In this paper, we investigate the physical layer security of a multiple-input and multiple-output (MIMO) relay system under imperfect channel state information (CSI). We propose using multiple antennas at the source and destination to increase the signal-to-noise (SNR) gain of the primary channel, thus improving the system's security performance. Exact closed-form expression of the secure outage probability (SOP) and secrecy capacity (SC) are derived and verified by Monte-Carlo simulations. A close match between the theoretical and simulation results confirms the accurateness of our mathematical analysis. We show that the SOP decreases while the SC increases as the average SNR is higher. Furthermore, the saturated minimum and maximum values highly depend on the number of antennas at source and destination, the degree of imperfect CSI, and the location of eavesdropper.
In this paper, we investigate the physical layer security of a multiple-input and multiple-output (MIMO) relay system under imperfect channel state information (CSI). We propose using multiple antennas at the source and destination to increase the signal-to-noise (SNR) gain of the primary channel, thus improving the system's security performance. Exact closed-form expression of the secure outage probability (SOP) and secrecy capacity (SC) are derived and verified by Monte-Carlo simulations. A close match between the theoretical and simulation results confirms the accurateness of our mathematical analysis. We show that the SOP decreases while the SC increases as the average SNR is higher. Furthermore, the saturated minimum and maximum values highly depend on the number of antennas at source and destination, the degree of imperfect CSI, and the location of eavesdropper.
Transmit beamforming is a diversity technique in multiple-input multiple-output (MIMO) systems. It improves the diversity order and enhances the information security of the MIMO systems. In this paper, we mathematically analyze the secure performance of a MIMO decode-and-forward (DF) relay system under the presence of an eavesdropper and with the imperfect channel state information (CSI) of the eavesdropping channel. To enhance the secrecy performance, we employ multiple antennas at all legitimate nodes and utilize two linear beamforming schemes, i.e., maximal ratio transmission (MRT) and transmission zero-forcing (TZF), at the transmitter and maximal ratio combining (MRC) scheme at the receiver. The probability density function (PDF) of the output SNR for different numbers of antennas at the transmitter and receiver is plotted and discussed. After that, we apply this PDF to derive the closed-form expressions of the secrecy outage probability (SOP) and ergodic secrecy capacity (ESC) of the considered MIMO-DF relay system over Rayleigh fading channels for MRT/MRC and TZF/MRC schemes. In addition, based on the obtained analysis results, we provide the location of the relay that minimizes the system SOPs. All the analysis results are validated by Monte-Carlo simulations. The results show that the TZF/MRC scheme provides better SOP and ESC than the MRT/MRC scheme. Moreover, the number of antennas at the legitimate nodes and the location of the eavesdropper significantly impact the secrecy performance.
This paper presents an investigation of the physical layer secrecy outage performance of the cooperative system in the typical four-node (source, relay, destination, and eavesdropper) scenario with imperfect channel state information (CSI). Specifically, we consider the single-input multiple-output wiretap channels, where the source (S) and the relay (R) are equipped with a single antenna, and the destination (D) and the eavesdropper (E) are equipped with multiple antennas. D and E adopt maximal ratio combining to process multiple copies of signals, and the relay adopts decode-and-forward (DF) and randomize-and-forward (RF) schemes to forward the received signal to the destination. E overhears the information transmitted over both the S-R and R-D links. We derive the closed-form and asymptotic expressions for the secrecy outage probability under both the DF and RF schemes with imperfect CSI, respectively, the accuracy of which is verified by simulation results.
Physical layer security is an important method to improve the secrecy performance of wireless communication systems. In this paper, we analyze the effect of employing channel correlation to improve security performance in multiple-input multiple-output (MIMO) scenario with antenna selection (AS) scheme. We first derive the analytical expressions of average secrecy capacity (ASC) and secrecy outage probability (SOP) by the first order Marcum Q function. Then, the asymptotic expressions of ASC and SOP in two specific scenarios are further derived. The correctness of analytical and asymptotic expressions is verified by Monte Carlo simulations. The conclusions suggest that the analytical expressions of ASC and SOP are related to the product of transmitting and receiving antennas; increasing the number of antennas is beneficial to ASC and SOP. Besides, when the target rate is set at a low level, strong channel correlation is bad for ASC, but is beneficial to SOP.
The impact of feedback errors on the security performances of multiple-input multiple-output (MIMO) wiretap channels is analyzed. For the legitimate MIMO system, two schemes are considered: 1) transmit antenna selection/maximal ratio combining (TAS/MRC) and 2) transmit antenna selection/receive antenna selection (TAS/RAS). The eavesdropper uses either MRC or RAS techniques. We derive closed-form expressions for the exact secrecy outage probability (SOP) and the probability of strictly positive secrecy capacity (PSPSC). In order to obtain the secrecy diversity order and the secrecy array gain, on asymptotic SOP expression is also derived.
This paper studies the achievable secrecy performance of multiple-input multiple-output wiretap channels in the presence of imperfect channel state information (CSI) with practical low-complexity transmission schemes. In particular, we propose a general order transmit antenna selection and power-efficient output-threshold maximal ratio combining scheme. Two separate cases depending on the availability of the eavesdropper's CSI at the transmitter are considered. New closed-form expressions of the secrecy outage probability and the average secrecy rate are obtained. In addition, the secrecy diversity order and array gains, high signal-to-noise ratio slope, and power offset are characterized through asymptotic analysis, which enables the characterization of the effect of imprecise transmit antenna selection, output-threshold, and imperfect CSI on the secrecy performance. Numerical results are presented to validate the main outcomes of this paper.
In this paper, we propose general-order transmit antenna selection to enhance the secrecy performance of multiple-input-multiple-output multieavesdropper channels with outdated channel state information (CSI) at the transmitter. To evaluate the effect of the outdated CSI on the secure transmission of the system, we investigate the secrecy performance for two practical scenarios, i.e., Scenarios I and II, where the eavesdropper's CSI is not available at the transmitter and is available at the transmitter, respectively. For Scenario I, we derive exact and asymptotic closed-form expressions for the secrecy outage probability in Nakagami-m fading channels. In addition, we also derive the probability of nonzero secrecy capacity and the ε-outage secrecy capacity, respectively. Simple asymptotic expressions for the secrecy outage probability reveal that the secrecy diversity order is reduced when the CSI is outdated at the transmitter, and it is independent of the number of antennas at each eavesdropper NE, the fading parameter of the eavesdropper's channel mE, and the number of eavesdroppers M. For Scenario II, we make a comprehensive analysis of the average secrecy capacity obtained by the system. Specifically, new closed-form expressions for the exact and asymptotic average secrecy capacity are derived, which are valid for general systems with an arbitrary number of antennas, number of eavesdroppers, and fading severity parameters. Resorting to these results, we also determine a high signal-to-noise ratio power offset to explicitly quantify the impact of the main channel and the eavesdropper's channel on the average secrecy capacity.