This paper investigates the secrecy performance of multiple-input multiple-output systems under generalized α - μ fading conditions. To this end, we focus on two distinct scenarios: 1) the transmitter has knowledge of the channel state information (CSI) of the eavesdropper channel and 2) the transmitter is not aware of the CSI of the wiretap link. By considering transmit antenna selection in the underlying system, we develop closedform analytical expressions for the lower bound of the secrecy outage probability (SOP) and the probability of the strictly positive secrecy capacity. Furthermore, two novel approaches are proposed to derive an analytical expression of the average secrecy capacity (ASC). First, the ASC is expressed as a function of the average capacity of the desired link and an interaction term regarded as the ASC loss. Second, the ASC is expressed in terms of the average capacities of the desired and eavesdropper links, plus an interaction term that can be regarded as some sort of ASC gain due to the statistical independence between the desired and eavesdropper links. In addition, asymptotic studies of the SOP and the ASC at high signal-to-noise ratio are carried out, which precisely reveal the secrecy diversity and array gains.
Transmit Antenna Selection in Secure MIMO Systems Over α−μ Fading Channels
This paper investigates the secrecy performance of multiple-input multiple-output systems under generalized α - μ fading conditions. To this end, we focus on two distinct scenarios: 1) the transmitter has knowledge of the channel state information (CSI) of the eavesdropper channel and 2) the transmitter is not aware of the CSI of the wiretap link. By considering transmit antenna selection in the underlying system, we develop closedform analytical expressions for the lower bound of the secrecy outage probability (SOP) and the probability of the strictly positive secrecy capacity. Furthermore, two novel approaches are proposed to derive an analytical expression of the average secrecy capacity (ASC). First, the ASC is expressed as a function of the average capacity of the desired link and an interaction term regarded as the ASC loss. Second, the ASC is expressed in terms of the average capacities of the desired and eavesdropper links, plus an interaction term that can be regarded as some sort of ASC gain due to the statistical independence between the desired and eavesdropper links. In addition, asymptotic studies of the SOP and the ASC at high signal-to-noise ratio are carried out, which precisely reveal the secrecy diversity and array gains.
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.
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.
Secrecy Analysis of a TAS/MRC Scheme in α−μ Fading Channels
This paper investigates the secrecy performance of a multiple-input multiple-output (MIMO) system with transmit antenna selection (TAS) and maximal-ratio combining (MRC) over generalized α-μ fading. In the underlying wireless communication system, a single antenna is selected to transmit confidential messages to a multi-antenna receiver in the presence of a passive multi-antenna eavesdropper. In our analysis, new closed-form expressions are obtained for the secrecy outage probability (SOP) and the probability of strictly positive secrecy capacity (SPSC), and are subsequently corroborated through Monte Carlo simulations to assess their validity. Moreover, asymptotic studies of the secrecy outage probability are derived and explicitly show the effects of various system parameters on the secrecy diversity gain.
Information-Theoretic Security of MIMO Networks Under κ-μ Shadowed Fading Channels
This paper investigates the impact of realistic propagation conditions on the achievable secrecy performance of multiple-input multiple-output systems in the presence of an eavesdropper (Eve). Specifically, we concentrate on theκ-μshadowed fading model because its physical underpinnings capture a wide range of propagation conditions, while, at the same time, it allows for a much better tractability than other state-of-the-art fading models. By considering transmit antenna selection and maximal ratio combining reception at the legitimate (Bob) and Eve's receiver sides, we study two relevant scenarios: 1) the transmitter knows Bob's channel state information (CSI) but not Eve's CSI, and 2) the transmitter is aware of the CSI of both Bob and Eve channels. For this purpose, we first obtain novel and tractable expressions for the statistics of the maximum of independent and identically distributed (i.i.d.) variates related to the legitimate channel. Based on these results, we derive novel closed-form expressions of the two aforementioned scenarios to assess the secrecy performance of the underlying system. Specifically, for cases: 1) the secrecy outage probability (SOP), the probability of strictly positive secrecy capacity (SPSC), and 2) the average secrecy capacity (ASC). Moreover, we develop analytical asymptotic expressions of the SOP and ASC in the high signal-to-noise ratio regime. In all instances, secrecy performance metrics are characterized in closed-form, without requiring the evaluation of Meijer-G or Fox-H functions. Some useful insights on how the different propagation conditions and the number of antennas impact the secrecy performance are also provided.
This paper investigates the impact on the achievable secrecy performance of multiple-input multiple-output systems by dealing with realistic propagation conditions. Specifically, we focus on the κ-μ shadowing fading model, which has proven to be more accurate in characterizing mm-wave scenarios than traditional Rice and Rayleigh ones. By considering transmit antenna selection and maximal ratio combining at the receiver ends, we study two different scenarios, namely: (i) the transmitter has knowledge of the channel state information (CSI) of the eavesdropper link, and (ii) the transmitter does not know eavesdropper's CSI. Based on these assumptions, we derive novel analytical expressions for the secrecy outage probability (SOP) and the average secrecy capacity (ASC) to assess the secrecy performance in passive and active eavesdropping scenarios, respectively. Moreover, we develop analytical asymptotic expressions of the SOP and ASC at high signal-to-noise ratio regime. Some useful insights on how to obtain noticeable improvements in the secrecy performance are also provided.