Max-ratio relay selection in secure buffer-aided cooperative wireless networks

Transcription

1 Loughborough University Institutiona Repository Max-ratio reay seection in secure buffer-aided cooperative wireess networks This item was submitted to Loughborough University's Institutiona Repository by the/an author. Citation: CHEN, G.... et a., 214. Max-ratio reay seection in secure bufferaided cooperative wireess networks. IEEE Transactions on Information Forensics and Security, 9 (4), pp Additiona Information: This is an Open Access Artice. It is pubished by the IEEE under the Creative Commons Attribution 3. Unported Licence (CC BY). Fu detais of this icence are avaiabe at: Research data for this paper is avaiabe on request from the authors. Metadata Record: Version: Pubished Pubisher: c the authors. Pubished by IEEE Pease cite the pubished version.

2 This item is distributed via Loughborough University s Institutiona Repository ( and is made avaiabe under the foowing Creative Commons Licence conditions. For the fu text of this icence, pease go to:

3 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 9, NO. 4, APRIL Max-Ratio Reay Seection in Secure Buffer-Aided Cooperative Wireess Networks Gaojie Chen, Member, IEEE, Zhao Tian, Student Member, IEEE, Yu Gong, Member, IEEE, Zhi Chen, Member, IEEE, and Jonathon A. Chambers, Feow, IEEE Abstract This paper considers the security of transmission in buffer-aided decode-and-forward cooperative wireess networks. An eavesdropper which can intercept the data transmission from both the source and reay nodes is considered to threaten the security of transmission. Finite size data buffers are assumed to be avaiabe at every reay in order to avoid having to seect concurrenty the best source-to-reay and reay-to-destination inks. A new max-ratio reay seection poicy is proposed to optimize the secrecy transmission by considering a the possibe source-to-reay and reay-to-destination inks and seecting the reay having the ink which maximizes the signa to eavesdropper channe gain ratio. Two cases are considered in terms of knowedge of the eavesdropper channe strengths: exact and average gains, respectivey. Cosed-form expressions for the secrecy outage probabiity for both cases are obtained, which are verified by simuations. The proposed max-ratio reay seection scheme is shown to outperform one based on a max-min-ratio reay scheme. Index Terms Secure wireess communications, cooperative networks, reay seection, secrecy capacity. I. INTRODUCTION TRADITIONALLY security in wireess networks has been focused on higher ayers using cryptographic methods [1]. However, retaining security at high ayers is becoming more chaenging due to the increased potentia for attack, therefore, there has been growing interest in impementing security at the physica ayer. Reated work was described as eary as in the 197s [2] [5], and more recenty for physica ayer security in wireess communications [6] [1]. The purpose of physica ayer security is to prevent eavesdroppers from intercepting the data transmitted between the source and intended destination. The secrecy is quantified by the secrecy capacity, or the maximum rate of reiabe information sent Manuscript received September 2, 213; revised December 24, 213 and February 18, 214; accepted February 18, 214. Date of pubication February 21, 214; date of current version March 14, 214. This work was supported in part by the Engineering and Physica Sciences Research Counci under Grant EP/K1437/1 and in part by the MOD University Defence Research Coaboration in Signa Processing. The associate editor coordinating the review of this manuscript and approving it for pubication was Prof. T. Chares Cancy. G. Chen, Z. Tian, Y. Gong, and J. A. Chambers are with the Advanced Signa Processing Group, Schoo of Eectronic, Eectrica and Systems Engineering, Loughborough University, Loughborough LE11 3TU, U.K. (e-mai: g.chen@boro.ac.uk; z.tian@boro.ac.uk; y.gong@boro.ac.uk; j.a.chambers@boro.ac.uk). Z. Chen is with the Nationa Key Laboratory of Science and Technoogy on Communications, University of Eectronic Science and Technoogy of China, Chengdu , China (e-mai: chenzhi@uestc.edu.cn). Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier 1.119/TIFS from the source to the intended destination in the presence of eavesdroppers [5]. Recent research shows that cooperative communication not ony significanty improves the transmission capacity for wireess networks (e.g. [11] and [12]), but aso provides an effective way to improve the secrecy capacity. This is achieved by carefuy designing the reays to maximize the information rate at the intended destination and minimize that at the eavesdroppers [13]. In genera, there are three ways to improve the secrecy capacity in a cooperative network: Distributed beamforming - The secrecy capacity can be maximized by optimizing the transmission weights (or the beamforming weights) at the reay and source nodes (e.g. [14] and [15]). Such distributed beamforming however requires high coordination (such as synchronization and centra optimization) among source and reay nodes, which usuay requires high overhead in impementation, i.e. a arge amount of information needs to be exchanged between the reay nodes. Jamming - A jammer is used to inject artificia interference into the system. When the injected interfering power is higher at the eavesdroppers than that at the intended destination, the secrecy capacity can be improved (e.g. [16] [18]). This often requires the jammer to be ocated coser to the eavesdroppers than to the destination node, which is not aways possibe in practice. Reay seection - Reay seection can increase the secrecy capacity by choosing an appropriate reay node with strong transmission ink to the intended destination node and weak ink to the eavesdropper [19] [22]. The reay seection provides an attractive way to improve the secrecy capacity with itte overhead in impementation. The performance of the reay seection depends strongy on the number of avaiabe inks for seection, which again depends on not ony the number of reays but aso the reay seection scheme. When the number of avaiabe inks is imited, so is the secrecy performance. Thus it is important to investigate reay seection schemes to have the best secrecy performance for a given number of reays, which is the main objective of this paper. In traditiona reay seection to improve wireess communications, the best reay is seected with the strongest ink connecting the source and destination (e.g. [23] and [24]). It is shown in [19] that by using reay seection the secrecy capacity can aso be improved when the best reay is seected This work is icensed under a Creative Commons Attribution 3. License. For more information, see

4 72 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 9, NO. 4, APRIL 214 to maximize the signa to eavesdropper channe gain ratio, which is abbreviated as the gain ratio in this paper. The reay seection scheme in [19] is based on the scenario that the eavesdropper can ony intercept the signas from the reays but not the source node. On the other hand, if the eavesdropper intercepts signas from both the reay and source nodes, the best reay is seected as having the maximum secrecy capacity among every pair of source-to-reay and reay-to-destination inks [18], which is termed as the max-min-ratio scheme in this paper. Aternativey, it is aso possibe to seect a jammer from the avaiabe reays (e.g [2]), but this is at the price of injecting more inference not ony to the intended receivers but aso to other users in the system. As was shown in [2], incuding a jammer does not necessariy ead to improvement in secrecy capacity, and thus a switching scheme was described to activate/deactivate the jammer. Recent research shows that, by introducing data buffers at the reays, it is possibe to reax the constraint that the best source-to-reay and reay-to-destination inks for a packet transmission must be determined concurrenty, and achieve significant performance advantage [25] [3]. A typica bufferaided reay seection is the max-max scheme described in [27], where the strongest source-to-reay and reay-to-destination inks are seected aternativey so that it has significant coding gain over the traditiona max-min scheme. Because the maxmax reay seection sti foows the traditiona transmission order, that is the source-to-reay and reay-to-destination transmissions aways carry on in an aternative manner, it can ony attain a diversity order of N which is the same as that for the max-min scheme, where N is the number of avaiabe reay nodes. In the recent max-ink approach [25], this constraint on the transmission order is further reaxed so that, at any time, a best ink is seected among a avaiabe source-to-reay and reay-to-destination inks. Depending on whether a source-toreay or a reay-to-destination ink is seected, either the source transmits a packet to the seected reay or the seected reay forwards a stored packet to the destination. It is shown in [25] that the max-ink reay seection not ony has coding gain over the max-min scheme, but aso has higher diversity order than both the max-min and max-max schemes. In particuar, the diversity order can approach 2N when the reay buffer size is arge enough. Inspired by the max-ink scheme, in this paper, we propose a nove max-ratio reay seection scheme for secure transmission in decode-and-forward (DF) reay networks with an eavesdropper which can intercept signas from both the source and reay nodes. In the proposed max-ratio scheme, every reay is equipped with a data buffer, and the best ink is aways seected with the highest gain ratio among a avaiabe sourceto-reay and reay-to-destination inks. We consider two cases for which either the exact, or the average gain, for the eavesdropping channe is avaiabe; the atter case is of particuar interest in practice since it is not aways possibe to obtain the exact channe information describing the eavesdropping channes. Both theoretica and simuation resuts show that the proposed max-ratio reay seection has significanty better performance than the conventiona max-min-ratio scheme, confirming that it represents an attractive approach for secure wireess transmission. The main contributions of this paper are summarized as foows to: Propose the buffer-aided max-ratio reay seection poicy for secure communications in a DF cooperative network. This is the first approach in using buffer-aided reay seection in secure transmission under the scenario that the eavesdropper can intercept signas from both the source and reay nodes. Existing reay seection schemes for secure transmission mainy assume no source-toeavesdropper ink for simpicity (e.g. [19]). Whie in [22] both the source and reay to eavesdropper inks are considered, the proposed scheme is for the two-way reay network and furthermore no cosed form expression is obtained for the secrecy outage probabiity. Derive cosed-form expressions for the secrecy outage probabiity of the max-ratio scheme for both cases when either the exact, or average, gains of the eavesdropping channes are avaiabe. Because the gain-ratios for the source-to-reay and reay-to-destination transmissions have different statistica distributions, the secrecy outage performance of the proposed max-ratio scheme is much more invoved to anayze than existing approaches such as the reay seection scheme for secure transmission in [19] and the buffer-aided max-ink scheme for wireess communications in [25]. In this paper, the probem arising from such unbaanced distribution has been successfuy soved, and the anaysis aso provides a usefu way in anayzing simiar systems such as a typica reay seection scheme but without the usua assumption that the source-to-reay and reay-to-destination channes are independent and identicay distributed (i.i.d.). The remainder of the paper is organized as foows: Section II describes the system mode; Section III proposes the max-ratio reay seection scheme; Sections IV and V anayze the secrecy outage probabiity for the cases with exact and average knowedge of the eavesdropping channes, respectivey; Section VI discusses the performance of the max-ratio scheme when the reay buffer sizes go to infinity; Section VII gives numerica simuations to verify the proposed max-ratio scheme; finay, Section VIII summarizes the paper. II. SYSTEM MODEL The system mode of the reay network with an eavesdropper is shown in Fig. 1, where there is one source node (S), one destination node (D), a set of K reays {R 1, R 2,...,R K }, and one eavesdropper (E) which can intercept signas from both the source and reay nodes. The reay nodes appy the DF protoco and perform the haf-dupex mode so that they do not transmit and receive simutaneousy. In our mode, we assume no direct ink between the source and the destination due to path oss or shadowing effects. 1 The channe coefficients for S R k, S E, R k D and R k E at time t are denoted as h srk (t), h se (t), h rk d(t) and h rk e(t) respectivey, where simiar subscripts are aso used for other parameters to indicate different channes in 1 Incuding the direct ink has itte effect on the reay seection which is the main issue in this paper.

5 CHEN et a.: MAX-RATIO RELAY SELECTION IN SECURE BUFFER-AIDED COOPERATIVE WIRELESS NETWORKS 721 Fig. 1. Reay seection system mode in secure transmission, where the eavesdropper intercepts signas from both the source and reay nodes. this paper. We assume the channes are quasi-static Rayeigh fading so that the channe coefficients remain unchanged during one packet duration but independenty vary from one packet time to another. We aso assume that a source-toreay inks are independent and identicay distributed (i.i.d.) fading and that E h srk (t) 2 γ sr for a k; a reay-todestination channe gains are aso i.i.d. and E h rk d(t) 2 γ rd, as are a reay-to-eavesdropper channe gains for which E h rk e(t) 2 γ re. The source-to-eavesdropper channe gain is denoted as E h se (t) 2 γ se. It is noted that we do not require any two of γ sr, γ rd, γ se and γ re to be the same, thereby representing a practica scenario. A noises are additive white Gaussian noise (AWGN), and without osing generaity the noise variances are a normaized to unity. The transmission powers for source and reay nodes are a assumed to be E s. With the DF appied at the reays, if the reay R k is seected for the data transmission, the instantaneous secrecy capacity for the overa system is obtained as [31] C k (t)max { 1 2 og 2 min{1+ E s h srk (t) 2, 1+ E s h rk d(t) 2 } 1+ E s h se (t) 2 + E s h rk e(t) 2 If the exact knowedge of the eavesdropping channes are avaiabe, the best reay node can be seected with the maximum C k (t). On the other hand, if ony the average gains of the eavesdropping channes are known, the best reay maximizes C k (t) with h se (t) 2 and h rk e(t) 2 being repaced with the average gains γ se and γ re in (1) respectivey. This scheme is termed as the max-min-ratio reay seection in this paper. For convenience in deveopment, the time index t is ignored in the rest of the paper uness necessary. III. MAX-RATIO RELAY SELECTION The performance of the max-min-ratio scheme is imited by the constraint that the best source-to-reay and reay-todestination inks must be determined concurrenty. In this paper, we propose a new max-ratio seection scheme by making use of data buffers at the reays. To be specific, we assume that every reay is equipped with a data buffer Q k (1 k K ) of finite size L (in the number of data packets), and the data packets in the buffer foow the first-in-first-out rue. } (1) At any time, the best transmission ink with the highest gain-ratio is seected among a avaiabe source-to-reay and reay-to-destination inks. Depending on the knowedge of the eavesdropper channe, we have two seection criteria: Case 1 - If the exact knowedge of a channes, 2 incuding the eavesdropping channes h se and h rk e, are avaiabe, the max-ratio seects the best reay as R (max ratio) case 1 arg max R k max { h sr k 2 } R k : (Q k ) L h se 2, max R k : (Q k ) { hrk d 2 h rk e 2 }, where (Q k ) gives the number of data packets in buffer Q k. Case 2 - If ony the average channe gains for the eavesdropping channes, i.e. γ se and γ re, are avaiabe (but the exact knowedge for a other channes is known), the best reay for the max-ratio scheme is seected as: R (max ratio) case 2 arg max R k max { h sr k 2 } R k : (Q k ) L, γ se (2) max { h r k d 2 } R k : (Q k ). (3) A. Secrecy Outage Probabiity The secrecy outage probabiity is defined as P out P(C < r sc ), where C is the instantaneous secrecy capacity, r sc is the target secrecy capacity and P(.) gives the probabiity of the encosed. In the max-ratio reay seection scheme, at any time, the numbers of data packets in every buffer form a state. Because there are K avaiabe reays and every reay is equipped with a buffer of size L, thereare(l + 1) K states in tota. The -th state vector is defined as s [ (Q 1 ),..., (Q K )] T, 1,...,(L + 1) K, (4) where (Q k ) gives the number of data packets in buffer Q k at state s. It is cear that (Q k ) L. Everystate corresponds to one pair of (K 1, K 2 ),wherek 1 and K 2 are the numbers of avaiabe inks for source-to-reay and reayto-destination transmission, respectivey. A source-to-reay or a reay-to-destination ink is considered avaiabe when the buffer of the corresponding reay node is not fu or not empty respectivey. It is cear that K 1 K and K 2 K. Specificay, if none of the buffers is fu or empty, a inks are avaiabe such that K 1 K 2 K. At state s, the best ink is seected among a K 1 source-toreay and K 2 reay-to-destination inks. We denote p s out as the outage probabiity for state s. Considering a possibe states, we obtain the secrecy outage probabiity for the max-ratio reay seection as P out (L+1) K 1 γ re π p s out, (5) 2 The CSI is usuay estimated through piots and feedback (e.g. [32]), and the CSI estimation without feedback may aso be appied (e.g [33]). Further detai of the CSI estimation is beyond the scope of this paper.

6 722 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 9, NO. 4, APRIL 214 where π p(s ) which is the stationary probabiity for state s. B. State Transition Matrix Suppose at time t, the state for the reay buffers is s. At time (t + 1), there is one reay seected for either receiving or transmitting a data packet, so that the number of packets in the corresponding buffer is increased or decreased by one respectivey. Depending on which reay receives or transmits data, at time (t + 1), the buffers may move from state s to severa possibe states, forming a Markov chain. We denote A as the (L + 1) K (L + 1) K state transition matrix, where the entry A n, P(X t+1 s n X t s ) is the transition probabiity that the state moves from s at time t to s n at time (t + 1). If the secrecy outage event occurs, the state s remain unchanged at time (t + 1). Otherwise, s moves to another state. Thus the probabiity for s to eave for another state is given by p eave s 1 p s out. (6) It is cear from the seection rues (2) and (3) that, for both Cases 1 and 2, the probabiities to seect the source-to-reay and reay-to-destination transmission at any time are not the same. This is very different from the max-ink approach in [25] where the seection of any avaiabe ink is equay ikey. We divide a states which can be moved from s into two sets, U + and U,whereU + contains a states to which s can move when a source-to-reay ink is seected and U contains a states to which s can move when a reay-to-destination ink is seected. We et ps S D and ps R D be the probabiities that the source-to-reay and reay-to-destination transmissions are seected at state s, respectivey. It is cear that ps S D + ps R D 1. On the other hand, because we assume a source-to-reay channes are i.i.d. fading and a reay-to-destination channes are aso i.i.d. frequency fat fading and so are the reay-toeavesdropper channes, the seection of one particuar ink within either U + or U is equay ikey. Therefore, the probabiity to seect a source-to-reay or reay-to-destination ink at state s is given by ( ) 1 p s + ps eave ps S R K 1 (1 p s 1 K out)(1 ps R D ), ( ) 1 1 ps eave ps R D K 1 (1 p s 2 K out)ps R D, (7) 2 p s respectivey. With these observations, the (n, )-th entry of the state transition matrix A is expressed as p s p s out, if n, p s + A n, K 1 1 (1 p s out)(1 ps R D ), if s n U +, ps K 1 2 (1 p s out)ps R D, if s n U,, esewhere. (8) Because the transition matrix A in (8) is coumn stochastic, irreducibe and aperiodic, 3 the stationary state probabiity vector is obtained as (see [35] and [36]) π (A I + B) 1 b, (9) where π [π 1,,π (L+1) K ] T, b (1, 1,...,1) T, I is the identity matrix and B n, is an n a one matrix. Finay, substituting (8) and (9) into (5) re-formats the secrecy outage probabiity as P out (L+1) K 1 π p s out diag(a) π diag(a) (A I + B) 1 b, (1) where diag(a) is a vector consisting of a diagona eements of A. It is cear from (1) that the secrecy outage probabiity P out is determined by A which again, from (8), is determined by p s out and ps R D. The secrecy outage probabiities for both Cases 1 and 2 can be expressed as (1), but with different p s out and ps R D which are derived beow. IV. CASE 1-EXACT KNOWLEDGE OF EAVESDROPPING CHANNELS In Case 1, we assume exact knowedge for the instantaneous gains for a channes, incuding the eavesdropping channes. This is a typica assumption in many existing approaches (e.g. [2] and [21]). A. p s out: Outage Probabiity at State s for Case 1 The reay seection rue for Case 1 is shown in (2). For better exposition, we et x max { h sr k 2 }/ h se 2, y (Q k ) L max { h r k d 2 / h rk e 2 } and z max(x, y). In order to concentrate on the secrecy capacity, we assume the channe SNR (Q k ) is high enough so that the decoding is aways successfuy at the reay and destination nodes. 4 The probabiity of outage event at state s at the high SNR is given by p s out P(z < 2 2r sc ) F Z (z) z2 2rsc, (11) where F Z (z) is the cumuative-probabiity-function (CDF) of z which is derived beow. Reca that state s corresponds to (K 1, K 2 ). From the theory of order statistics [37], if the number of avaiabe source-toreay inks is K 1,theCDFofx 1 max { h sr k 2 } is given (Q k ) L by F X1 (x) [1 e γsr x ] K 1, (12) Noting that x x 1 / h se 2,theCDFofx is then obtained as K 1 F X (x) CK i 1 ( 1) i M 1, (13) ix + M 1 i 3 Coumn stochastic means a entries in any coumn sum up to one, irreducibe means that it is possibe to move from any state to any state, and aperiodic means that it is possibe to return to the same state at any steps [34], [35]. 4 This is a typica assumption in most existing secure communications iterature (e.g. [19], [2]).

7 CHEN et a.: MAX-RATIO RELAY SELECTION IN SECURE BUFFER-AIDED COOPERATIVE WIRELESS NETWORKS 723 where CK i 1 K 1!/[i!(K 1 i)!] which is the binomia coefficient, and M 1 γ sr /γ se which is the average gain ratio between the source-to-reay and source-to-eavesdropper channes. On the other hand, because the number of avaiabe reayto-destination inks is K 2,theCDFofy is given by [ ] y K2 F Y (y), (14) M 2 + y where M 2 γ rd /γ re which is the average gain ratio between the reay-to-destination and reay-to-eavesdropper channes. Because x and y are mutuay independent, from (13) and (14), the CDF of z max(x, y) is obtained as: K 1 [ ] F Z (z) F X (z)f Y (z) CK i 1 ( 1) i M 1 z K2. iz+m 1 M 2 +z i (15) Substituting (15) into (11) gives p s K 1 [ out CK i 1 ( 1) i M 1 2 2r ] K2 sc i2 2r sc + M 1 M r. (16) sc i The next subsection wi provide the probabiity of seecting the reay to destination transmission at state s. B. ps R D : Probabiity of Seecting the Reay-to-Destination Transmission at State s for Case 1 If there are no reay-to-destination inks avaiabe (or K 2 ), we have ps R D. On the other hand, if there are no source-to-reay inks avaiabe (or K 1 ), we have ps R D 1. For other cases, ps R D is obtained in Appendix I. In summary, we have obtained ps R D (17), as shown at the bottom of the page, where B(x, y) 1 t x 1 (1 t) y 1 dt which is the Beta function and F 2,1 (a, b, c, z) is the first hypergeometric function. Finay, substituting (16) and (17) into (1) gives the secrecy outage probabiity at the high SNR for Case 1. V. CASE 2-KNOWLEDGE OF THE AVERAGE CHANNEL GAINS FOR EAVESDROPPING CHANNELS In case 2, we ony have knowedge of the average gains for eavesdropping channes, whie the exact information for a other channes are sti avaiabe. A. p s out: Outage Probabiity at State s for Case 2 We et u ab h ab 2 /γ ab be the normaized gain for channe h ab, where {ab} {sr k, se, r k d, r k e}. Because of the normaization, a u ab have the same probabiity-densitydistribution (PDF) as f U (u) e u, (18) The seection rue in (3) can then be expressed as R (2) b arg max R k { max R k : (Q k ) L { } { } } M1 u srk, max M2 u rk d, R k : (Q k ) (19) where M 1 and M 2 are defined in (13) and { (14), respectivey. } We further et f max M1 u srk, g { } R k : (Q k ) L max M2 u rk d and w max{ f, g}. It is cear that w is R k : (Q k ) directy obtained from the seection rue (3) which is based on the average gain of the eavesdropping channes. On the other hand, the secrecy outage is determined by the instantaneous gains of the data and eavesdropping channes. Therefore, in order to obtain the outage probabiity, w needs to be divided by u which is normaized exponentiay distributed with PDF given by (18). Or the outage probabiity for state s for Case 2 is given by p s out P(v < 2 2r sc ) F V (v) v2 2rsc, (2) where v w/u. The CDF-s of f and g are given by F F ( f ) [ 1 e 1] f/m K1 [ and F G (g) 1 e 2] g/m K2, (21) respectivey. Because f and g are mutuay independent, the CDF of w max{ f, g} is obtained as [ ] F W (w) F F (w)f G (w) 1 e w/m K1 [ K e 2] w/m (22) Then the CDF of v w/u is [ ] F V (v) 1 e uv/m K1 [ 1 1 e 2] uv/m K2 e u du K 1 K 2 i j C i K 1 C i K 2 ( 1) i+ j M 1 M 2 v(m 2 i + M 1 j) + M 1 M 2. (23), K 2, < K 1 K, 1 K 1 /2+ K 1 i 2 Ci K 1 ( 1) i i[n(i) 1]+1 (i 1) 2, < K 1 K, K 2 1, M 1 M 2 ps R D 1+ K 1 i 1 Ci K 1 ( 1) i M 2 in(i)+in(m 2 )M 2 in(m 1 )M 2 M 2 i +M 1 M 1 (M 1 im 2 ) 2, < K 1 K, K 2 1, M 1 M 2 1+ K 1 i 1 Ci K 1 ( 1) i K 2 ( M 1 M 2 i )K 2 B(2, K 2 )F 2,1 ([K 2 +1, K 2 ], K 2 +2, 1 M 1 M 2 i ), < K 1 K, 1 < K 2 K, 1, K 1, < K 2 K, (17)

8 724 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 9, NO. 4, APRIL 214 Substituting (23) into (11) gives K 1 K 2 p s out i j C i K 1 C i K 2 ( 1) i+ j M 1 M 2 2 2r sc(m 2 i + M 1 j) + M 1 M 2. (24) The next subsection wi provide the probabiity of seecting the reay to destination transmission at state s. B. ps R D : Probabiity of Seecting the Reay-to-Destination Transmission at State s for Case 2 SimiartothatinCase1,wehaveps R D fork 2, and ps R D 1forK 1. But otherwise, we have ps R D P( f < g) f FG ( f, g)dfdg, (25) f <g where f FG ( f, g) is the joint PDF of f and g. From (21), the PDFs of f and g are obtained as f F ( f ) K 1 e f M 1 (1 e f M 1 ) K 1 1 M 1 f G (g) K 2 e g M 2 (1 e g M 2 ) K2 1, (26) M 2 respectivey. Because f and g are mutuay independent, we have f FG ( f, g) f F ( f ) f G (g). Substituting (26) into (25) gives (27), as shown at the bottom of the page. Therefore, we have ps R D in (28), as shown at the bottom of the page. Finay, substituting (24) and (28), into (1) gives the secrecy outage probabiity at high SNR for Case 2. VI. DISCUSSION In this section, we consider a specific scenario that the average gain ratios for the source-to-reay and reay-to-destination transmissions are the same, or M 1 M 2. Of particuar interest is the outage performance for L which shows the best potentia performance for the max-ratio scheme. First we consider Case 2. Because M 1 M 2, the probabiities to seect a source-to-reay and reay-to-destination ink are the same, and both equa 1/(K 1 + K 2 ). This is simiar to the max-ink scheme in [25]. Thus buiding upon the anaysis in [25], we can obtain that, if L, the stationary probabiity for any state corresponding to K 1 K or K 2 K must be, or we have P(s ) 1. (29) s :K 1 K 2 K This impies that, if L, at any time, the best ink is aways seected from K 1 + K 2 2K avaiabe channes with the max-ratio scheme in Case 2. In Case 1, unfortunatey, we cannot have a simpe form as in (29) for L, because the probabiities to seect a source-to-reay and reay-to-destination ink are not equa, even with M 1 M 2. In order to iustrate the performance for L, the origina scheme can be assumed to be equivaent to a virtua reay section scheme having equa probabiity to seect a source-to-reay and reay-to-destination ink, or P(x < y).5 wherex and y are defined in Section IV-A. Then in the virtua scheme with L, the number of avaiabe source-to-reay and reay-to-destination inks are aways K 1 and K 2, respectivey, or s :K 1 K 1,K 2K 2 P(s ) 1. If we et K 1 K,thenK 2 can be obtained by soving P(x < y).5 as (3), as shown at the bottom of the page, where P(x < y) is given by (35) in the Appendix I. Since K 2 obtained from (3) is usuay not an integer, the virtua seection scheme cannot be reaized in practice. However, it provides interesting insight in understanding the secrecy performance of the origina max-ratio scheme in Case 1 for L. Normay, we have K 2 < K,which impies that, on the average, the best ink is aways seected from K 1 + K 2 avaiabe channes at any time and K K 1 + K 2 2K. For both Case 1 and 2, with a imited buffer size L, we aways have K 1 + K 2 K at any time. On the contrary, in the max-min-ratio seection scheme, the best ink is seected from ony K inks. Therefore, it foows that the max-ratio scheme has significanty better secrecy outage performance than the benchmark max-min-ratio scheme, and the best potentia performance for the max-ratio scheme is reached when L. This wi be verified the next section. VII. NUMERICAL RESULTS In this section, simuation resuts are given to verify the secrecy outage probabiities for the proposed max-ratio reay seection scheme. Both Case 1 and 2 are considered. In the s s y K 1 K 2 M 1 M 2 e x M1 e y M 2 (1 e x M 1 ) K 1 1 (1 e y K 1 M 2 ) K2 1 dxdy i K 2 1, K 2, < K 1 K, K1 K2 1 i j Ci K 1 C j K 2 1 ( 1)i+ j M 1 K 2 M 1 + M 1 j + M 2 i, < K 1 K, < K 2 K, 1, K 1, < K 2 K. j C i K 1 C j K 2 1 ( 1)i+ j M 1 K 2 M 1 +M 1 j +M 2 i. (27) (28) K 1 P(x < y) C i K 1 ( 1) i+1 K 2 ( M 1 M 2 i )K 2B(2, K 2 )F 2,1([K 2 + 1, K 2 ], K 2 + 2, 1 M 1 ).5, (3) M 2 i i1

9 CHEN et a.: MAX-RATIO RELAY SELECTION IN SECURE BUFFER-AIDED COOPERATIVE WIRELESS NETWORKS 725 Fig. 2. The secrecy outage probabiities for different reay seection schemes. (a) Case 1. (b) Case 2. Fig. 4. The secrecy outage probabiities of the max-ratio scheme for different reay numbers K. (a) Case 1. (b) Case 2. Fig. 3. The secrecy outage probabiities of the max-ratio scheme for Cases 1 and 2. simuation, a noise variance and transmission powers are normaized to unity, and the average channe gains for sourceto-reay and reay-to-destination transmissions are set as γ sr γ rd 3 db. Thus the corresponding average channe SNR is aso 3 db which is high enough to guarantee successfu decoding at the reays and destination. The average eavesdropping channe gains, i.e. γ se and γ re, are determined through the settings of the average gain ratios M 1 γ sr /γ se and M 2 γ rd /γ re,whereweetm 1 M 2 for various vaues in the simuations. In every simuation beow, both theoretica and simuated secrecy outage probabiities are shown to essentiay perfecty match, where the theoretica resuts are based on (1) and simuation resuts are obtained by averaging 5,, independent runs. This verifies the cosed-form secrecy outage probabiities obtained in this paper. Fig. 2 compares the secrecy outage performance of the proposed max-ratio scheme with those for the no reay seection and the traditiona max-min-ratio schemes, where the reay number is set as K 5 in a reay seection schemes. It is ceary shown that the no reay seection scheme has the worst outage performance and the proposed max-ratio has the best. It is interesting to observe that, for both Cases 1 and 2, with buffer size L 1, the max-ratio sti performs significanty better than the max-min-ratio scheme. We highight that the max-min-ratio scheme is effectivey aso equipped with a buffer of size 1, because the reays need to store the decoded data at one time and transmit out at the next time. However, even with L 1, the max-ratio does not reduce to the maxmin-ratio scheme. This is because, for any reay receiving a data packet in the max-ratio scheme, it has the choice of whether to transmit the packet out at the next time or not.

10 726 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 9, NO. 4, APRIL 214 Fig. 5. The secrecy outage probabiities of the max-ratio scheme for different reay buffer sizes L. (a) Case 1. (b) Case 2. Fig. 6. The secrecy outage probabiities vs SNR, where γ se γ re 3 db and target secrecy capacity is unity. (a) Case 1. (b) Case 2. On the contrary, the reays in the max-min-ratio schemes do not have such choices. Therefore, the max-ratio scheme has coding gain over the max-min-ratio approach. On the other hand, with L, the best potentia performance of the max-ratio is reached, which is ceary shown in Fig. 2(a) and (b) for both Case 1 and 2 respectivey. Fig. 3 compares the secrecy outage probabiities of the maxratio scheme for Cases 1 and 2, where the buffer size is fixed at L 3, the average gain ratios are set as M 1 M 2 2 or 5, and the reay number is set as K 2 or 5. It is ceary shown that the max-ratio scheme in Case 1 has consistenty better performance than that in Case 2. Fig. 4 compares the secrecy outage probabiities of the max-ratio scheme for different numbers of reays, where the buffer size is fixed as L 5 and the average gain ratios are set as M 1 M 2 5. It is ceary shown that, in both cases, the increase of the reay number can significanty improve the secrecy outage performance. For exampe, for the target secrecy capacity γ sc.5, when the reay number is increased from K 2 to K 5, the secrecy outage probabiity decreases by approximatey 1 db in Case 1, and by amost 6 db in Case 2. This verifies the effectiveness of using the max-ratio reay seection in improving the secrecy performance. Fig. 5 compares the secrecy outage probabiities of the max-ratio scheme for different reay buffer sizes, where the reay number and average gain ratio are fixed at K 4 and M 1 M 2 5, respectivey. Whie both the theoretica and simuation resuts have been obtained and perfecty match each other, ony the theoretica resuts are shown in Fig. 5 as otherwise it woud be too congested for iustration. Particuary, for L in Case 1, K 1 and K 2 for the virtua seection scheme (described in Section VI) are obtained as K 1 K 4andK respectivey. The theoretica resut for Case 1 is then obtained by using K 1 4, K to cacuate the outage probabiity in (1). On the other hand, the theoretica resut for L in Case 2 is obtained by using K 1 K 2 K 4 in the corresponding outage probabiity expression. In both Cases 1 and 2, for L, the simuation resuts are actuay obtained by using a very arge buffer size L 5. It is ceary shown that, for both Cases 1 and 2, the secrecy outage probabiity decreases with the increase of the buffer size L, but the improvement becomes ess significant as L increases. In fact, when L 5, the

11 CHEN et a.: MAX-RATIO RELAY SELECTION IN SECURE BUFFER-AIDED COOPERATIVE WIRELESS NETWORKS 727 secrecy outage probabiity is aready very cose to that for L. Fig. 6 shows the secrecy outage probabiities vs the SNR for the proposed max-ratio scheme. It is cear that, in both Cases 1 and 2, the secrecy outage probabiity improves significanty with increased number of the reay nodes. VIII. CONCLUSION This paper proposed a new max-ratio reay seection poicy for secure buffer-aided cooperative DF networks. With the hep of buffers at the reays, the best reay was seected with the argest gain ratio among a avaiabe source-to-reay and reayto-destination inks. Both cases with knowedge of exact and average gain for eavesdropping inks were considered, and for the first time, in the chaenging secure transmission context, cosed-form expressions for the secrecy outage probabiities for both cases were derived. Both anaysis and simuations show that the proposed max-ratio reay seection has significanty better performance in secrecy outage probabiity than the benchmark max-min-ratio scheme, and provides an attractive way to reaize and improve secure transmission at the physica ayer of wireess communications. APPENDIX I PROOF OF (17) Noting the definition of x and y in Section IV-A, we have s P(x < y) x<y y f XY (x, y)dxdy f XY (x, y)dxdy, (31) where f XY (x, y) is the joint PDF of x and y. From the CDF-s of x and y given by (13) and (14) respectivey, the PDF-s of x and y are obtained as f X (x) K 1 i C i K 1 ( 1) i+1 M 1 i (M 1 +ix) 2 and f Y (y) y K2 1 K 2 M 2 (M 2 +y) K 2+1, (32) respectivey. Because x and y are mutuay independent, we have K 1 CK i f XY (x, y) f X (x) f Y (y) 1 ( 1) i+1 M 1 M 2 K 2 iy K 2 1 (M 1 +ix) 2 (M 2 +y) K. 2+1 i Substituting (33) into (31) gives s K 1 y K 1 i CK i 1 ( 1) i+1 M 1 M 2 K 2 iy K 2 1 (M 1 + ix) 2 (M 2 + y) K dxdy 2+1 (33) 1+ CK i 1 ( 1) i y K 2 1 M 1 M 2 K 2 (M 1 + iy)(m 2 + y) K 2+1 dy. i1 (34) Then according to [38], if K 2 > 1, we obtain K 1 ( ) K2 s 1 + CK i 1 ( 1) i M1 K 2 B(2, K 2 ) M 2 i i1 F 2,1 ( [K 2 + 1, K 2 ], K 2 + 2, 1 M 1 M 2 i if K 2 1andM 1 M 2,wehave K 1 i2 ) ; (35) s 1 K 1 /2 + CK i i i[n(i) 1]+1 1 ( 1) (i 1) 2 ; (36) and if K 2 1andM 1 M 2,wehave s 1 + CK i 1 ( 1) i M 1 K 1 i1 in(i)m 2 + in(m 2 )M 2 in(m 1 )M 2 im 2 + M 1 (M 1 im 2 ) 2. (37) ACKNOWLEDGMENT We woud ike to thank the anonymous reviewers and the editor for their constructive comments. REFERENCES [1] E. D. Siva, A. L. D. Santos, L. C. P. Abini, and M. Lima, Identitybased key management in mobie ad hoc networks: Techniques and appications, IEEE Trans. Wireess Commun., vo. 15, no. 5, pp , Oct. 28. [2] A. D. Wyner, The wire-tap channe, Be Syst. Tech. J., vo. 54, pp , Jan [3] R. Liu, I. Maric, P. Spasojevic, and R. D. Yates, Discrete memoryess interference and broadcast channes with confidentia messages: Secrecy rate regions, IEEE Trans. Inf. Theory, vo. 54, no. 6, pp , Jun. 28. [4] M. Boch, J. Barros, M. R. D. Rodrigues, and S. W. McLaughin, Wireess information-theoretic security, IEEE Trans. Inf. Theory, vo. 54, no. 6, pp , Jun. 28. [5] S. K. L. Y. Cheong and M. E. Heman, The Gaussian wiretap channe, IEEE Trans. Inf. Theory, vo. 24, no. 4, pp , Ju [6] Y. Liang, H. V. Poor, and S. Shamai, Secure communication over fading channes, IEEE Trans. Inf. Theory, vo. 54, no. 6, pp , Jun. 28. [7] P. K. Gopaa, L. Lai, and H. E. Gama, On the secrecy capacity of fading channes, IEEE Trans. Inf. Theory, vo. 54, no. 1, pp , Oct. 28. [8] Y. Liang and H. V. Poor, Mutipe-access channes with confidentia messages, IEEE Trans. Inf. Theory, vo. 54, no. 3, pp , Mar. 28. [9] I. Csiszr and P. Narayan, Secrecy capacities for mutitermina channe modes, IEEE Trans. Inf. Theory, vo. 54, no. 6, pp , Jun. 28. [1] A. Khisti, A. Tchamkerten, and G. W. Worne, Secure broadcasting over fading channes, IEEE Trans. Inf. Theory, vo. 54, no. 6, pp , Jun. 28. [11] A. Papadogiannis, H. Bang, D. Gesbert, and E. Hardouin, Efficient seective feedback design for mutice cooperative networks, IEEE Trans. Veh. Techno., vo. 6, no. 1, pp , Jan [12] Y. J. Fan, C. Wang, J. Thompson, and H. V. Poor, Recovering mutipexing oss through successive reaying using repetition coding, IEEE Trans. Wireess Commun., vo. 6, no. 12, pp , Dec. 27. [13] P. Popovski and O. Simeone, Wireess secrecy in ceuar systems with infrastructure-aided cooperation, IEEE Trans. Inf. Forensics Security, vo. 4, no. 2, pp , Jun. 29.

12 728 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 9, NO. 4, APRIL 214 [14] L. Dong, Z. Han, A. P. Petropuu, and H. V. Poor, Secure wireess communications via cooperation, in Proc. 46th Ann. Aerton Conf. Commun., Contro, Comput., Champaign, IL, USA, Sep. 28, pp [15] L. Dong, Z. Han, A. P. Petropuu, and H. V. Poor, Ampify-and-forward based cooperation for secure wireess communications, in Proc. IEEE Int. Conf. Acoust., Speech, Signa Process., Taipei, Taiwan, Apr. 29, pp [16] E. Tekin and A. Yener, The mutipe access wire-tap channe: Wireess secrecy and cooperative jamming, in Proc. Inf. Theory App. Workshop, San Diego, CA, USA, Jan. 27, pp [17] E. Tekin and A. Yener, The genera Gaussian mutipe access and two-way wire-tap channes: Achievabe rates and cooperative jamming, IEEE Trans. Inf. Theory, vo. 54, no. 6, pp , Jun. 28. [18] Z. Ding, M. Peng, and H. H. Chen, A genera reaying transmission protoco for MIMO secrecy communications, IEEE Trans. Commun., vo. 6, no. 11, pp , Nov [19] I. Krikidis, Opportunistic reay seection for cooperative networks with secrecy constraints, IET Commun., vo. 4, no. 15, pp , Oct. 21. [2] I. Krikidis, J. Thompson, and S. Mcaughin, Reay seection for secure cooperative networks with jamming, IEEE Trans. Wireess Commun., vo. 8, no. 1, pp , Oct. 29. [21] G. Chen, V. Dwyer, I. Krikidis, J. S. Thompson, S. McLaughin, and J. A. Chambers, Comment on Reay seection for secure cooperative networks with jamming, IEEE Trans. Wireess Commun., vo. 11, no. 6, pp , Jun [22] J. C. Chen, R. Q. Zhang, L. Y. Song, Z. Han, and B. L. Jiao, Joint reay and jammer seection for secure two-way reay networks, IEEE Trans. Inf. Forensics Security, vo. 7, no. 1, pp , Feb [23] Z. Ding, Y. Gong, T. Ratnarajah, and C. Cowan, On the performance of opportunistic cooperative wireess networks, IEEE Trans. Commun., vo. 56, no. 8, pp , Aug. 28. [24] A. Betsas, A. Khisti, D. P. Reed, and A. Lippman, A simpe cooperative diversity method based on network path seection, IEEE J. Se. Areas Commun., vo. 24, no. 3, pp , Mar. 26. [25] I. Krikidis, T. Charaambous, and J. S. Thompson, Buffer-aided reay seection for cooperative diversity systems without deay constraints, IEEE Trans. Wireess Commun., vo. 11, no. 5, pp , May 212. [26] H. Liu, P. Popovski, E. Carvaho, and Y. Zhao, Sum-rate optimization in a two-way reay network with buffering, IEEE Commun. Lett., vo. 17, no. 1, pp , Jan [27] A. Ikhef, D. S. Michaopouos, and R. Schober, Max-max reay seection for reays with buffers, IEEE Trans. Wireess Commun., vo. 11, no. 3, pp , May 212. [28] N. Zatanov, R. Schober, and L. Lampe, Buffer-aided reaying in a three node network, in Proc. IEEE Int. Symp. Inf. Theory, Cambridge, MA, USA, Ju. 212, pp [29] N. Zatanov, R. Schober, and P. Popovski, Buffer-aided reaying with adaptive ink seection, IEEE J. Se. Areas Commun., vo. 31, no. 8, pp , Aug [3] B. Xia, Y. Fan, J. Thompson, and H. V. Poor, Buffering in a threenode reay network, IEEE Trans. Wireess Commun., vo. 7, no. 11, pp , Nov. 28. [31] L. Lai and H. E. Gama, The reay eavesdropper channe: Cooperation for secrecy, IEEE Trans. Inf. Theory, vo. 54, no. 9, pp , Sep. 28. [32] A. Ghasemi and E. S. Sousa, Fundamenta imits of spectrum-sharing in fading environment, IEEE Trans. Wireess Commun., vo. 6, no. 2, pp , Feb. 27. [33] K. Hamdi, W. Zhang, and K. B. Letaief, Power contro in cognitive radio systems based on spectrum sensing side information, in Proc. IEEE Int. Conf. Commun., Gasgow, Scotand, Jun. 27, pp [34] C. M. Grinstead and J. L. Sne, Introduction to Probabiity, 2nd ed. Providence, RI, USA: Amer. Math. Soc., 1991, ch. 11. [35] J. R. Norris, Markov Chains. Cambridge, U.K.: Cambridge Univ. Press, [36] A. Berman and R. J. Pemmons, Nonnegative Matrices in the Mathematica Sciences. Phiadephia, PA, USA: Soc. Ind. App. Math, [37] H. A. David, Order Statistics, 2nd ed. Hoboken, NJ, USA: Wiey, [38] I. S. Gradshteyn and I. M. Ryzhik, Tabe of Integras, Series, and Products, 7th ed. New York, NY, USA: Esevier, 27. Gaojie Chen (S 9 M 12) received the B.Eng. and B.Ec. degrees in eectrica information engineering and internationa economics and trade from the Northwest University, Shaanxi, China, in 26, and the M.Sc. and Ph.D. degrees in eectrica and eectronic engineering from Loughborough University, Loughborough, U.K., in 28 and 212, respectivey. From 28 to 29, he was a Software Engineer with DTmobie, Beijing, China, and from 212 to 213, as a Research Associate with the Schoo of Eectronic, Eectrica, and Systems Engineering, Loughborough University. He is currenty a Research Feow with the Facuty of Engineering and Physica Sciences, University of Surrey, Guidford, U.K. His current research interests incude information theory, wireess communications, cooperative communications, cognitive radio, and secrecy communications. Zhao Tian (S 12) received the B.Eng. degree from the Schoo of Eectronic, Eectrica, and Systems Engineering, Loughborough University, U.K., in 212. He is currenty pursuing the Ph.D. degree at the Advanced Digita Signa Process Group, Schoo of Eectronic, Eectrica, and Systems Engineering, Loughborough University, U.K., with a fu postgraduate schoarship from the Engineering and Physica Sciences Research Counci. His current research interests incude the genera fied of wireess communications with emphasis on buffer-aided reaying. Yu Gong was with the Schoo of Eectronic, Eectrica, and Systems Engineering, Loughborough University, U.K., in 212. He received the B.Eng. and M.Eng. degrees in eectronic engineering from the University of Eectronics and Science Technoogy, China, in 1992 and 1995, respectivey, and the Ph.D. degree in communications from the Nationa University of Singapore, in 22. After the Ph.D. graduation, he took severa research positions with the Institute of Inforcomm Research, Singapore, and the Queen s University of Befast, U.K. From 26 to 212, he has been an Academic Member with the Schoo of Systems Engineering, University of Reading, U.K. His current research interests are in the area of signa processing and communications, incuding wireess communications, cooperative networks, and noninear and nonstationary system identification and adaptive fiters. Zhi Chen (M 4) received the B.Eng., M.Eng., and Ph.D. degrees in eectrica engineering from the University of Eectronic Science and Technoogy of China (UESTC), in 1997, 2, and 26, respectivey. After the Ph.D. graduation, he joined the Nationa Key Laboratory of Science and Technoogy on Communications, UESTC, where he was promoted to Professor in 213. He was a Visiting Schoar with the University of Caifornia, Riverside, from 21 to 211. His current research interests incude wireess communication and signa processing, specificay reay and cooperative communications, interference coordination, and canceation. He has served as a Reviewer for various internationa journas and conferences, incuding the IEEE TRANSACTIONS ON SIGNAL PROCESSING and the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.

13 CHEN et a.: MAX-RATIO RELAY SELECTION IN SECURE BUFFER-AIDED COOPERATIVE WIRELESS NETWORKS 729 Jonathon A. Chambers (S 83 M 9 SM 98 F 11) received the Ph.D. and D.Sc degrees in signa processing from the Imperia Coege of Science, Technoogy, and Medicine (Imperia Coege London), London, U.K., in 199 and 214, respectivey. From 1991 to 1994, he was a Research Scientist with the Schumberger Cambridge Research Center, Cambridge, U.K. In 1994, he returned to Imperia Coege London, as a Lecturer in signa processing and was promoted as a Reader (Associate Professor) in From 21 to 24, he was the Director with the Centre for Digita Signa Processing and a Professor of signa processing with the Division of Engineering, King s Coege London, London. From 24 to 27, he was a Cardiff Professoria Research Feow with the Schoo of Engineering, Cardiff University, Waes, U.K. In 27, he joined the Department of Eectronic and Eectrica Engineering, Loughborough University, Loughborough, U.K., where he heads the Advanced Signa Processing Group and serves as the Associate Dean (Research) for Loughborough University. He is a coauthor of the books Recurrent Neura Networks for Prediction: Learning Agorithms, Architectures, and Stabiity (Hoboken, NJ, USA: Wiey, 21) and EEG Signa Processing (Hoboken, NJ, USA: Wiey, 27). He has advised more than 5 researchers through to Ph.D. graduation and pubished more than 35 conference proceedings and journa artices, many of which are in IEEE journas. His current research interests incude adaptive and bind signa processing, and their appications. He is a feow of the Roya Academy of Engineering, U.K., and the Institution of Eectrica Engineers. He was the Technica Program Chair of the 15th Internationa Conference on Digita Signa Processing and the 29 IEEE Workshop on Statistica Signa Processing, both hed in Cardiff, U.K., and a Technica Program Cochair for the 36th IEEE Internationa Conference on Acoustics, Speech, and Signa Processing, Prague, Czech Repubic. He received the first QinetiQ Visiting Feowship in 27 for his outstanding contributions to adaptive signa processing and his contributions to QinetiQ as a resut of his successfu industria coaboration with the internationa defense systems company QinetiQ. He has served on the IEEE Signa Processing Theory and Methods Technica Committee for six years, the IEEE Signa Processing Society Awards Board for three years, and is currenty a member of the IEEE Signa Processing Conference Board and the European Signa Processing Society Best Paper Awards Seection Pane. He has served as an Associate Editor of the IEEE TRANSACTIONS ON SIGNAL PROCESSINGfor three terms from 1997 to 1999, from 24 to 27, and since 211, and is currenty a Senior Area Editor.