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Impact of Frequency Offset on Artificial Noise Suppression in SIMO Physical Layer Security Systems

Yu Mao, Hongzhi Zhao, Changqing Song, Shihai Shao

Published Dec 4, 2022• 4 citations
Publisher

Abstract

Artificial noise (AN) is an effective physical security measure against eavesdropping in wireless communication. In previous literatures, AN is generally analyzed in multiple transmit antenna systems and is suppressed by zero-forcing algorithm, which is implemented by using the spatial degrees of freedom. In this paper, an AN suppression model under single-input multi-output (SIMO) systems is presented, and the impact of imperfect frequency synchronization on the AN suppressed performance is analyzed. Specifically, we first analyze the AN suppression performance of single branch with imperfect frequency synchronization. Then the output signal to interference plus noise ratio (SINR) after multi-branch merging is derived. Finally, the secrecy capacity of AN based on SIMO systems is extracted on the basis of the obtained SINR. Theoretical and simulation results show that imperfect frequency synchronization reduces the SINR of each branch, and thus degrades both the output SINR and secrecy capacity in SIMO systems. Moreover, when the residual AN power is greater than noise power, no diversity gain will be achieved by multi-branch merging.

DOI
10.1109/globecom48099.2022.10001464

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Artificial noise (AN) is an effective physical security measure against eavesdropping in wireless communication. In previous literatures, AN is generally analyzed in multiple transmit antenna systems and is suppressed by zero-forcing algorithm, which is implemented by using the spatial degrees of freedom. In this paper, an AN suppression model under single-input multi-output (SIMO) systems is presented, and the impact of imperfect frequency synchronization on the AN suppressed performance is analyzed. Specifically, we first analyze the AN suppression performance of single branch with imperfect frequency synchronization. Then the output signal to interference plus noise ratio (SINR) after multi-branch merging is derived. Finally, the secrecy capacity of AN based on SIMO systems is extracted on the basis of the obtained SINR. Theoretical and simulation results show that imperfect frequency synchronization reduces the SINR of each branch, and thus degrades both the output SINR and secrecy capacity in SIMO systems. Moreover, when the residual AN power is greater than noise power, no diversity gain will be achieved by multi-branch merging.
In this paper, we investigate the impact of antenna correlation on secure transmission in a multi-eavesdropper single-input multiple-output (SIMO) system, where the receiver and eavesdroppers are equipped with correlated antennas.Based on the practical passive eavesdropping system, the new closed-form expressions of secrecy outage probability (SOP) and non-zero secrecy capacity probability are derived to explore the effect of antenna correlation on the system with multiple eavesdroppers.To further analyze the secrecy performance of the investigated system, we theoretically derive the expression of asymptotic SOP to clearly show the diversity order and array gain.Finally, Monte Carlo simulations verify the effectiveness of our theoretical results.
Transmitting the information-bearing signal simultaneously with artificial noise (AN) can guarantee secure data exchange on the open wireless channel. One of the key technologies is AN reconstruction and cancellation at the legitimate receiver, but its performance will be deteriorated by the ineluctable clock jitter at the analog-to-digital converter (ADC). In this paper, first, the received signal distorted by clock jitter is mathe-matically modelled. Then, the closed-form expression of signal to interference-plus-noise ratio (SINR) after AN cancellation is deduced, and the secrecy capacity is derived to evaluate the system security. Furthermore, to alleviate the effect of clock jitter, the optimized transmitting power allocation scheme for AN and information signal is provided. Theoretical and simulation results demonstrate that the secrecy performance is limited by the 3 dB coherence bandwidth of the phase noise caused by clock jitter, time synchronization period, and transmitting power allocation factor. With the optimized power scheme, the secrecy capacity can be increased by up to 11 % in comparison to the equal power allocation, and the optimal power allocation factor equals one when there is no clock jitter.
For the cases of imperfect channel state information (CSI) on the main channel in the physical-layer-security communications, we study the artificial-noise-aided robust transmit designs. We consider two optimization problems for the multi-input single-output single-antenna eavesdropper (MISOSE) and multi-input multi-output multi-antenna eavesdropper (MIMOME) systems. Under the deterministic uncertainty model (DM), the optimization problem aims to minimize the total transmit power while guaranteeing the probabilistic constraint for the signal to interference and noise ratios (SINR) at the eavesdropper, and the SINR constraint at the legitimate receiver. For the stochastic uncertainty model (SM), the optimization problem is also to minimize the total transmit power under the probabilistic constraints for the SINRs at the legitimate receiver and the eavesdropper. These problems are hard to be solved directly. We transform the optimization problems into a single-variable optimization problem with solving a sequence of semidefinite programs. By comparison, we propose another low-complexity method based on the expectation value. Finally, we verify the performance for the proposed robust transmit designs by the simulation results.
Artificial noise (AN)-aided techniques have been considered to be promising and practical candidates for enhancing physical layer security. However, there has been a lack of analysis regarding the AN effect on the eavesdropper (EV) from the perspective of the signal-to-interference plus noise ratio (SINR) regarding the existence of the EV’s channel state information (CSI) at the legitimate transmitter. In this paper, we analyze the performance of AN-aided secure transmission from the SINR perspective when a legitimate transmitter has and does not have the EV’s CSI. Based on the analyzed EV’s SINRs for the above two cases, the secrecy gap, which is the difference between the two secrecy capacities, is defined and analyzed. Based on the derived secrecy gap, we have analyzed the asymptotic performances of the secrecy capacity and gap when the number of antennas of the legitimate transmitter and the number of antennas of the EV have large values. Through asymptotic analysis, it is demonstrated that the AN-aided secure transmission under the practical environment (i.e., the case that the EV’s CSI is not available at the legitimate transmitter) can nearly achieve an ideal performance (i.e., the performance when the EV’s CSI is available at the legitimate transmitter) in a massive antenna system.
Cooperative jamming (CJ) combined with single-input multiple-output (SIMO) technology can effectively improve the security and reliability of Internet of Things (IoT) systems. However, imperfect main channel state information (CSI) leads to incomplete CJ cancellation, which degrades the performance after combining. In this paper, by considering channel estimation errors and residual CJ at each receiving antenna, the residual CJ power after jamming suppression is analyzed, and the optimal combining coefficient for maximizing the signal-to-jamming-noise ratio (SJNR) is derived. The output SJNR of optimal diversity combining is given, and the achievable secrecy rate is analyzed on this basis. The theoretical and simulation results verify the combined effect of channel estimation errors and residual CJ on the combining performance. Moreover, it is worth noting that the combining performance is closely related to the spatial correlation of residual CJ.
Consider the multi-input single-output multi-eavesdroppers (MISOMEs) wireless communication system. Our goal is to design an artificial noise (AN)-aided secure transmit strategy to safeguard this system from the perspective of quality-of-service (QoS). Specifically, we propose two design formulas: (1) total power minimization design under signal-to-interference-plus-noise ratio (SINR) constraints on receiver and eavesdroppers; (2) receiver's SINR maximization design under constraints of transmitted total power and eavesdroppers' SINRs. The proposed design problems jointly optimizing the information covariance and AN covariance are solved by semidefinite program (SDP) optimization approach. Through exploring the Karush-Kuhn-Tucker conditions of SDP problems, it is proved that transmit beamforming is the optimal strategy for confidential information transmission in the two designs. Finally, simulation results demonstrate that the proposed AN-aided approach in the two designs provides the best performance compared to isotropic AN and no-AN approach.