.5 b/s/Hz when Fig. 4 :Encoding method Pb = Pe = 20 dB. It can be seen that at very low SNR, the secrecy outage probability is close to 1, here weB. Positive Secrecy cannot expect any secrecy when the channel condition is Positive secrecy is achievable when 𝑅 𝑏 ≥ 𝑅 𝑒. In very poor. At moderate to high SNR, the secrecy outageterms of secrecy outage probability, probability increases with an increase in the number of receive antennas at e, which is expected. The simulationProb [ 𝑅d ≥ 𝑅 𝑒] = 1 – 𝑃nbso ( 𝑅 = 0, 𝑃) ≥ 0. result presented in Fig. 6 shows the effects of increasing both the number of transmit antennas at s, and theUsing Eq, we now have number of receive antennas at e on the secrecy outage probability. The simulation is performed for Pe = Pb =Prob [ 𝑅d ≥ 𝑅 𝑒] = 1 – 𝑃nb so (0, 𝑃) 20 dB for a target secrecy rate R = 2 b/s/Hz. The = 1−1/Γ ( 𝑀 𝑒) ∫ Γ ( 𝑀 𝑒, 𝜏 𝛼) 𝑓𝛼 ( 𝛼) 𝑑𝛼 simulation is performed for different value of Me. = 1−1/Γ ( 𝑀 𝑡) (1+ 𝜏) 𝑀𝑡 𝑀𝑒−1Σ 𝑘=0 ( 𝜏/(1 An interesting observation is that for a ≤ 4.2, + 𝜏) ) 𝑘 Γ ( 𝑘 + 𝑀 𝑡 − 1)/Γ ( 𝑘 + 1) secrecy outage probability increases with an increasing Me, while for a ≥ 4.2, secrecy outage probability actually This means that the additional gain in secrecy decreases with an increasing Me. It shows that, when a isprobability due to naive beam forming decays large, a change in Me also means many more transmitexponentially with the number of received antennas antennas.employed at Attacker. In practical cases, it is not We have performed additional simulation forpossible to estimate the number of receive antennas different values of SNR and target secrecy rate, andAttacker uses. Therefore, we focus on the case of observed that the cross-off point as seen in Fig. 6 is aAttacker with very large number of antennas and function of both SNR and target rate. Fig. 5 also showsinvestigate the effect of different number of transmit the secrecy performance when the codewordantennas in this situation. corresponding to CDI is used as beam forming vector. When the attacker channel information at source is accurate (i.e. low 𝜎𝑒), However, for high value of 𝜎𝑒, All Rights Reserved © 2012 IJARCET 53
  5. 5. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 3, May 2012beam forming in the direction of destination provides REFERENCES:similar performance results obtained. [1] A. D. Wyner, “The wire-tap channel,” The Bell System Technical J., vol. 54, p. 1355, Oct. 1975. [2] P. K. Gopala, L. Lai, and H. E. Gamal, “On the secrecy of capacity of fading channels,” IEEE Trans. Inf. Theory, vol. 54, no. 10, p. 4687, Oct.2008. [3] Y. Liang, H. V. Poor, and S. Shamai, “Secure communication over fading channels,” IEEE Trans. Inf. Theory, vol. 54, p. 2470, June 2008. [4] S. Shafiee, N. Liu, and S. Ulukus, “Towards the secrecy capacity of the Gaussian MIMO wire-tap channel: the 2-2-1 channel,” IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4033–4039, Sep. 2009. [5] Bruce Schneier 2003, “Applied Cryptography”. John Wiley & Sons, Inc. [6] D. Love, R. Heath Jr., and T. Strohmer, “Grassmannian beamforming for multiple-input multiple-output wireless systems,” IEEE Trans. Inf. Theory, vol. 49, 2003. [7] K. Mukkavilli, A. Sabharwal, E. Erkip, and B. Aazhang, “On beamforming with finite rate feedback in multiple-antenna systems,” IEEE Trans. Inf. Theory, vol. 49, 2003. [8] “IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems,” 2006. [9] T. GPP,“36.211,” Physical Channels and Modulation (Release 8).– 3GPPvol. 12. [10] S. Leung-Yan-Cheong and M. Hellman, “The Gaussian wire-tap channel,” IEEE Trans. Inf. Theory, vol. 24, 1978. [11] Brian Carter, Russell Shumway, 2002, “Wireless Security End to End”. Wiley Publishing, Inc. Authors profile: R.Raicheal received B.E Electronics and communicationFig.6 Effect of received SNR on secrecy outage Engineering in the year 2010. Currently doing M.Eprobability for different values of Pb. Here, received Communication systems Engineering.SNR of both Bob and Eve are assumed to be same,VII. CONCLUSION: C.Arunachala Perumal received B.E Electronics and In this work, we have analyzed the performance communication Engineering in the year 1997.Pursed M.Eof codebook based beam forming transmission with the degree in 2004 and completed MBA Production management in 2005 MPhil in Management in 2007.help of finite bit receiver feedback in a security setting. Currently working as Assistant professor.We presented the naive beam forming scheme in thedirection of the intended receiver in presence of multi-antenna attacker.In this paper we study the MIMO wire-tap channel when there are stringent delay constraintsand short-term power constraint. First, we study no CSITcase with isotropic Gaussian codebook. Our results showthat the eavesdropper decreases the degrees of freedomin the direct link, min{m,n}, by the degrees of freedom inthe source-eavesdropper channel, min{m,k}. Therefore,if k ≥ m, then no degrees of freedom is left. Otherwise,the secret DMT is equivalent to that of a (m − k) × (n −k) MIMO without secrecy constraints. In this paper whenthere is CSIT, we assumed the source knows both themain channel CSI and the eavesdropper channel CSI tofind the fundamental limits. ACKNOWLEDGMENT I thank Jesus almighty for extending myopportunity to do this work and I thank everyone whosupported me internally and externally for doing thiswork. I forward my thanks to my parents and director,chairman, principal, HOD, Guide for boosting my talentsto do this work. All Rights Reserved © 2012 IJARCET 54