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IEEE Transactions on Vehicular Technology

Large-System Analysis of Artificial-Noise-Assisted Communication in the Multiuser Downlink: Ergodic Secrecy Sum Rate and Optimal Power Allocation

Na Li, Xiaofeng Tao, Huici Wu, Jin Xu, Qimei Cui

Published Oct 20, 2015• 50 citations
Publisher

Abstract

Security and privacy have become increasingly critical demands in wireless networks, which, however, are particularly susceptible to eavesdropping attacks due to the broadcast nature of radio signals. This paper considers the problem of secure communication in the multiuser downlink with a passive eavesdropper (Eve), whose channel state information (CSI) is unavailable. The transmitter simultaneously transmits concurrent information signals to the users and artificial noise (AN) to Eve. We first assume that all users' CSI is perfectly known by the transmitter and derive a closed-form expression for the ergodic secrecy sum rate (SSR) in the large-system limit. We then use it as an objective function to optimize the power allocation between information signals and the AN. It shows that more power needs to be used for AN when Eve has more antennas and when the system serves fewer users. We also extend the analysis to the imperfect-CSI scenario, where the SSR saturates at high transmit power, and it is better to create more AN than to increase the signal strength when the channel estimation error is large. We derive a scale law of feedback bits (for frequency-division duplexing (FDD) systems) to maintain a constant rate offset compared with the perfect-CSI case and the optimal length of training sequence (for time-division duplexing (TDD) systems) to maximize the effective SSR. It shows that more feedback bits and longer training sequences are required to deal with the eavesdropping problem. Closed-form expressions derived in this paper can reduce the complexity of system analysis and design.

DOI
10.1109/tvt.2015.2493178

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Security and privacy have become increasingly critical demands in wireless networks, which, however, are particularly susceptible to eavesdropping attacks due to the broadcast nature of radio signals. This paper considers the problem of secure communication in the multiuser downlink with a passive eavesdropper (Eve), whose channel state information (CSI) is unavailable. The transmitter simultaneously transmits concurrent information signals to the users and artificial noise (AN) to Eve. We first assume that all users' CSI is perfectly known by the transmitter and derive a closed-form expression for the ergodic secrecy sum rate (SSR) in the large-system limit. We then use it as an objective function to optimize the power allocation between information signals and the AN. It shows that more power needs to be used for AN when Eve has more antennas and when the system serves fewer users. We also extend the analysis to the imperfect-CSI scenario, where the SSR saturates at high transmit power, and it is better to create more AN than to increase the signal strength when the channel estimation error is large. We derive a scale law of feedback bits (for frequency-division duplexing (FDD) systems) to maintain a constant rate offset compared with the perfect-CSI case and the optimal length of training sequence (for time-division duplexing (TDD) systems) to maximize the effective SSR. It shows that more feedback bits and longer training sequences are required to deal with the eavesdropping problem. Closed-form expressions derived in this paper can reduce the complexity of system analysis and design.
Wireless communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy issues have become increasingly critical for wireless networks. This paper considers the problem of secret communication in the multiuser downlink eavesdropped by a passive eavesdropper (EVE). The well-known zero-forcing preceding is adopted at the transmitter to produce concurrent data streams to the users, and at the same time an artificial noise (AN) is generated to prevent EVE from intercepting the information. We first derive an analytical closed-form expression for the secrecy sum-rate in the large system limit. We then use it as the objective function to optimize the power allocation (PA) between the information signals and the AN to maximize the secrecy sum-rate. A simple analytical expression of the optimal PA is derived in the high transmit power regime, which proves to be a near-optimal and generic strategy. The large system results are quite accurate for finite-size systems and thus can provide useful insights into system analysis and design. Our analytical and simulation results show that the AN assisted strategy achieves the same multiplexing gain as in the multiuser downlink without eavesdropping. Moreover, more power should be allocated to AN when the system serves fewer users and EVE has more antennas.
We consider the problem of secure communication in the multiuser downlink with an external eavesdropper. The transmitter simultaneously transmits concurrent information signals to the users and an artificial noise (AN) to the eavesdropper. We derive a closed-form expression for the secrecy sum-rate in the large system limit and use it as the objective function to optimize the power allocation between the information signals and the AN to maximize the secrecy sum-rate. We obtain a simple approximation for the optimal power allocation in the high signal-to-noise ratio regime, which proves to be a generic and near-optimal strategy. Analytical and simulation results show that more power needs to be allocated to AN if the system serves fewer users and the eavesdropper has more antennas.
In this paper, we consider the problem of secure communication in multiuser downlink wiretap networks where there exist a base-station (BS) equipped with multiple antennas, multiple legitimate receivers and a passive eavesdropper. The transmitter simultaneously transmits an information signal and artificial noise (AN) separately to the intended receivers and the eavesdropper, in which way, the secrecy rate at the eavesdropper can be seriously degraded without thinking about it location. Different schemes are studied about the power allocation of the multiple antennas in the BS, namely the average power allocation scheme and the Water-filling scheme. And in the average power allocation scheme, Zero-forcing (ZF) pre-coding scheme is used at the BS to eliminate the internal interference of all the security users. We obtain an analytical closed form expression of an achievable ergodic secrecy rate and use it as the objective function to optimize the power allocation rate between the information signal and the AN in the two schemes.
We study the secrecy sum-rate (SSR) of a multi-user system in the presence of artificial noise (AN) and determine conditions under which it is necessary to add AN assuming eavesdropper (Eve) cannot remove the interference. We first derive a closed-form expression for the asymptotic SSR of the system and determine the optimum power allocation. The closed form expressions for the SSR and optimum power allocation closely match our simulation results. We also show that as the number of receive antennas at Eve increases, we need to allocate more power to AN in order to degrade reception at Eve.
In this thesis, we study the physical layer security in downlink multi-user wireless networks. Traditionally, security has been addressed by cryptography at the higher layers of the communication stack. Security at the physical layer has been a major research topic in recent years. We study two different precoder designs alongside artificial noise (AN) to mitigate multi-user interference and deteriorate reception at the eavesdropper (Eve). We study the large scale analysis to calculate the secrecy sum-rate for these two cases and analyze the effect of AN on the system. First, we consider the worst case scenario, when eavesdropper's (Eve's) rate is not deteriorated by the interference caused by the legitimate users. Later, we investigate how interference from legitimate users would affect the large scale security sum rate. At the end, we assume more practical situation where the channel state information at the transmitter is not perfect due to feedback limitation and estimation error. We first study block diagonalization (BD) precoding. We derive the asymptotic secrecy sum-rate of BD for physical layer security in downlink multi-user wireless networks using artificial noise (AN). We first derive the secrecy sum-rate assuming that the channel of the eavesdropper is not known at the transmitter and derive the asymptotic secrecy sum-rate. Then we derive the optimum power allocation for asymptotic secrecy sum-rate. We design the system based on large scale analysis for different special cases. Simulation results show that the proposed precoders outperform channel inversion (CI) and regularized channel inversion (RCI) schemes at all SNRs. We also show that as the number of receive antennas of each user increases, the sum-rate gap between the proposed scheme and existing methods increases. We, then, study two methods of regularized block diagonalization (RBD) precoding using artificial noise (AN) for physical layer security in downlink multi-user MIMO wireless networks. We compare the complexity analysis of these two methods in terms of floating point operations per second (FLOPS). We derive the secrecy and asymptotic secrecy sum-rates for these schemes. We also derive closed form expressions for the asymptotic optimal power allocation to the AN signal and legitimate users. Simulations show RBD precoding outperform regularized channel inversion (RCI) in terms of secrecy sum-rate with a margin of 0.5 bits/s/Hz. Also, simulation results show our closed-form asymptotic secrecy sum-rates matches closely with the simulations for perfect and imperfect CSIT. We also study the effect of interference on BD precoding scheme. In the first two studies the worst case scenarios was considered and the effect of interference was not considered at the eavesdropper. We first derive the closed-form secrecy and asymptotic secrecy sum-rates for this scheme. Then, we derive the optimum power allocation. Using the derived optimum power allocation, we determine the conditions under which adding AN helps. We also investigate the optimum number of users, number of antennas at the eavesdropper, and the number of transmit antennas to fully study the conditions where using AN improves performance. We show that as the number of users increases or the number of receive antennas at the eavesdropper decreases, improved performance is achieved by allocating a smaller fraction of the total power to transmit the AN. The closed form expressions for the secrecy sum rate (SSR) and optimum power allocation closely match our simulation results. In Chapter 5, we study the effect of imperfect channel state information at the transmitter (CSIT) for each case studied in earlier chapters. We first study the effect of imperfect CSIT for BD precoding in both scenarios when interference does and does not exist at eavesdropper. We show that the imperfect CSI play the same role as interference for the desired users. Then, we study the effect of imperfect CSIT for RBD precoding when interference does not exist at eavesdropper. We show as channel estimation error increases, the secrecy sum-rate decreases. This is due to the fact that channel estimation error just affects the desired users' rate and has no effect on eavesdropper's performance. Finally, in the last chapter, we conclude our thesis and provide some road map for future--Author's abstract
In this letter, we consider the problem of secure communication in the downlink of a multi-cell multiple-input multiple-output (MIMO) system under imperfect channel state information (CSI) at the base stations (BSs). The passive eavesdroppers are considered, whose CSI are unavailable at the BSs. Coordinated Beamforming (CBf) and artificial noise (AN) are employed for secrecy enhancement. Based on regularized channel inversion (RCI) precoding, we derive a novel closed-form expression of secrecy sum-rate in the large-system regime. Based on the result, the regularization parameter and the power allocation ratio between the information signal and AN are optimized. Compared to the perfect CSI case, it shows that the channel estimation error can drastically reduce the secrecy sum-rate, and more power needs to be allocated for AN when the channel estimation error grows larger. The analytical results are validated with the finite-size system by simulation.