Secrecy capacity and outage probability of multiuser MIMO systems with zero forcing receivers

Unlike prior works assuming perfect attack detection, this paper investigates the physical layer security of a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided network under a full-duplex active eavesdropper in the more realistic scenario where its jamming remains undetected by the legitimate transmitter. Assuming Nakagami-m fading channels, we first derive the probability density functions (PDFs) of the signal-to-interference ratios (SIRs) at both the legitimate user and the eavesdropper. Then, using the PDFs, we obtain novel closed-form expressions for key secrecy metrics, including the probability of nonzero secrecy capacity (PNSC), secrecy outage probability (SOP), and average secrecy capacity (ASC). Moreover, the asymptotic PNSC, SOP, and ASC at high signal-to noise ratio (SNR) are also derived. Based on those asymptotic expressions, we present compact expressions for several key performance indicators: 1) the secrecy diversity order and the secrecy array gain of the SOP, and 2) the high SNR slope and the high SNR power offset of the ASC. Results demonstrate that, compared to the passive eavesdropper scheme, the active jamming attack carried out by Eve will not cause any loss in secrecy diversity gain and high SNR slope, but only result in the loss of secrecy array gain and high SNR power offset. Finally, we verify our analytical results via simulations.

<p>This thesis considers the analysis of current and future cellular communication systems. The main focus is on multiuser multiple-input multiple-output (MU-MIMO) antenna systems. The goal of this work is to characterize the achievable spectral efficiency of MU-MIMO systems, as well as to analyze the performance of practical, linear MU-MIMO transceiver structures in heterogeneous propagation environments. The analytical derivations in this thesis are based on the mathematical theory of finite and large dimensional random matrices. A collection of new general random matrix theory results, which permit efficient numerical evaluation are derived. With downlink regularized zero-forcing (RZF) processing at a cellular base station (BS), a general framework for the analysis of the expected (average) signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency is developed for uncorrelated and semi-correlated Rayleigh fading, as well as uncorrelated Ricean fading propagation channels. In contrast to existing results, the presented analyses are extremely general, applicable to single-cellular, multi-cellular, as well as distributed antenna systems. These systems could consist of arbitrary numbers of transmit and receive antennas, link signal-to-noise-ratios (SNRs), equal and unequal transmit correlation structures, and line-of-sight (LoS) levels, respectively. Numerical results are presented for single-cellular, as well as for two-tier multi-cellular systems demonstrating the impact of novel BS coordination strategies to suppress dominant inter-cellular interference. With dominant LoS directions in the propagation channel, the instantaneous downlink zero-forcing (ZF) SNR of a given terminal is analyzed. The ZF SNR is shown to be approximated by a gamma distribution for any number of transmit and receive antennas, link SNRs, and LoS levels. Furthermore, for moderately sized MU-MIMO systems, simplified instantaneous and ergodic sum spectral efficiency analyses are presented with RZF, ZF and matched-filter (MF) transmission on the downlink, and minimum-mean-squared-error, ZF and maximum-ratio combining (MRC) on the uplink, respectively. The simple nature of the derived expressions lead to the discovery of several valuable system level insights as a function of the contributing network parameters. Numerical results are presented for conventional and moderate MU-MIMO systems. Considering downlink semi-correlated Rayleigh fading channels with spatial correlation at the BS, it is mathematically proven that common correlation patterns for each terminal predicts lower ergodic sum spectral efficiencies in comparison to terminal specific correlation patterns. Closed-form approximations for the expected SINR and ergodic sum spectral efficiency are derived for both MF and ZF precoding, demonstrating the sensitivity of unequal correlation structures on the expected signal, interference and noise powers, respectively. The presented numerical results provide a cautionary tale of the impact of unequal correlation patterns on MU-MIMO performance and the importance of modeling this phenomenon. Finally, an approximate uplink performance analysis of large MU-MIMO systems with MRC and space-constrained uniform linear antenna arrays (ULA) is presented for semi-correlated Ricean fading channels. A space-constrained channel model is proposed, encapsulating the effects of unequal receive spatial correlation, unequal LoS levels, and unequal link gains for each terminal. The per-terminal and cell-wide ergodic sum spectral efficiencies are characterized and numerous practical special cases are presented. A limiting analysis of the ergodic per-terminal and cell-wide spectral efficiencies is also carried out, as the number of BS antennas grow without bound with a finite number of terminals and fixed physical dimensions of the ULA. Numerical results demonstrate the impact of space-constrained ULAs on the MU-MIMO system performance with variation in the LoS levels, correlation structures, physical array dimensions, and system size, respectively.</p>

This paper studies Wireless Information-Theoretic Security for low-speed mobility in autonomic networks. More specifically, the impact of user movement on the Probability of Non-Zero Secrecy Capacity and Outage Secrecy Capacity for different channel conditions has been investigated. This is accomplished by establishing a link between different user locations and the boundaries of information-theoretic secure communication. Human mobility scenarios are considered, and its impact on physical layer security is examined, considering quasi-static Rayleigh channels for the fading phenomena. Simulation results have shown that the Secrecy Capacity depends on the relative distance of legitimate and illegitimate (eavesdropper) users in reference to the given transmitter.

This paper considers the uplink of a single-cell large-scale multiuser multiple-input multiple-output (MU-MIMO) system. The transmitted data is detected by linear receivers at the base station (BS), that is, maximum ratio combining (MRC), zero-forcing (ZF) and minimum mean square error (MMSE). New non-asymptotic outage expressions that are valid for any number of BS antennas are derived. It is shown that the MMSE scheme always achieves the best outage performance, and the ZF scheme outperforms the MRC scheme in the high signal-to-noise-ratio (SNR) regime, while the opposite holds in the low SNR regime. We also demonstrate that when the number of BS antennas is very large and the number of users is fixed, the asymptotic outage probability tends to zero, providing that the channel state information (CSI) is perfect. However, if both the number of BS antennas and the number of users grow large, it would be a different matter. Extensive numerical results are presented to verify the theoretical analysis.

The past ten years have seen notable research activity and significant advancements in multiuser multiple-input multiple-output (MU-MIMO) antennas. An MU-MIMO antenna system must accommodate many subscribers without additional bandwidth or energy. User scheduling becomes a critical strategy to take advantage of multiuser heterogeneity and acquire maximum gain in systems where the total number of recipients exceeds the number of transmitting antennas. Due to their high computational cost, many user selection methods currently in use, such as greedy algorithms and exhaustive search are unsuitable for MU-MIMO systems. A suitable scheduling mechanism is essential for the various users in an MU-MIMO system to utilise bandwidth and enhance the system’s total rate effectively. In this article, we proposed a user and antenna scheduling with a population-based meta-heuristic approach, namely the binary salp swarm algorithm (binary SSA), to increase the system sum rate with low computing complexity. We specifically used a population-based meta-heuristics optimisation technique to simulate the user scheduling problem in MU-MIMO systems, characterising complicated issues with binary decisions. Additionally, binary SSA significantly outperforms existing population-based models, such as the binary bat algorithm (binary BA), PSO, SSA, FPA and binary flower pollination algorithm (binary FPA), regarding system throughput/sum rate. The proposed binary SSA technique also effectively achieves a system sum rate compared to a random search scheme and other existing suboptimal scheduling methods. Compared to binary BA and binary FPA approaches, the binary SSA has a higher convergence rate and superior searching capabilities. The simulation outcomes show the proposed binary SSA-based scheduling scheme delivers noticeable performance benefits.

Vehicle to vehicle (V2V) communications under dense urban scenarios are usually influenced by keyhole effect, which leads to rank deficiency and diminishes communication security. This paper investigates the physical layer security (PLS) in V2V communications with keyhole effect, where multiple-input multiple-output (MIMO) is involved in both legitimate and wiretap channels. Secrecy performance of the considered MIMO-V2V systems is evaluated by deriving closed-form expressions of the probability of non-zero secrecy capacity, secrecy outage probability (SOP) and average secrecy capacity (ASC), respectively. The analytical results are validated by numerical simulations and are in excellent agreement.

The Low Earth Orbit (LEO) small satellites are extensively used for global connectivity to enable services in underpopulated, remote or underdeveloped areas. Their inherent broadcast nature exposes LEO–terrestrial communication links to severe security threats, which always reveal new challenges. The secrecy performance of the satellite-to-ground user link in the presence of a ground eavesdropper is studied in this paper. We observe both scenarios of the eavesdropper’s channel state information (CSI) being known or unknown to the satellite. Throughout the analysis, we consider that locations of the intended and unauthorized user are both arbitrary in the satellite’s footprint. On the other hand, we analyze the case when the user is in the center of the satellite’s central beam. In order to achieve realistic physical layer security features of the system, the satellite channels are assumed to undergo Gamma-shadowed Ricean fading, where both line-of-site and scattering components are influenced by shadowing effect. In addition, some practical effects, such as satellite multi-beam pattern and free space loss, are considered in the analysis. Capitalizing on the aforementioned scenarios, we derive the novel analytical expressions for the average secrecy capacity, secrecy outage probability, probability of non-zero secrecy capacity, and probability of intercept events in the form of Meijer’s G functions. In addition, novel asymptotic expressions are derived from previously mentioned metrics. Numerical results are presented to illustrate the effects of beam radius, satellite altitude, receivers’ position, as well as the interplay of the fading or/and shadowing impacts over main and wiretap channels on the system security. Analytical results are confirmed by Monte Carlo simulations.

Peta-Hertz (PHz) communication technology is envisioned to provide an enormously high data rate with true sense global coverage ranging from air to underwater deployment. However, both line-of-sight (LOS) and non-LOS (NLOS) components are needed to characterize the fading channels of the PHz communication system. Recently, the proposed α-Beaulieu-Xie fading distribution, with α as a modified parameter, appropriately characterizes wireless channels with multiple LOS and NLOS components simultaneously. In addition, α-Beaulieu-Xie distribution exhibits a high degree of trade-off between mathematical tractability and match with experimental data. This research presents various measures of physical layer security over α-Beaulieu-Xie fading channel under the SC diversity scheme. In particular, analytical expressions for Secrecy Outage Probability (SOP)(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>), Probability of Non-Zero Secrecy Capacity (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>nz</i>−<i>SC</i></sub>), and Average Secrecy Capacity (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub>) are derived over α-Beaulieu-Xie fading channel under the SC diversity scheme. Further, asymptotic expressions for respective secrecy measures are presented as (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Aymp</i></sub><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i>), <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>nz</i>−<i>SC</i></sub>|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Aymp</i></sub>, and (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub>|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Aymp</i></sub>). Furthermore, the effect of various physical parameters, such as the overall severity parameter of both LOS and NLOS (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_X</i>), the severity parameter of LoS (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_Y</i>), and the fading parameter (α) on the presented secrecy measures, is quantified numerically. Numerical quantification reveals that the decrease in the value of (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>) with an increase in the value of α is proportional to the value of α for a lower regime of γ only. Whereas a decrease in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> with an increase in the value of α reflects that the value of (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</sub>(γ)|<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Out</i>−<i>SC</i></sub>) depends more dominantly on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> than that of α. In addition, it is noticeable that an increase in either <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> or α increases the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub>. However, an increase in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> and α by the same amount, say 0.2, results in a higher increase in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SAv</i>−<i>SC</i></sub> with an increase in the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_x</i> than that of an increase in the value of α. In addition, each analytical expression is quantified numerically with respect to the respective asymptotic expressions.

Physical layer security in SWIPT-based cooperative vehicular relaying networks

Cognitive radio network with secrecy and interference constraints

In this paper, we discuss the influence of feedback channel delay on throughput of linear multi-user multiple-input multiple-output (MIMO) systems employing vector quantization (VQ) algorithms for encoding channel state information (CSI). We consider an approach where the mobile receiver estimates the downlink channel and chooses one of the predefined channel characterization codewords whose indices are transmitted back to the base station transmitter. In practice, the feedback channel introduces delay in transmission of the indices and we evaluate the resulting channel throughput loss for different system setups. Moreover, we define two new parameters of VQ MIMO systems: the channel eigenmode coherence time and singular value coherence time, and discuss their influence on system design. We demonstrate the performance of two types of systems, one using time division multiplexing of individual mobile users and another transmitting to multiple users at the same time. The simulation results show that feedback delay sensitivity of the multiple-user system throughput is much higher than in the TDM approach. Based on those results we propose a simple method allowing a selection of the VQ resolution for the given channel characteristics and system setup.

Multiple-input multiple-output (MIMO) wireless communications systems have attracted a lot of attentions, because of their potential for high gain in channel capacity. Recently, attention has shifted to multiuser MIMO (MU-MIMO) systems. In the schemes for downlink MU-MIMO system, dirty paper coding (DPC) and block diagonalization (BD) algorithms can provide higher sum rate capacity of MU-MIMO systems; however, exhaustive user scheduling for them may cause prohibitive computation complexity. The greedy scheduling algorithms were proposed for DPC and for BD; and proportionally fair (PF) scheduling for MU-MIMO was also discussed in the previous works. However, the discussions in where mainly based on the system model with equal average signal to noise power ratio (SNR) users. In this paper, we focus on the user scheduling for the downlink of MU-MIMO systems with DPC transmission scheme, where each user is assumed to have only one receive antenna, which will simplify the analysis and is expected to give more insight of PF scheduling. We also assume each individual user has different average transmit SNR in the system. We modify the conventional user scheduling algorithm for DPC to modified Gram-Schmidt orthogonalization (M-GSO) based algorithm and extend it into PF scheduling. We also propose a modified PF metric corresponding to the unequal SNR users system model, that increases the sum rate capacity of MU-MIMO system.

This paper investigates the secrecy outage probability (SOP), the lower bound of SOP, and the probability of non-zero secrecy capacity (PNZ) of reconfigurable intelligent surface (RIS)-assisted systems from an information-theoretic perspective. In particular, we consider the impacts of eavesdroppers’ location uncertainty and the phase adjustment uncertainty, namely imperfect coherent phase shifting and discrete phase shifting on RIS. More specifically, analytical and simulation results are presented to show that (i) the SOP gain due to the increase of the RIS reflecting elements number gradually decreases; and (ii) both phase shifting designs demonstrate the same PNZ secrecy performance, in other words, the random discrete phase shifting outperforms the imperfect coherent phase shifting design with reduced complexity.

Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

In multi-user millimeter wave (mmWave) multiple input multiple output (MIMO) systems, obtaining accurate information/knowledge regarding the channel state is crucial to achieving multi-user interference cancellation and reliable beamforming (BF)–to compensate for severe path loss. This knowledge is nonetheless very challenging to acquire in practice since large antenna arrays experience a low signal-to-noise ratio (SNR) before BF. In this paper, a multi-user channel estimation (CE) scheme namely generalized-block compressed sampling matching pursuit (G-BCoSaMP), is proposed for multi-user mmWave MIMO systems over frequency selective fading channels. This scheme exploits the cluster-structured sparsity in the angular and delay domain of mmWave channels determined by the actual spatial frequencies of each path. As the corresponding spatial frequencies of multi-user mmWave MIMO systems with Hybrid BF often fall between the discrete Fourier transform (DFT) bins due to the continuous Angle of Arrival (AoA)/Angle of Departure (AoD), the proposed G-BCoSaMP algorithm can address the resulting power leakage problem. Simulation results show that the proposed algorithm is effective and offer a better CE performance in terms of MSE when compared to the generalized block orthogonal matching pursuit (G-BOMP) algorithm that does not possess a pruning step.