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Secure Communication Over Fading Channels with Statistical Qos Constraints

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Secure Communication Over Fading Channels with Statistical Qos Constraints University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications from the Department of Electrical & Computer Engineering, Department Electrical and Computer Engineering of 2010 Secure Communication over Fading Channels with Statistical QoS Constraints Deli Qiao University of Nebraska-Lincoln, [email protected] M. Cenk Gursoy University of Nebraska-Lincoln, [email protected] Senem Velipasalar University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/electricalengineeringfacpub Part of the Electrical and Computer Engineering Commons Qiao, Deli; Cenk Gursoy, M.; and Velipasalar, Senem, "Secure Communication over Fading Channels with Statistical QoS Constraints" (2010). Faculty Publications from the Department of Electrical and Computer Engineering. 128. https://digitalcommons.unl.edu/electricalengineeringfacpub/128 This Article is brought to you for free and open access by the Electrical & Computer Engineering, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications from the Department of Electrical and Computer Engineering by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. IEEE International Symposium on Information Theory, Proceedings (ISIT), 2010 Digital Object Identifier: 10.1109/ISIT.2010.5513448 ISIT 2010, Austin, Texas, U.S.A., June 13 - 18, 2010 Secure Communication over Fading Channels with Statistical QoS Constraints Deli Qiao, Mustafa Cenk Gursoy, and Senem Velipasalar Department of Electrical Engineering University of Nebraska-Lincoln, Lincoln, NE 68588 Email: [email protected], [email protected], [email protected] Abstract— 1 In this paper, secure transmission of information delay constraints. In this paper, we consider statistical QoS over an ergodic fading channel is studied in the presence of constraints in the form of limitations on the buffer length, and statistical quality of service (QoS) constraints.We employ effective incorporate the concept of effective capacity [4], which can be capacity to measure the secure throughput of the system, i.e., effective secure throughput. We assume that the channel side seen as the maximum constant arrival rate that a given time- information (CSI) of the main and the eavesdropper channels varying service process can support while satisfying statistical is available at the transmitter side. Under this assumption, we QoS guarantees. The analysis and application of effective investigate the optimal power control policies that maximize the capacity in various settings have attracted much interest re- effective secure throughput. In particular, it is noted that oppor- cently (see e.g., [5]–[7] and references therein). We define the tunistic transmission is no longer optimal and the transmitter should not wait to send the data at a high rate until the main effective secure throughput as the maximum constant arrival channel is much better than the eavesdropper channel. Moreover, rate that can be supported while keeping the eavesdropper it is shown that the benefits of adapting the power with respect to ignorant of these messages in the presence of QoS constraints. the CSI of both the eavesdropper and main channels rather than We assume that the channel side information (CSI) of the the CSI of only the main channel diminish as QoS constraints main and eavesdropper channels is available at the transmitter become more stringent. side. Under this assumption, we derive the optimal power I. INTRODUCTION control policies that maximize the effective secure throughput. We analyze two types of control policies by adapting the Security is an important consideration in wireless systems power with respect to both the main and eavesdropper channel due to the broadcast nature of wireless transmissions. In the conditions and also with respect to only the main channel pioneering work [1], Wyner addressed the security problem conditions. Through this analysis, we find that, due to the from an information-theoretic point of view and considered a introduction of the QoS constraints, the transmitter cannot wire-tap channel model. He proved that secure transmission reserve its power for times at which the main channel is much of confidential messages to a destination in the presence of stronger than the eavesdropper channel. Also, we find that a degraded wire-tapper can be achieved, and he established adapting the power allocation strategy with respect to both the the secrecy capacity which is defined as the highest rate of main and eavesdropper channel CSI rather than only the main reliable communication from the transmitter to the legitimate channel CSI provides little improvement when QoS constraints receiver while keeping the wire-tapper completely ignorant of become more stringent. the transmitted messages. Recently, there has been numerous The rest of the paper is organized as follows. Section II studies addressing information theoretic security. For instance, briefly describes the system model and the necessary prelim- the impact of fading has been investigated in [2], where it has inaries on statistical QoS constraints and effective capacity. been shown that a non-zero secrecy capacity can be achieved In Section III, we present our results on power adaptation even when the eavesdropper channel is better than the main policies. Finally, Section IV concludes the paper. channel on average. The secrecy capacity region of the fading broadcast channel with confidential messages and associated II. SYSTEM MODEL AND PRELIMINARIES optimal power control policies have been identified in [3], where it is shown that the transmitter allocates more power A. System Model as the strength of the main channel increases with respect to The system model is shown in Fig. 1. It is assumed that the that of the eavesdropper channel. transmitter generates data sequences which are divided into In addition to security issues, providing acceptable perfor- frames of duration T . These data frames are initially stored mance and quality is vital to many applications. For instance, in the buffer before they are transmitted over the wireless voice over IP (VoIP) and interactive-video (e.g,. videocon- channel. The channel input-output relationships are given by ferencing) systems are required to satisfy certain buffer or Y1[i]=h1[i]X[i]+Z1[i] (1) 1This work was supported by the National Science Foundation under Grants Y i h i X i Z i CNS–0834753, and CCF–0917265. 2[ ]= 2[ ] [ ]+ 2[ ] (2) 978-1-4244-7892-7/10/$26.00 ©2010 IEEE 2503 ISIT 2010 ISIT 2010, Austin, Texas, U.S.A., June 13 - 18, 2010 can support in order to guarantee a statistical QoS requirement specified by the QoS exponent θ. If we define Q as the stationary queue length, then θ is the decay rate of the tail of the distribution of the queue length Q: log P (Q ≥ q) lim = −θ. (3) q→∞ q Therefore, for large qmax, we have the following approxima- tion for the buffer violation probability: P (Q ≥ qmax) ≈ e−θqmax . Hence, while larger θ corresponds to more strict QoS constraints, smaller θ implies looser QoS guarantees. Similarly, if D denotes the steady-state delay experienced in −θδdmax the buffer, then P (D ≥ dmax) ≈ e for large dmax, where δ is determined by the arrival and service processes [6]. Fig. 1. The general system model. The effective capacity is given by −θ Λ( ) 1 −θS[t] C(θ)=− = − lim loge E{e } bits/s, (4) θ t→∞ θt i X i t where is the frame index, [ ] is the channel input in the where the expectation is with respect to S[t]= s[i], i Y i Y i i=1 th frame, and 1[ ] and 2[ ] represent the channel outputs at which is the time-accumulated service process. {s[i],i = i receivers 1 and 2 in frame , respectively. We assume that 1, 2,...} denotes the discrete-time stationary and ergodic {h i } j , the sequences of fading coefficients j[ ] for =12 stochastic service process. We define the effective capacity are jointly stationary and ergodic discrete-time processes, and obtained when the service rate is confined by the secrecy we denote the magnitude-square of the fading coefficients capacity as the effective secure throughput. by zj[i]=|hj[i]|2. Considering that receiver 1 is the main user and receiver 2 is the eavesdropper, we in the rest of In this paper, in order to simplify the analysis while consid- the paper express z1 and z2 as zM and zE, respectively, ering general fading distributions, we assume that the fading for more clarity. The channel input is subject to an average coefficients stay constant over the frame duration T and vary energy constraint E{|X[i]|2}≤P/B¯ , where B denotes the independently for each frame and each user. In this scenario, bandwidth available in the system. Assuming that there are s[i]=TR[i], where R[i] is the instantaneous service rate for B complex symbols per second, we can easily see that the confidential messages in the ith frame duration [iT, (i +1)T ]. symbol energy constraint of P/B¯ implies that the channel Then, (4) can be written as P¯ input has a power constraint of . Above in the channel input- 1 −θTR[i] C(θ)=− loge Ez{e } bits/s, (5) output relationships, the noise component Zj[i] is a zero-mean, θT circularly symmetric, complex Gaussian random variable with where R[i] in general depends on the fading magnitudes z = variance E{|Zj[i]|2} = Nj for j =1, 2. The additive Gaussian (zM ,zE). (5) is obtained using the fact that instantaneous rates {Z i } noise samples j[ ] are assumed to form an independent and {R[i]} vary independently over different frames. The effective identically distributed (i.i.d.) sequence. secure throughput normalized by bandwidth B is We denote the average transmitted signal to noise ratio with P¯ C θ respect to receiver 1 as SNR = . We also denote P [i] ( ) N1B C(θ)= bits/s/Hz.
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