This paper studies physical layer security for Alamouti space–time block code (STBC) with joint maximum likelihood (JML) or zero forcing (ZF) detection techniques particularly over multi-input single-output (MISO) wiretap time-selective Rayleigh fading channels. Specifically, we derive the secrecy outage probabilities (SOPs) and their concise but effective approximations for various combinations of JML and ZF at the legitimate receiver and eavesdropper. We also investigate the secrecy diversity gain by applying the high signal-to-noise ratio (SNR) approximation of SOP and prove that the corresponding asymptotic diversity order of two, two, one, and one can be achieved for JML-JML, JML-ZF, ZF-JML, and ZF-ZF, respectively. Our asymptotic analytical results corroborate that the secrecy diversity order is dominantly affected by the detection strategy of the legitimate receiver rather than that of the eavesdropper.
This paper studies physical layer security for Alamouti space–time block code (STBC) with joint maximum likelihood (JML) or zero forcing (ZF) detection techniques particularly over multi-input single-output (MISO) wiretap time-selective Rayleigh fading channels. Specifically, we derive the secrecy outage probabilities (SOPs) and their concise but effective approximations for various combinations of JML and ZF at the legitimate receiver and eavesdropper. We also investigate the secrecy diversity gain by applying the high signal-to-noise ratio (SNR) approximation of SOP and prove that the corresponding asymptotic diversity order of two, two, one, and one can be achieved for JML-JML, JML-ZF, ZF-JML, and ZF-ZF, respectively. Our asymptotic analytical results corroborate that the secrecy diversity order is dominantly affected by the detection strategy of the legitimate receiver rather than that of the eavesdropper.
This letter studies the secrecy outage probability (SOP) and the secrecy diversity order of Alamouti STBC with decision feedback (DF) detection over the time-selective fading channels. For given temporal correlations, we have derived the exact SOPs and their asymptotic approximations for all possible combinations of detection schemes including joint maximum likehood (JML), zero-forcing (ZF), and DF at Bob and Eve. We reveal that the SOP is mainly influenced by the detection scheme of the legitimate receiver rather than eavesdropper and the achievable secrecy diversity order converges to two and one for JML only at Bob (i.e., JML-JML/ZF/DF) and for the other cases (i.e., ZF-JML/ZF/DF, DF-JML/ZF/DF), respectively. Here, p-q combination pair indicates that Bob and Eve adopt the detection method p ∈ {JML, ZF, DF} and q ∈ {JML, ZF, DF}, respectively.
Quasi-orthogonal space time block codes with power scaling (QSTBC-PS) that linearly combines two Alamouti codes with unequal power scaling has been known to achieve full diversity in multi-input multi-output (MIMO) systems. In this correspondence, we evaluate the physical layer security performance of QSTBC-PS in MIMO wiretap channels under Rayleigh fading. We derive the tight closed-form approximate formula of secrecy outage probability for QSTBC-PS by using moment matching approximation technique. Further, we derive the high signal-to-noise ratio (SNR) approximation and the probability of strictly positive secrecy capacity in explicit form. The numerical examples validate that our analytical results match well to the Monte-Carlo simulation results for general number of receive antennas at the desired receiver and eavesdropper.
This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U), where det(U) is the determinant of correlation matrix U. In contrast, in the high signal-to-noise ratio regime at the legitimate receiver, correlation between the main channels and the eavesdropper channels has a positive effect on SOP. Moreover, for multiple input and multiple output wiretap channels, the SOP of two transmit antenna selection (TAS) schemes are analyzed for the considered correlated channel model. The SOP relationship of the both TAS schemes is quantified by the secrecy array gain. Finally, numerical simulations are conducted to corroborate the analytical results.
This paper presents a detailed secrecy performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single-input multiple-output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U), where det(U) is the determinant of correlation matrix U. In contrast, when the average SNR at the legitimate receiver is much larger than that at the eavesdropper, correlation between the main channels and the eavesdropper channels has a positive effect on SOP. Moreover, in the case of multiple-input and multiple-output wiretap channels, two transmit antenna selection schemes with or without the eavesdropper's channel state information are evaluated by the SOP and the average secrecy capacity for the considered correlated channel model, respectively. Finally, numerical simulations are conducted to corroborate the analytical results.
In this paper, a decoding method of joint zero-forcing and successive interference cancellation (ZF-SIC) is put forward to assist the study of the individual secrecy in the quasi-static Rayleigh fading single-input multiple-output multiple access wiretap channel. We first evaluate the individual secrecy performance by deriving the closed-form expressions in terms of positive secrecy capacity probability, secrecy outage probability, and effective secrecy throughput (EST). Besides the expected impact of the SIC order, we find, in high signal-to-noise ratio (SNR) regime, the secrecy performance is only determined by the transmitter’s relative distance to eavesdropper over legitimate receiver rather than the SNR. Such a result prompts us to propose an SIC order scheduling scheme (alternative scheme) on basis of the transmitters’ relative distances from the shortest to the longest. It is proved optimal in achieving total maximum EST in high SNR regime. Finally, we also investigate the problem of optimal power allocation to each transmitter under the constraint of the limited total power. An interesting solution to this problem is disclosed with the aid of numerical analysis.
Recently, a new paradigm of multiple access (MAC) along with one eavesdropper to achieve secrecy transmissions has been getting in focus. However, all existing work on such multiple access wiretap channel (MAC-WT) mainly concentrates on the secrecy performance of the system as a whole from an information theoretic perspective. In this work, we investigate the secrecy performance of a single transmitter in the quasi-static Rayleigh fading MAC-WT on basis of two decoding methods, zero-forcing (ZF) and minimum mean-square error (MMSE), jointly with successive interference cancellation (SIC). We evaluate the secrecy performance in three metrics: positive secrecy capacity probability, secrecy outage probability and effective secrecy throughput. The analytical and simulation results show that, 1) the SIC order has great impacts on the secrecy performance for both methods; 2) MMSE-SIC outperforms ZF-SIC, while the performance gap can be overcome via adjusting SIC order, or increasing SNR, or enhancing the spatial diversity gain; 3) in high SNR regime, the secrecy performance is only determined by the relative distance to eavesdropper over legitimate receiver rather than the SNR.