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arXiv:2012.09952 · IEEE Transactions on Information Forensics and Security

Secrecy of Multi-Antenna Transmission With Full-Duplex User in the Presence of Randomly Located Eavesdroppers

Ishmam Zabir, Ahmed Maksud, Gaojie Chen, Brian M. Sadler, Yingbo Hua

Published Dec 28, 2020• 12 citations
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Abstract

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.

DOI
10.1109/tifs.2020.3047763

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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.
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.
In this letter, we study the interacting effects of the exclusion zone and eavesdropper colluding strategy on the secrecy performance of multiple-antenna transmission system. In particular, a base station (BS) applies random beamforming and user scheduling to enhance the legitimate user channel while multiple eavesdroppers try, either individually or jointly, to overhear the transmitted signal. We derive the closed-form expressions of secrecy outage probability (SOP) of the system with and without exclusion zone under different colluding strategies. Through selected numerical examples, we develop the design guideline on the size of the exclusion zone for a target security level subject to eavesdroppers' density and colluding strategy.
In this paper, we study the secure multi-antenna transmission with artificial noise (AN) under slow fading channels coexisting with randomly located eavesdroppers. We provide a comprehensive secrecy performance analysis and system design/optimization under a stochastic geometry framework. Specifically, we first evaluate the secrecy outage performance, and derive a closed-form expression for the optimal power allocation ratio of the information signal power to the total transmit power that minimizes the secrecy outage probability (SOP). Subject to a SOP constraint, we then propose a dynamic parameter transmission scheme (DPTS) and a static parameter transmission scheme (SPTS) to maximize secrecy throughput, and provide explicit solutions on the optimal transmission parameters, including the wiretap code rates, the on-off transmission threshold and the power allocation ratio. Our results give new insight into secure transmission designs. For example, secrecy rate is a concave function of the power allocation ratio in DPTS, and AN plays a significant role under SOP constraints and in dense eavesdropper scenarios. In SPTS, transmission probability is a concave function of the power allocation ratio, and secrecy throughput is a quasi-concave function of the secrecy rate. Numerical results are demonstrated to validate our theoretical analysis.
This letter studies the physical-layer security of a multi-antenna transmission system in the presence of Poisson distributed eavesdroppers. The transmission secrecy outage probability (TSOP) is adopted to evaluate the security. We derive an accurate integral expression as well as a closed-form upper bound on TSOP for the noncolluding eavesdroppers' case and a closed-form solution for the colluding eavesdroppers' case, respectively. Based on these, we define a novel concept of security region to intuitively illustrate the security from a spatial perspective. We further analyze the impacts of various factors on the security, such as the number of transmit antennas, the node intensity, and the target secrecy rate.