We propose a new secure transmission scheme in the multi-input multi-output multi-eavesdropper wiretap channel. In this channel, the NA-antenna transmitter adopts transmit antenna selection (TAS) to choose the antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver to transmit, while the NB-antenna receiver and the NE-antenna eavesdropper adopt maximal-ratio combining (MRC) to combine the received signals. We focus on the practical scenario where the channel state information (CSI) during the TAS process is outdated. In this scenario, we propose a new transmission scheme to prevent the detrimental effect of the outdated CSI on the wiretap codes design at the transmitter. To thoroughly assess the secrecy performance achieved by the proposed scheme, we derive new closed-form expressions for the exact secrecy outage probability and the probability of non-zero secrecy capacity for arbitrary SNRs. We also derive new compact expressions for the asymptotic secrecy outage probability at high SNRs. Notably, in the analysis, we take spatial correlation at the receiver into consideration. Apart from the advantage of our scheme over the conventional TAS/MRC scheme, we demonstrate that the outdated TAS reduces the secrecy diversity order from NANBto NB. We also demonstrate that antenna correlation improves the secrecy performance at low SNR but deteriorates the secrecy performance at medium and high SNRs, by affecting the secrecy array gain only.
We propose a new secure transmission scheme in the multi-input multi-output multi-eavesdropper wiretap channel. In this channel, the NA-antenna transmitter adopts transmit antenna selection (TAS) to choose the antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver to transmit, while the NB-antenna receiver and the NE-antenna eavesdropper adopt maximal-ratio combining (MRC) to combine the received signals. We focus on the practical scenario where the channel state information (CSI) during the TAS process is outdated. In this scenario, we propose a new transmission scheme to prevent the detrimental effect of the outdated CSI on the wiretap codes design at the transmitter. To thoroughly assess the secrecy performance achieved by the proposed scheme, we derive new closed-form expressions for the exact secrecy outage probability and the probability of non-zero secrecy capacity for arbitrary SNRs. We also derive new compact expressions for the asymptotic secrecy outage probability at high SNRs. Notably, in the analysis, we take spatial correlation at the receiver into consideration. Apart from the advantage of our scheme over the conventional TAS/MRC scheme, we demonstrate that the outdated TAS reduces the secrecy diversity order from NANBto NB. We also demonstrate that antenna correlation improves the secrecy performance at low SNR but deteriorates the secrecy performance at medium and high SNRs, by affecting the secrecy array gain only.
We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with multiple antennas at the transmitter, the receiver, and the eavesdropper. We consider the practical scenario of passive eavesdropping, where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. In the main channel between the transmitter and the receiver, we select a single antenna at the transmitter that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. At the receiver and the eavesdropper, we consider two combining techniques: 1) maximal-ratio combining (MRC) and 2) selection combining (SC). For non-identical Rayleigh fading between the main channel and the eavesdropper's channel, we first derive new closed-form expressions for the exact and asymptotic secrecy outage probabilities. The asymptotic results accurately reveal the secrecy diversity order and the secrecy array gain. Next, we derive new closed-form expressions for the probability of positive secrecy and characterize the ε-outage secrecy capacity. We show that, under TAS/MRC and TAS/SC protocols, the secrecy outage probability approaches zero and the ε-outage secrecy capacity increases with increasing number of transmitter antennas.
In this paper, we introduce transmit antenna selection/maximal-ratio combining (TAS/MRC) scheme in dual-hop randomize-and-forward (RaF) cognitive multiple-input multiple-output (MIMO) wiretap networks with outdated channel state information (CSI). In this network, the secondary transmitter adopts the TAS scheme to choose the antenna with the maximal received signal-to-noise ratio (SNR), while the secondary receiver and the eavesdropper adopt the MRC scheme to combine the received signals. To thoroughly assess the secrecy performance achieved by the TAS/MRC scheme and the impact of outdated CSI on the secrecy performance, we derive a new closed-form expression for the secrecy outage probability of dual-hop RaF cognitive MIMO wiretap networks. In order to achieve more insights on the application of TAS/MRC scheme, we further present tractable asymptotic secrecy outage probability at high SNR regimes under two distinct scenarios. From our analysis, several important concluding remarks are obtained as follows: 1) the RaF relaying strategy achieves better secrecy performance than that of the decode-and-forward relaying strategy for dual-hop cognitive MIMO wiretap networks; 2) outdated CSI decreases the secrecy diversity gain of the TAS/MRC scheme from NRmin (NA, NB) to (NR, NB) ; and 3) although TAS/MRC scheme cannot attain full secrecy diversity gain for the considered system with outdated CSI, it still can achieve an extra secrecy coding gain compared with the random antenna selection/MRC scheme.
We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with NAantennas at the transmitter, NBantennas at the receiver, and NEantennas at the eavesdropper. We focus on the practical scenario where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. The transmitter selects a single antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. The receiver and the eavesdropper employ either maximal-ratio combining (MRC) or selection combining (SC) to combine the received signals. For the proposed protocols, we derive new closed-form expressions for the probability of non-zero secrecy capacity. We consider Nakagami-m fading with non-identical fading parameters of the main channel, mB, and of the eavesdropper's channel, mE. Next, we derive new closed-form expressions for the exact secrecy outage probability, based on which the ε-outage secrecy capacity is characterized. Based on the exact expressions, we derive the asymptotic secrecy outage probability which accurately reveals the secrecy diversity order and the secrecy array gain. We confirm that the proposed protocols achieve identical secrecy diversity orders of NANBmB. An interesting conclusion is reached that this diversity order is independent of NEand mE. Furthermore, we prove that under the proposed protocols, the secrecy outage probability and the ε-outage secrecy capacity improve with increasing NA.
This paper proposes a new transmit antenna selection (TAS) scheme which provides enhanced physical layer security in multiple-input multiple-output (MIMO) wiretap channels. The practical passive eavesdropping scenario we consider is where channel state information (CSI) from the eavesdropper is not available at the transmitter. Our new scheme is carried out in two steps. First, the transmitter selects the two strongest antennas based on the feedback from the receiver, which maximizes the instantaneous signal-to-noise ratio (SNR) of the transmitter-receiver channel. Second, the Alamouti scheme is employed at the selected antennas in order to perform data transmission. At the receiver and the eavesdropper, maximal-ratio combining is applied in order to exploit the multiple antennas. We derive a new closed-form expression for the secrecy outage probability in non-identical Rayleigh fading, and using this result, we then present the probability of non-zero secrecy capacity in closed form and the ε-outage secrecy capacity in numerical form. We demonstrate that our proposed TAS-Alamouti scheme offers lower secrecy outage probability than a single TAS scheme when the SNR of the transmitter-receiver channel is above a specific value.
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.
This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in the multiple-input-multiple-output wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mB and mE, respectively. In order to assess the secrecy performance, we present a new unifying framework for the average secrecy rate and the secrecy outage probability. We first derive expressions for the probability density function and the cumulative distribution function of the signal-to-noise ratio with TAS/GSC, from which we derive exact expressions for the average secrecy rate and the secrecy outage probability. We then derive compact expressions for the asymptotic average secrecy rate and the asymptotic secrecy outage probability for two distinct scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. For these scenarios, we present new closed-form expressions for several key performance indicators: 1) the capacity slope and the power offset of the asymptotic average secrecy rate, and 2) the secrecy diversity order and the secrecy array gain of the asymptotic secrecy outage probability. For the first scenario, we confirm that the capacity slope is one and the secrecy diversity order is mBNBNA. For the second scenario, we confirm that the capacity slope and the secrecy diversity order collapse to zero.