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arXiv:1701.00982 · IEEE Transactions on Information Forensics and Security

Secrecy Outage Analysis for Downlink Transmissions in the Presence of Randomly Located Eavesdroppers

Gaojie Chen, Justin P. Coon, Marco Di Renzo

Published Jan 20, 2017• 100 citations
arXivHTMLPDF

Abstract

We analyze the secrecy outage probability in the downlink for wireless networks with spatially (Poisson) distributed eavesdroppers (EDs) under the assumption that the base station employs transmit antenna selection (TAS) to enhance secrecy performance. We compare the cases, where the receiving user equipment (UE) operates in half-duplex (HD) mode and full-duplex (FD) mode. In the latter case, the UE simultaneously receives the intended downlink message and transmits a jamming signal to strengthen secrecy. We investigate two models of (semi)passive eavesdropping: 1) EDs act independently and 2) EDs collude to intercept the transmitted message. For both of these models, we obtain expressions for the secrecy outage probability in the downlink for the HD and FD UE operation. The expressions for the HD systems have very accurate approximate or exact forms in terms of elementary and/or special functions for all path loss exponents. Those related to the FD systems have exact integral forms for general path loss exponents, while exact closed forms are given for specific exponents. A closed-form approximation is also derived for the FD case with colluding EDs. The resulting analysis shows that the reduction in the secrecy outage probability is logarithmic in the number of antennas used for TAS and identifies conditions, under which HD operation should be used instead of FD jamming at the UE. These performance trends and exact relations between system parameters can be used to develop adaptive power allocation and duplex operation methods in practice. Examples of such techniques are alluded to herein.

DOI
10.1109/tifs.2017.2656462

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We analyze the secrecy outage probability in the downlink for wireless networks with spatially (Poisson) distributed eavesdroppers (EDs) under the assumption that the base station employs transmit antenna selection (TAS) to enhance secrecy performance. We compare the cases, where the receiving user equipment (UE) operates in half-duplex (HD) mode and full-duplex (FD) mode. In the latter case, the UE simultaneously receives the intended downlink message and transmits a jamming signal to strengthen secrecy. We investigate two models of (semi)passive eavesdropping: 1) EDs act independently and 2) EDs collude to intercept the transmitted message. For both of these models, we obtain expressions for the secrecy outage probability in the downlink for the HD and FD UE operation. The expressions for the HD systems have very accurate approximate or exact forms in terms of elementary and/or special functions for all path loss exponents. Those related to the FD systems have exact integral forms for general path loss exponents, while exact closed forms are given for specific exponents. A closed-form approximation is also derived for the FD case with colluding EDs. The resulting analysis shows that the reduction in the secrecy outage probability is logarithmic in the number of antennas used for TAS and identifies conditions, under which HD operation should be used instead of FD jamming at the UE. These performance trends and exact relations between system parameters can be used to develop adaptive power allocation and duplex operation methods in practice. Examples of such techniques are alluded to herein.
This letter investigates the secrecy outage probability in the downlink with ordered user equipment (UE) based on two ordering metrics. UEs and independently acting eavesdroppers (EDs) are positioned randomly according to a Poisson point process. We consider a transmit antenna selection (TAS) scheme at the base station (BS) to enhance secrecy performance and propose two metrics to order the UEs: one based on long-term average channel gain information from the BS to the UEs, and the other based on instantaneous channel gains. We derive closed form expressions for the secrecy outage probability subject to each of these ordering policies and verify our calculations through Monte Carlo simulations. Our results show that while TAS yields a performance improvement relative to single-antenna systems, the secrecy outage probability for TAS systems actually increases with the path loss exponent. Furthermore, we show that the importance of the specific user ordering policy that is adopted in these systems is reduced for high path loss environments or situations where large numbers of antennas are employed.
This paper considers the secrecy performance of several schemes for multi-antenna transmission to single-antenna users with full-duplex (FD) capability against randomly distributed single-antenna eavesdroppers (EDs). These schemes and related scenarios include transmit antenna selection (TAS), transmit antenna beamforming (TAB), artificial noise (AN) from the transmitter, user selection based their distances to the transmitter, and colluding and non-colluding EDs. The locations of randomly distributed EDs and users are assumed to be distributed as Poisson Point Process (PPP). We derive closed form expressions for the secrecy outage probabilities (SOP) of all these schemes and scenarios. The derived expressions are useful to reveal the impacts of various environmental parameters and user's choices on the SOP, and hence useful for network design purposes. Examples of such numerical results are discussed.
We present a statistical analysis of the secrecy capacity for two downlink transmission schemes: transmitantenna selection (TAS) and transmit- antenna beamforming (TAB), where the transmitter (Alice) has multiple antennas, the receiver (Bob) is a single-antenna full-duplex radio, and the eavesdroppers are randomly distributed each with a single antenna. We focus on the secrecy outage probability (SOP) or its related measure, show closed-form expressions of SOP for the two schemes, and present insights into how various system parameters such as the jamming powers from both Alice and Bob affect SOP. The SOP performance of TAB is shown to be significantly better than that of TAS although TAB requires more on channel estimation than TAS.
In this paper, we study the secrecy performance in a hybrid wiretapping wireless system, where the half-duplex (HD) or full-duplex (FD) eavesdroppers may wiretap the confidential signal and/or transmit a jamming signal. To evaluate the secrecy performance, we derive the approximate closed-form results for the secrecy outage probability and mean secrecy rate by means of the random matrix theory (RMT). The RMT method can greatly simplify the complicated mathematical analysis with high accuracy, and can provide a useful analytical framework for other researches. The Monte Carlo simulations and numerical results are provided to validate the theoretical analysis and demonstrate the impacts of the system parameters. From the perspective of BS transmission, increasing BS transmission power can greatly improve the secrecy performance in the low transmit power region, but the secrecy performance is constant in the high BS transmit power region. Moreover, in terms of adversaries, FD eavesdroppers have better wiretapping performance than HD eavesdroppers when the jamming power is relatively low; otherwise, this result is reversed.
This paper studies secrecy rate optimization in a wireless network with a single-antenna source, a multi-antenna destination and a multi-antenna eavesdropper. This is an unfavorable scenario for secrecy performance as the system is interference-limited. In the literature, assuming that the receiver operates in half duplex (HD) mode, the aforementioned problem has been addressed via use of cooperating nodes who act as jammers to confound the eavesdropper. This paper investigates an alternative solution, which assumes the availability of a full duplex (FD) receiver. In particular, while receiving data, the receiver transmits jamming noise to degrade the eavesdropper channel. The proposed self-protection scheme eliminates the need for external helpers and provides system robustness. For the case in which global channel state information is available, we aim to design the optimal jamming covariance matrix that maximizes the secrecy rate and mitigates loop interference associated with the FD operation. We consider both fixed and optimal linear receiver design at the destination, and show that the optimal jamming covariance matrix is rank-1, and can be found via an efficient 1-D search. For the case in which only statistical information on the eavesdropper channel is available, the optimal power allocation is studied in terms of ergodic and outage secrecy rates. Simulation results verify the analysis and demonstrate substantial performance gain over conventional HD operation at the destination.
This paper investigates the secrecy outage performance for a large-scale downlink system with full-duplex (FD) non-orthogonal multiple access (NOMA) transmission aided by artificial noise (AN). In the system, legitimate users (LUs) are randomly distributed according to homogeneous Poisson point processes whereas a passive eavesdropper (Eve) is certainly located. We introduce a secure cooperative communication scheme, in which nearby NOMA users operating in FD mode act as jammers and generate AN to enhance the physical layer security (PLS) of the legitimate transmission. Closed-form expressions in terms of the secrecy outage probability (SOP) for a user pair are acquired. Following the mathematical results, secrecy diversity order analysis is further carried out for two scenarios, i.e., 1) fixed transmit signal-to-noise ratio (SNR) at the Eve, and 2) transmit SNR at the Eve being proportional to that of LUs. Closed-form expressions of asymptotic SOP for the two scenarios are also obtained. Monte Carlo simulations are performed to certify the veracity of the theoretic analysis and illustrate that the proposed scheme employing both AN and FD-NOMA is superior in the secrecy outage to the NOMA scheme without AN and the orthogonal multiple access scheme with AN. Furthermore, the SOP performance enhancement through proper secrecy rate target selection and power allocation optimization is also evidenced by the simulations.