RADIOENGINEERING, VOL. 24, NO. 1, APRIL Chenguang SHI, Fei WANG, Jianjiang ZHOU, Jun CHEN

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1 RADIOENGINEERING, VOL. 4, NO., APRIL 5 99 Fuzzy Chance-Constained Pogamming Based Secuity Infomation Optimization fo Low Pobability of Identification Enhancement in Rada Netwok Systems Chenguang SHI, Fei WANG, Jianiang ZHOU, Jun CHEN Key Laboatoy of Rada Imaging and Micowave Photonics, Ministy of Education, Naning Univesity of Aeonautics and Astonautics, No. 9, Yudao Steet, Qinhuai Distict, Naning city, Jiangsu Povince, Naning 6, P. R. China zee@nuaa.edu.cn Abstact. In this pape, the poblem of low pobability of identification (LPID) impovement fo ada netwok systems is investigated. Fistly, the secuity infomation is deived to evaluate the LPID pefomance fo ada netwok. Then, without any pio knowledge of hostile intecept eceive, a novel fuzzy chance-constained pogamming (FCCP) based secuity infomation optimization scheme is pesented to achieve enhanced LPID pefomance in ada netwok systems, which focuses on minimizing the achievable mutual infomation (MI) at intecepto, while the attainable MI outage pobability at ada netwok is enfoced to be geate than a specified confidence level. Regading to the complexity and uncetainty of electomagnetic envionment in the moden battlefield, the tapezoidal fuzzy numbe is used to descibe the theshold of achievable MI at ada netwok based on the cedibility theoy. Finally, the FCCP model is tansfomed to a cisp equivalent fom with the popety of tapezoidal fuzzy numbe. Numeical simulation esults demonstating the pefomance of the poposed stategy ae povided. Keywods Secuity infomation, low pobability of identification (LPID), powe allocation, fuzzy chance-constained pogamming (FCCP), ada netwok systems. Intoduction Rada netwok achitectue, which often efes to distibuted multiple-input multiple-output (MIMO) ada [], is pioneeed by Fishe in [] and has dawn consideable attentions due to its advantage of signal and spatial divesities. Moeove, ada netwok outpefoms taditional monostatic ada in taget detection, localization accuacy and infomation extaction []. Recent yeas have witnessed an inceasing inteest on the ada netwok configuation which has been extensively studied fom vaious pespectives. The authos in [4] conside the optimal wavefom design fo MIMO ada in coloed noise based on imization of mutual infomation (MI) and elative entopy. Yang and Blum pesent two ada wavefom design schemes with constaints on wavefom powe [5]: the one is imization of the MI between the taget impulse esponse and the eflected wavefom, the othe is minimization of the minimum mean-squae eo (MMSE) in estimating the taget impulse esponse. A novel two-stage wavefom optimization algoithm fo distibuted MIMO ada is poposed in [6], whee it is demonstated that this method can povide geat pefomance impovement in taget infomation extaction. In [7], the authos pesent thee powe allocation citeia integating popagation losses into distibuted MIMO ada signal model: imizing the MI, minimizing the MMSE and imizing the echo enegy. Shi et al. in [8], [9] investigate the low pobability of intecept (LPI) optimization stategies in ada netwok configuations fo the fist time, which ae shown to be effective to enhance the LPI pefomance fo ada netwoks. In ecent yeas, pusing high physical-laye (PHY) secuity is becoming a cental issue in wieless communications, in which sececy capacity is utilized as a metic fo sececy communication pefomance []. In [], the authos study the use of atificial intefeence in imizing sececy capacity, whee a potion of the tansmitting powe is allocated to boadcast the infomation signal with enough powe to guaantee a cetain signal-to-intefeenceplus-noise atio (SINR) fo the intended eceive, while the est of the powe is utilized to boadcast atificial intefeence to am the passive eavesdoppes. Zhou et al. in [] investigate the poblem of secue communication in fading channels. While [] poposes an optimization stategy fo achieving secuity ove multiple-input single-output (MISO) channels by beamfoming and atificial intefeence combined with the potected zone. Mukheee and Swindlehust model the inteactions between the legitimate tansmitte and active eavesdoppe as a two-peson zeosum game [4]. The authos in [5] pesent a multiuse scheduling algoithm to impove the cognitive tansmission secuity. Futhe, Wang et al. in [6] popose secuity DOI:.64/e.5.99 SIGNALS

2 C. G. SHI, F. WANG, J. J. ZHOU, J. CHEN, FUZZY CHANCE-CONSTRAINED PROGRAMMING BASED SECURITY infomation facto to evaluate ada adio fequency (RF) stealth, whee it is illustated aibone ada RF stealth effects based on secuity infomation facto concept unde some conditions. Shi et al. extend the wok in [6] and povide a secuity infomation based optimal powe allocation scheme fo LPID pefomance in ada netwoks [7], [8]. Howeve, most eseaches on sececy capacity ae mainly towads imizing the sececy ate fo communication with guaanteeing system equiements. The use of secuity infomation fo LPID pefomance in ada netwok systems has aely been studied peviously, which motivates us to conside this poblem. In addition, the moden electomagnetic envionment is becoming moe and moe complicated, lage difficulties fo ada mission ae caused by amounts of uncetain factos in electonic wafae, which cannot be completely solved by stochastic theoy. The theoy of fuzzy set has dawn consideable attentions since this concept was initiated by Zadeh [9] in 965. In, Liu [] poposed the concept of cedibility measue, and established the theoy of fuzzy chance-constained pogamming (FCCP) [], which is a banch of mathematics fo studying fuzzy phenomena. This pape will investigate the FCCP based secuity infomation optimization fo LPID enhancement in ada netwoks. The main contibutions of this pape ae summaized as follows. Fistly, we deive an analytical closedfom expession of secuity infomation. Secondly, when the pio knowledge of intecept eceive is unavailable, a novel FCCP based secuity infomation optimization algoithm is fomulated to minimize the achievable MI at intecept eceive, while the achievable MI outage pobability at ada netwok is enfoced to be geate than a specified confidence level. Regading to the complexity and uncetainty of electomagnetic envionment in the moden electonic wafae, the tapezoidal fuzzy numbe is utilized to descibe the theshold of achievable MI at ada netwok. Finally, the FCCP model is tansfomed to a cisp equivalent fom with the popety of cedibility theoy. Numeical simulations ae povided to demonstate that ou poposed algoithm can impove the LPID pefomance fo ada netwoks to defend against passive intecept eceives. To the best of authos knowledge, no liteatue discussing FCCP based secuity infomation optimization fo impoved LPID pefomance in ada netwok systems was conducted pio to this wok. The emainde of this pape is oganized as follows. Section intoduces the basic concepts of cedibility theoy and the system model fo ada netwok. We fist deive the analytical closed-fom expession of secuity infomation with coopeative amming (CJ) fo ada netwok in Sec. and fomulate the FCCP based secuity infomation optimization algoithm fo ada netwok system. Section 4 povides some numeical simulation esults. Finally, conclusion emaks ae dawn in Sec. 5.. Peliminaies and System Model. Cedibility Theoy The theoy of fuzzy set has eceived close attention by the scientific community ove the last seveal decades, which was pioneeed by Zadeh via membeship function in 965. In 978, Zadeh pesented the concept of possibility measue, which is utilized to measue a fuzzy set. Although possibility measue has been widely used in both theoy and pactice, it has no self-duality popety. In, Liu poposed the concept of cedibility measue to define a self-dual measue. Afte that, Liu established the cedibility theoy in 4, which is a banch of mathematics fo studying fuzzy phenomena. Some basic concepts of cedibility theoy ae povided in the following. Definition.: (Liu & Liu []) Let Θ be a nonempty set, and P the powe set of Θ. The set function C is called a cedibility measue if it satisfies the following fou axioms: Axiom : CΘ. Axiom : CA CB Axiom : CA CA c, wheneve A B. fo any event A P. Axiom 4: CiAi supicai fo any events A i with supicai.5. Then, the tiplet, PC, is called a cedibility space. Definition.: (Liu []) A fuzzy vaiable is a measuable function fom a cedibility space, PC, to the set of eal numbes. Definition.: (Liu []) Let be a fuzzy vaiable defined on the cedibility space, PC,. Then its membeship function is deived fom the cedibility measue by: x C x, x. () Theoem. (Cedibility Invesion Theoem): (Liu []) Let be a fuzzy vaiable with membeship function x. Then fo any set B of eal numbes, we have: C B sup x sup x xb c xb. () Definition.4: (Liu []) The cedibility distibution Φ :, of a fuzzy vaiable is defined by: Φ x C x. () Φ x is the cedibility that the fuzzy vaiable That is, takes a value less than o equal to x.

3 RADIOENGINEERING, VOL. 4, NO., APRIL 5. Rada Netwok SNR Equation Let us conside a ada netwok system with N t tansmittes and N eceives, which can be boken down into N t N tansmitte-eceive pais each with a bistatic component contibuting to the entiety of the ada netwok signal-to-noise atio (SNR), as depicted in Fig.. The ada netwok system has a common pecise knowledge of space and time. In addition, it is woth pointing out that othogonal polyphase codes ae utilized in ada netwok system, which have a lage main lobe-to-side lobe atio. These codes have a moe complicated signal stuctue making it hade to intecept and identify by a noncoopeative intecept eceive. Y = [y, y,, y ] K N. Fo convenience, it is assumed that the noise matix W does not depend on the tansmitted wavefom X, and H and W ae mutually independent. Accoding to the discussions in [7], the path gain h n contains the taget eflection coefficient g mn and the popagation loss facto p mn. Based on the cental limit theoem, g mn ~ CN(, σg ), whee g mn denotes the taget eflection gain between the ada m and ada n. The popagation loss facto p mn can be expessed as: p G G tm n mn. (6) RtmRn Futhemoe, with the consideation of popagation losses and taget scatteed matix, the ada netwok signal model (5) can be ewitten as: Y X G P W (7) whee G = [g, g,, g N ], P = [p, p,, p N ], w n ~ CN(, σ w I K ), and denotes the Hadamad poduct. Fig.. Example of a ada netwok. The ada netwok SNR can be calculated by summing up the SNR of each tansmit-eceive pai as in []: SNR net N PG G (4) m n 4 tm tm n tmn m ktomnbm Fn Rtm Rn Lmn whee the P tm is the m th tansmitte powe, G tm is the mth tansmit antenna gain, G n is the n th eceive antenna gain, σ tmn is the ada coss section (RCS) of the taget fo the mth tansmitte and nth eceive, λ m is the m th tansmitted wavelength, k is Boltzmann s constant, T omn is the eceiving system noise tempeatue at the n th eceive, B m is the bandwidth of the matched filte fo the mth tansmitted wavefom, F n is the noise facto fo the nth eceive, L mn is the system loss between the mth tansmitte and nth eceive, R tm is the distance fom the mth tansmitte to the taget and R n is the distance fom the taget to the nth eceive.. Rada Netwok Signal Model Let K denote the discete time index, then we can expess the ada netwok signal model as: Y = XH +W (5) whee X = [x, x,, x ] K N t, is the set of tansmission sequences, H = [h, h,, h ] N N t efes to the path gain matix fo ada netwok system, W = [w, w,, w N ] K N epesents the system noise, and the eceived signal matix can be witten as. Poblem Fomulation. Secuity Infomation fo Rada Netwok Systems With the definition of MI in [7], [8], we can obtain the MI between the tansmitting signal of ada netwok X and the backscatte signal Y as follows: X,Y Y Y X HY HW I H H N Ptmσ g p mn ln + m= n= σ w N t N Ptmσ ggtmg n = ln + I net P m= n= σw R tmr n whee I(X, Y ) is the MI between Y and X, H(Y ) is the entopy of backscatte signal, and H(W ) is the entopy of Gaussian white noise. Similaly, we can expess the MI between the tansmitting signal of ada netwok X and the eceived signal of intecept eceive Y i as: XY Y Y X I, = H -H i i i PG tm tmg int ln + m= σ wi R tm whee G int is the antenna gain of intecept eceive, σ wi denotes the noise covaiance of intecept eceive. (8) (9)

4 C. G. SHI, F. WANG, J. J. ZHOU, J. CHEN, FUZZY CHANCE-CONSTRAINED PROGRAMMING BASED SECURITY As intoduced in [7], [8], in moden electonic wafae, coopeative amme is indispensable to keep the ada netwok in LPID state. This means that CJ is to am the hostile intecept eceive so that the achievable MI at intecepto can be degaded by the CJ signals while the ada netwok system is unaffected. With the consideation of CJ, we can modify () as follows: PG tm tmg I XY, ln int Iint P, P() i m PG G int w R i tm R whee P is the total tansmitting powe fo CJ signal, G is the antenna gain of coopeative amme, R is the distance fom the taget to coopeative amme. Fo convenience, we assume that the ada netwok system can simultaneously tansmit ada modulating signal to tack taget and CJ signal to intefee passive intecept eceive fo simplicity of discussion, while the CJ signal is designed to be completely othogonal to ada modulating signal and geneated to am the intecept eceive without affecting the ada netwok. I sec P, P int, Inet P I P P P ggg t NN t ln 4 w R net PGG t int ln PG G N int t w R i net R () whee [x] + = (, x). It has been pointed out in [7], [8] that I sec > means that ada netwok is in completely secue state while tacking taget, and that the lage the achievable secuity infomation I sec obtained, the bette LPID pefomance to finish the system mission. The notional sketch of ou poposed pefectly secue ada netwok system is illustated in Fig.. This amounts to say that, if the ada netwok system expeiences an SNR highe than that of the noncoopeative intecept eceive, a positive ate can be sustained, while the intecept eceive gets imally confused based on the utilized sececy citeion in ().. FCCP Based Secuity Infomation Optimization In pactical applications, it would be impossible to suppose that any pio infomation about the hostile intecept eceive is available, such as the sensitivity of intecepto, the pocessing gain, et al. The system model is illustated in Fig., whee the taget and the intecept eceive ae sepaated at diffeent places. Fig.. The notional sketch of ou poposed pefectly secue ada netwok system. Fo simplicity of deivation, it is supposed that: Rnet Rti R m,,, n,, N, () P Ptm m,, N () t whee R net is appoximately the distance fom taget to ada netwok system, P is the total tansmitting powe fo ada modulating signal. It is also assumed that each netted ada node in the netwok is the same. Theefoe, oiginating fom the sececy capacity in wieless communications, we define secuity infomation to measue the LPID pefomance fo ada netwok system [7], [8]: Fig.. The geomety of ada netwok, taget and intecepto. With the deivation of secuity infomation as (), we can obseve that secuity infomation is based on satisfying MI constaints both at ada netwok and at intecept eceive. With a pope choice of the powe allocation, a pefectly secuing channel can be devised such that: th Inet P P (4) Iint P, P whee δ th is the pedefined theshold of MI at ada netwok. Equation (4) means asymptotically pefect secuity in ada netwok system.

5 RADIOENGINEERING, VOL. 4, NO., APRIL 5 In this pape, we focus on minimizing the achievable MI at intecept eceive I int (P, P ) to guaantee a pedefined theshold of MI at ada netwok δ th. To be moe specific, minimization of the achievable MI at noncoopeative intecept eceive can significantly defend against intecepto, showing LPID pefomance enhancement of exploiting CJ when any pio knowledge about the intecept eceive is unavailable. The secuity infomation optimization stategy can be summaized as follows: ) Specify the desied MI theshold δ th fo ada netwok system, which is utilized as a metic fo taget detection pefomance. ) Allocate some tansmission powe to achieve the desied MI theshold δ th fo taget detection. ) Minimize the achievable MI at intecept eceive I int (P, P ) by distibuting the emaining tansmission powe to yield as much intefeence as possible, while guaanteeing that the CJ signal is designed to be completely othogonal to ada modulating signal and geneated to am the intecept eceive without affecting the ada netwok. Hence, the secuity infomation optimization fo enhanced LPID pefomance can be fomulated as: min Iint P, P P, P th st.. Inet P P P P tot P, P (5) whee P tot is the imum tansmitting powe fo ada netwok, P is the imum tansmitting powe fo ada modulating signal. While egading to the complexity and uncetainty of electomagnetic envionment in the moden electonic wafae, the pedefined theshold of MI at ada netwok δ th would be uncetain. Heein, a fuzzy vaiable δ th fuzzy is utilized to evaluate the pedefined theshold of MI at ada netwok. Based on the concepts of cedibility theoy, the achievable MI outage pobability at ada netwok is enfoced to be geate than a specified confidence level α, that is: th net fuzzy C I P (6) whee C{ } indicates the cedibility that { } will occu. Theefoe, we have the FCCP based secuity infomation optimization fo LPID enhancement in ada netwok as: min Iint P, P P, P th st.. CInet P fuzzy P P Ptot P, P (7) With the FCCP model (7), we can obseve that inceasing the confidence level leads to enlaging the feasible set of the tue poblem, which in tun may esult in deceasing of the optimal value of the tue poblem []. It is also woth pointing out that thee exists a estictive elationship between the confidence level and the achievable MI at intecept eceive.. The Cisp Equivalent Fom of FCCP Model The FCCP model (7) is a fuzzy linea pogamming, which can be tansfomed into the cisp equivalent fom. In this pape, we set δ th fuzzy = (a, b, c, d) (a < b c < d) to be a tapezoidal fuzzy vaiable. Definition.: (Liu, Zhao & Wang []) By a tapezoidal fuzzy vaiable, we mean that the fuzzy vaiable fully detemined by the quaduplet,,, 4 of cisp numbes with 4, whose membeship function is given by: x,if x, if x x (8) x 4,if x4 4, else Definition.: (Liu, Zhao & Wang []) The cedibility distibution of a tapezoidal fuzzy vaiable,,, 4 is:, if x x, if x x, if x (9) x 4, if x 4 4, if4 x Theoem.: (Liu [4]) If is a tapezoidal fuzzy numbe,,, 4 4, fo the given confidence level.5,,the following equivalent tansfomation can be deived as: C x x, (a) C x x. (b) 4 Based on the popeties of tapezoidal fuzzy numbe, we have that: th net fuzzy net C I P I P c d () The poposed FCCP based secuity infomation algoithm (7) could be tansfomed into the following

6 4 C. G. SHI, F. WANG, J. J. ZHOU, J. CHEN, FUZZY CHANCE-CONSTRAINED PROGRAMMING BASED SECURITY cisp equivalent fom: min Iint P, P P, P s.. tinet P c d P P P tot P, P () Poblem (7) takes ada netwok mission δ th fuzzy into consideation because ada netwok system must accomplish its mission in moden battlefield. To be specific, fo net the pedetemined system detection pobability P d and false alam pobability P net fa, if C{I net (P ) δ th fuzzy} α and I sec (P, P ) >, the detection pobability of intecept eceive P d would be significantly less than.5, which int means that the intecepto could not intecept and identify ada modulating signal, and that the ada netwok system is in completely LPID state [6]. Based on the above deivations as () and (), it is woth pointing out the simplicity of the poposed algoithm which elies on basic mathematical calculations and does not equie highly complex computation. Moeove, ou poposed algoithm is significantly simple to implement. So fa, we have completed the achievable secuity infomation deivation and the FCCP based secuity infomation optimization fo LPID enhancement in ada netwok systems. In what follows, some numeical simulations ae povided to show the feasibility and effectiveness of ou pesented algoithm. 4. Numeical Simulations and Analysis In this section, we evaluate the poposed algoithm though some numeical simulations. Let us conside a 4 4 ada netwok achitectue (N t = N = 4), which is depicted in Fig. 4 that the netted adas in the netwok ae spatially distibuted in the suveillance aea..5 ada netwok can detect the taget whose RCS is m in the distance 8 km by tansmitting the imum powe P = 4 kw. The sensitivity of intecept eceive S i min is set to be 8 dbmw. Based on some expeimental data, the tapezoidal fuzzy numbe is set to be δ th fuzzy = (4.4, 8.,., 5.6)nats, which equals to the fuzzy SNR (7.,.,., 8.) db. This is because that the ada netwok system can tack the taget steadily when the SNR is between. db and. db, and the value of the membeship function is set to be. 4. Secuity Infomation Analysis As shown in Fig. 5, fo all the cases N =, N = and N = 4, with an inceasing N t, the achievable secuity infomation is inceased coespondingly. As the numbe of tansmittes N t continues inceasing beyond a cetain value, the achievable secuity infomation of (6) leads to appoximate constant. Fig. 5 also demonstates that as the numbe of eceives inceases fom N = to N = 4, the achievable secuity infomation fo ada netwok can be significantly inceased. To be specific, inceasing the numbe of adas can effectively impove secuity infomation fo ada netwok. This is because that ada netwok can offe geat tansmit and eceive divesities in tems of the achievable secuity infomation, which confims the LPID benefits by exploiting ada netwok system to defend against passive intecept eceive attacks. Figue 6 shows the achievable secuity infomation vesus R net with P = 5 kw, P = 5 kw and diffeent R. It can be seen fom Fig. 6 that as R net and R decease, the achievable secuity infomation is inceased as theoetically poved in (6). Futhemoe, it is depicted that with the same R net, the available secuity infomation can be inceased as R deceases, which shows the advantage of exploiting CJ to defend against intecept eceive. Figue 7 illustates achievable MI at intecept eceive vesus the confidence level at ada netwok fo diffeent sensitivities of intecept eceive S imin with R net = km and R = km. In Fig. 7, fo all the cases, one can obseve that the achievable MI at intecept eceive is 9.5 Rada Rada 8 Y/km Rada Rada4 Netted Rada X/km Fig. 4. The ada netwok system configuation in two dimensions. Heein, we set the simulation paametes P tot = P + P = 5 kw, G t = G = G = db, G i = db, σ w = 4.57 W, σ wi = W and σ g =. The Achievable secuity infomation/nat P =.5KW P =.5KW N = N = N = Fig. 5. Achievable secuity infomation vesus the numbe of tansmittes N t fo diffeent numbe of eceives N with R net = 5 km, R = 5 km, and P =P =.5 kw.

7 RADIOENGINEERING, VOL. 4, NO., APRIL 5 5 Achievable secuity infomation/nat R = km R = km R = km Rnet/km Fig. 6. Achievable secuity infomation vesus R net with P = kw, P =5 kw and diffeent R. Achievable MI at intecept eceive/nat x - Simin = -8dBsm Simin = -6dBsm Simin = -4dBsm Rnet = km R = km Confidence level α Fig. 7. Achievable MI at intecept eceive vesus the confidence level α at ada netwok fo diffeent sensitivities of intecept eceive S imin with R net = km and R = km. Achievable MI at intecept eceive/nat.5 x x α =.6 with R = 5km α =.6 with R = 5km α =.7 with R = 5km α =.7 with R = 5km α =.8 with R = 5km α =.8 with R = 5km Rnet/km Fig. 8. Achievable MI at intecept eceive vesus R net fo diffeent confidence levels and diffeent R. inceased as the confidence level α at ada netwok inceases, which shows that thee exists a estictive elationship between the confidence level α and the achievable MI at intecept eceive. This is due to the fact that moe ada modulating signal would be tansmitted to satisfy the system equiement with the incease of confidence level at ada netwok. The ada modulating signal could be intecepted by intecepto easily, and the achievable MI at intecept eceive will incease subsequently. Moeove, the achievable MI at intecept eceive is educed as the sensitivity of intecept eceive S imin deceases. In Fig. 8, we depict the achievable MI at intecept eceive vesus the distance between ada netwok and taget R net fo diffeent confidence levels at ada netwok α and diffeent distances between ada netwok and intecept eceive R. One can obseve fom Fig. that fo all the cases, the achievable MI at intecept eceive is inceased as the distance between ada netwok and taget inceases fom R net = 5 km to R net = km. As mentioned befoe, this is because that moe ada modulating signal is tansmitted to satisfy the equiement fo taget detection as R net inceases, so less powe is emained to geneate CJ signal to am the intecept eceive. Moeove, one can obseve that as the distance between ada netwok and intecept eceive R deceases, the MI at intecepto is educed, showing the LPID pefomance enhancement of exploiting CJ to defend against inteceptos in ada netwok system. 4. Taget Tacking with FCCP Based Secuity Infomation Optimization This subsection pesents the numeical esults of ou poposed secuity infomation optimization scheme in taget tacking scenaio. We tack a single taget by employing paticle filteing (PF) method. Fo simplicity, it is assumed that the passive intecept eceive is caied by the taget. Figue 9 shows one ealization of the taget taectoy fo 5 s. Figue illustates the distance changing cuve between ada netwok and taget. Y/km Real taectoy Tack with PF t = s t = 5s X/km Fig. 9. Taget tacking scenaio. Distance/km Time/s Fig.. The distance between the ada netwok and the taget.

8 6 C. G. SHI, F. WANG, J. J. ZHOU, J. CHEN, FUZZY CHANCE-CONSTRAINED PROGRAMMING BASED SECURITY Figue illustates the achievable MI at intecept eceive with diffeent confidence levels. We can see fom Fig. that the achievable MI at intecept eceive is inceased as the confidence level inceases. This is due to the fact that moe ada modulating signal will be allocated to satisfy the system equiement with the incease of confidence level at ada netwok, in which way the ada signal would be intecepted and identified by hostile intecepto easily. It is also woth pointing out that the achievable MI at intecepto changes accodingly with the distance between ada netwok and taget. To be specific, when the taget is fa away fom the ada netwok, the netwok system would allocate moe powe fo modulating signal to obtain a bette capability of ada netwok to estimate the taget. In contast, as the distance deceases, moe powe fo CJ signal could be tansmitted to defend against the passive intecept eceive, which makes the achievable secuity infomation obust in tems of LPID pefomance. In Fig., we compae the pefomance of the poposed FCCP based secuity infomation optimization algoithm, the enegy-efficiency based algoithm [7] and the adaptive secuity infomation optimization algoithm [8]. The algoithm povided in [7] aims at optimizing the enegy-efficiency and will teminate to maintain cetain secuity infomation, while the algoithm poposed in [8] aims at the optimization of the oveall secuity infomation Achievable MI at intecept eceive/nat.4 x α =.6 α =.7 α = Time/s x -6 Fig.. Achievable MI at intecept eceive in the tacking pocess. Achievable MI at intecept eceive/nat Poposed algoithm α =.6 Poposed algoithm α =.7 Poposed algoithm α =.8 Poposed algoithm in [7] Poposed algoithm in [8] Time/s Fig.. Achievable MI at intecept eceive of vaious algoithms. by optimizing the tansmission powe allocation between ada modulating signal and CJ signal. As Fig. shows, the poposed algoithm significantly outpefoms the algoithms poposed in [7] and [8], which is due to the fact that the achievable MI at intecepto is emakable lowe than that of the compaed algoithms acoss the whole egion. In addition, the poposed algoithm is moe pactical than the algoithm poposed in [8] because of the fome s lowe complexity. 4. Conclusions This pape has poposed a novel FCCP based secuity infomation optimization algoithm to achieve impoved LPID pefomance in ada netwok systems without any pio knowledge of noncoopeative intecept eceive, whose pupose is to minimize the achievable MI at intecepto, while the achievable MI outage pobability at ada netwok is enfoced to be geate than a specified confidence level. It is woth pointing out that ou poposed algoithm is pesented by simple analytical closed-fom expession. Simulation esults demonstate that ou poposed algoithm is effective to enhance LPID pefomance fo ada netwok to defend against passive intecepto attacks. Fo futue eseach, othe optimization citeia need to be addessed to impove LPID pefomance fo ada netwok systems. Acknowledgements The authos would like to thank the anonymous eviewes fo thei comments that help to impove the quality of this aticle. The suppot povided by the National Natual Science Foundation of China (Gant No. 677), the Fundamental Reseach Funds fo the Cental Univesities (Gant No. NJ4), Funding of Jiangsu Innovation Pogam fo Gaduate Education (CXLX_54), the Fundamental Reseach Funds fo the Cental Univesities, the Pioity Academic Pogam Development of Jiangsu Highe Education Institutions (PADA) and Key Laboatoy of Rada Imaging and Micowave Photonics (Naning Univ. Aeonaut. Astonaut.), Ministy of Education, Naning Univesity of Aeonautics and Astonautics, Naning, 6, China ae gatefully acknowledged. Refeences [5] PACE, P. E. Detecting and Classifying Low Pobability of Intecept Rada. Boston: Atech House, 9, p [6] FISHER, E., HAIMOVICH, A., BLUM, R. S., CIMINI, L. J., CHIZHIK, D., VALENZUELA, R. A. Spatial divesity in adas: models and detection pefomance. IEEE Tansactions on Signal Pocessing, 6, vol. 54, no., p DOI:.9/TSP.5.868

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