Millimeter wave/Terahertz (mmWave/THz) communication with extremely large-scale antenna arrays (ELAAs) offers a promising solution to meet the escalating demand for high data rates in next-generation communications. A large array aperture, along with the ever increasing carrier frequency over the mmWave/THz bands, leads to a large Rayleigh distance. As a result, the traditional planar-wave assumption may not hold valid for mmWave/THz systems featuring ELAAs. In this paper, we consider the problem of hybrid near/far-field channel estimation by taking spherical wave propagation into account. By analyzing the coherence properties of any two near-field steering vectors, we prove that the hybrid near/far-field channel admits a block-sparse representation on a specially designed unitary matrix. Specifically, the percentage of nonzero elements of such a block-sparse representation is in the order of 1/√N, which tends to zero as the number of antennas,N, grows. Such a block-sparse representation allows to convert channel estimation into a block-sparse signal recovery problem. Simulation results are provided to verify our theoretical results and illustrate the performance of the proposed channel estimation approach in comparison with existing state-of-the-art methods.

As communications evolve into the terahertz (THz) band, the near-field region expands accordingly, providing additional distance-domain information that can be exploited for high-accuracy sensing. While the ultra-short THz wavelength offers high resolution, it in turn narrows the unambiguous estimation range and demands large-scale arrays for path loss compensation. Sparse arrays (SAs) are considered to reduce the cost of massive elements, but inevitably cause performance degradation. Moreover, near-field channels exhibit complex coupling among time, frequency, and angular parameters, complicating sensing information extraction. To address these challenges, we propose a coarse-to-fine velocity estimation algorithm, enabled by a tensor-based near-field channel decomposition, while balancing complexity through SAs. Simulation results show that the proposed scheme achieves near-CRB performance with an extended unambiguous speed range. Furthermore, analysis reveals that SAs significantly reduce the computational complexity, and the resulting performance loss can be effectively mitigated by moderately increasing the bandwidth or signal duration, enabling high-accuracy, low-complexity velocity estimation.

Terahertz (THz) integrated sensing and communication (ISAC) is a promising enabler for 6G networks, offering ultra-high data rates and environment-aware capabilities. However, realizing its full potential requires accurate construction of directional THz radio maps and environment map from sparse and noisy signal measurements, which is a highly ill-posed problem. While recent generative models, particularly conditional diffusion models, show promise in radio map construction, they fail to capture the physical characteristics of THz signal propagation, limiting generalization. To address this, we propose a THz propagation-informed diffusion model that jointly generates multi-directional radio maps and infers the environment map via an image-intersection strategy. Crucially, our model embeds two novel physics-guided loss functions: the intra-beam propagation-informed loss and inter-beam environmental consistency loss, which enforce geometric and semantic fidelity on THz propagation behaviors into the training process. Simulation results demonstrate superior performance over existing methods across varying sensor densities and environment complexities.

This paper considers channel estimation for extremely large-scale intelligent reflecting surface (XL-IRS)-assisted terahertz (THz) communication systems. Specifically, an XL-IRS is deployed close to users (UEs) to enhance communication performance between the base station (BS) and UE. With its large aperture, the XL-IRS has a Rayleigh distance of tens of meters. Therefore, the users are likely located in the near-field region of the XL-IRS, while the BS is in its far-field region. Consequently, a spherical wavefront propagation model should be considered to characterize the propagation property between the XL-IRS and the UE, while the planar wavefront propagation model is utilized in the BS-IRS link. By leveraging Khatri-Rao product and Kronecker product properties, we rephrase the channel estimation problem. In addition, we construct an orthogonal dictionary, which essentially modifies the well-known Discrete Fourier Transform (DFT) matrix. We further find that the considered channel can be block-sparsely represented by this dictionary. Hence, the channel estimation can be converted into a block sparse recovery problem, which can be efficiently solved by several off-the-shelf methods. The simulation results show that our proposed method achieves better estimation performance than the conventional polar-domain-based method.

This paper considers a single input multiple output (SIMO) integrated sensing and communication (ISAC) system, where orthogonal frequency division multiplexing (OFDM) communication signals are multiplexed to detect target locations, including the range and angle parameters. The two-dimensional multiple signal classification (2D-MUSIC) algorithm is applied to process such signals with a format of multiple subcarriers related to large arrays. However, the standard 2D-MUSIC suffers from high computational complexity and its estimation accuracy is limited by the two-dimensional grid-based exhaustive search step size. To overcome these issues, we propose a two-step improved 2D-MUSIC (I2D-MUSIC) algorithm, which replaces the original grid-based exhaustive search and performs dung beetle optimization (DBO) algorithm to get a coarse estimation of the parameters. Subsequently, a stochastic gradient descent (SGD) based method is derived to obtain fine estimation of the range and angle parameters. Simulation results and hardware-based experiments demonstrate that the proposed algorithm significantly reduces computational complexity while maintaining comparable estimation accuracy to the standard 2D-MUSIC algorithm, and its accuracy is not constrained by the search step size.

Non-terrestrial networks (NTN) have emerged as a transformative solution to bridge the digital divide and deliver essential services to remote and underserved areas. In this context, low Earth orbit (LEO) satellite constellations offer remarkable potential for efficient cache content broadcast in remote regions, thereby extending the reach of digital services. In this paper, we introduce a novel approach to optimize wireless edge content placement using NTN. Despite wide coverage, the varying NTN transmission capabilities must be carefully aligned with each content placement to maximize broadcast efficiency. In this paper, we introduce a novel approach to optimize wireless edge content placement using NTN, positioning NTN as a complement to TN for achieving optimal content broadcasting. Specifically, we dynamically select content for placement via NTN links. This selection is based on popularity and suitability for delivery through NTN, while considering the orbital motion of LEO satellites. Our system-level case studies, based on a practical LEO constellation, demonstrate the significant improvement in placement speed compared to existing methods, which neglect network mobility. We also demonstrate that NTN links significantly outperform standalone wireless TN solutions, particularly in the early stages of content delivery. This advantage is amplified when there is a higher correlation of content popularity across geographical regions.

Obstacle sensing is essential for terahertz (THz) communication since the subsequent beam management can avoid THz signals blocked by the obstacles. In parallel, radio environment, which can be manifested by channel knowledge such as the distribution of received signal strength (RSS), reveals signal propagation situation and the corresponding obstacle information. However, the awareness of the radio environment for obstacle sensing is challenging in practice, as the sparsely deployed THz sensors can acquire only little a priori knowledge with their RSS measurements. Therefore, we formulate in this paper a radio environment awareness problem, which for the first time considers a probability distribution of obstacle attributes. To solve such a problem, we propose a THz-based generative radio environment awareness framework, in which obstacle information is obtained directly from the aware radio environment. We also propose a novel generative model based on conditional generative adversarial network (CGAN), where U-net and the objective function of the problem are introduced to enable accurate awareness of RSS distribution. Simulation results show that the proposed framework can improve the awareness of the radio environment, and thus achieve superior sensing performance in terms of average precision regarding obstacles’ shape and location.

This paper investigates the joint estimation of multi-targets’ position and velocity for a terahertz multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system operating in the near field based on tensor decomposition. The waveforms transmitted from shared antennas carry communication messages and are orthogonal to each other in the frequency domain. The estimation of the position and velocity of multiple targets in the considered near-field scenario is challenging because it involves spherical wavefronts. A signal model based on spherical wavefronts enables higher resolution on spatial position, which, if properly designed, can be used to improve the estimation accuracy. In this paper, we propose a CANDE-COMP/PARAFAC (CP) decomposition-based near-field localization (CP-NFL) algorithm for the joint estimation of the position and velocity of multiple targets. In our proposed method, the received signal is expressed as a third-order tensor; based on its factor matrices we convert the original non-convex optimization problem into a convex one and solve it with CVX tools. Our analysis reveals that the uniqueness in CP decomposition can be guaranteed and the computational complexity of our proposed method is linear to the sum of the third powers of the number of sub-carriers, OFDM symbols, antennas, and targets. Numerical results show that our proposed method has a clear advantage over the existing method in terms of estimation accuracy and computational complexity.

Abstract Near-field technology is increasingly recognized due to its transformative potential in communication systems, establishing it as a critical enabler for sixth-generation (6G) telecommunication development. This paper presents a comprehensive survey of recent advancements in near-field technology research. First, we explore the near-field propagation fundamentals by detailing definitions, transmission characteristics, and performance analysis. Next, we investigate various near-field channel models—deterministic, stochastic, and electromagnetic information theory based models, and review the latest progress in near-field channel testing, highlighting practical performance and limitations. With evolving channel models, traditional mechanisms such as channel estimation, beamtraining, and codebook design require redesign and optimization to align with near-field propagation characteristics. We then introduce innovative beam designs enabled by near-field technologies, focusing on non-diffractive beams (such as Bessel and Airy) and orbital angular momentum (OAM) beams, addressing both hardware architectures and signal processing frameworks, showcasing their revolutionary potential in near-field communication systems. Additionally, we highlight progress in both engineering and standardization, covering the primary 6G spectrum allocation, enabling technologies for near-field propagation, and network deployment strategies. Finally, we conclude by identifying promising future research directions for near-field technology development that could significantly impact system design. This comprehensive review provides a detailed understanding of the current state and potential of near-field technologies.

The ultra-wide Terahertz (THz) band with jointly high-speed transmission and precise sensing has come into vision to realize integrated sensing and communication (ISAC) for emerging immersive applications. However, THz networks face a coverage bottleneck. Narrow beams are exploited to compensate for the limited signal power and path loss. But they bring in beam misalignment that degrades link connectivity and affects the THz network coverage, characterized by coverage probability. ISAC-THz networks can benefit from the sensing-aided beam alignment to improve the coverage probability. But there exists a trade-off between sensing assistance and its cost, that requires efficient resource allocation. This paper provides time-frequency resource allocation for sensing signal mapping schemes that maximize the coverage probability of the ISAC-THz networks with reduced sensing costs. Results show the effectiveness of the scheme in reducing the sensing cost with near-ideal coverage. We reveal design insights into the sensing signal insertion and preferable THz transmission band selection that achieves the desired coverage with the least sensing overhead. Wider coverage requires more sensing resources, which are more allocated to bandwidth for accurate long-range sensing. The high angular resolution of narrow beams helps reduce the sensing cost, sparing resources in the time domain for velocity estimation.

Integrated sensing and communication (ISAC) in terahertz (THz) networks for delay-sensitive services is regarded as a key enabler for future 6G networks, with ISAC helping to aid beam alignment and improve communication reliability in THz networks. Nevertheless, in ISAC systems, there exists resource and performance tradeoffs amongst sensing, communication and computation. For instance, while better sensing accuracy adds information to aid communication beam alignment, it reduces the temporal resources available for communication. Therefore, in this paper we present a joint sensing, communication and computation model, with a non-uniform frame structure allowing the sensing and communication time to be flexibly adjusted. Based on our model, we formulate an average communication outage probability minimization problem, which optimizes the time and carrier frequency allocation schemes, given constrained resources. We then derive in closed-form the available communication outage probability subject to a given delay threshold, decoupling the computation sub-problem from the original problem. Based on this result, we reformulate the original problem into a joint resource allocation problem between sensing and communication, and solve it by applying the Hungarian algorithm. Numerical results show that our strategy outperforms existing baselines in the average communication outage probability performance.

Array-of-subarrays (AoSA) is an appealing architecture in terahertz (THz) communications since the analog beamformers on sub arrays can provide beam gain to combat severe propagation loss, by low-cost phase shifters. However, the traditional beamforming scheme for AoSA, i.e., each subarray serves an exclusive user, cannot cope with the effect of beam split in THz wideband communications. In this paper, we propose a novel concept, i.e., beam split aggregation and multiplexing (BSAM), to support wideband THz communication with AoSA architecture. Specifically, we first characterize the direction of beam split and then derive the maximum bandwidth of a subband that will not cause beam split. Finally, based on the above results, we propose a criterion to plan the subbands and design the analog beamformers for BSAM.

As promising candidate frequency bands, millimeter wave (mmWave) and terahertz (THz) communications can provide ultrahigh transmission rate to enable vehicle-to-everything (V2X) networks for connected autonomous vehicles (CAVs). However, beam alignment is extremely challenging in mmWave/THz communications due to its narrow beam width and fast mobility of CAV. In this article, we propose a new joint communication and control algorithm for beam alignment, where the mutual positive effect of communications and motion control of CAV on each other is discussed. Specifically, we first provide a framework to show the interaction between motion control of CAV and beam alignment of transmission from base station (BS) to CAV. Then, we analyze the effect of CAV control on beam alignment in communications, where a theorem is obtained to show the closed-form expression of their relationship. Finally, we discuss the CAV control design affected by beam alignment. Simulation results show remarkable performance of the proposed method.

Multiple-input multiple-output (MIMO) and intelligent reflecting surface (IRS) are two appealing technologies in millimeter-wave (mmWave) and terahertz (THz) communications. The challenge of combining these two technologies lies in joint design for active beamforming (at the base-station (BS)/users) and passive beamforming (at the IRSs). In this paper, we consider a multi-IRS-aided multi-user MIMO scenario and propose a novel space-orthogonal scheme by applying zero-forcing techniques. Specifically, we first propose a multi-IRS-based zero-interference criterion, under which multi-user interference can be eliminated regardless of the IRS’s phase shifts. Based on this criterion, we decompose the precoder/decoder matrix into a product of two matrices, with one of them devised for interference cancellation and the other one of them devised for achievable rate maximization. Next, an approximate space-orthogonal technique referred to as partial zero-forcing (IRS-PZF) is proposed for proposed for devising the former matrix whose objective is to cancel the multi-user interference; while two efficient phase-shift schemes are proposed for the IRS passive beamforming, namely, water-filling segment matching (WSM) and phase iterative evolution (PIE), which balance between performance and complexity. Finally, we calculate the latter matrix of the precoder/decoder by applying the singular value decomposition (SVD) for the effective BS-user channels, so as to maximize the users’ achievable rates. Numerical results demonstrate the effectiveness and superiority of our proposed scheme compared with the benchmarks.

Terahertz (THz) communication is capable of providing ultra-wide bandwidth and high data rates. Therefore attracts widespread attention to its applications in next-generation networks. Highly directional antennas are used to compensate for the THz propagation loss, which also incurs beam management challenges. Specifically, caused by node mobility and blockage, frequent beam reselections and beam misalignment greatly degrade THz network performance in terms of reliability and spatial throughput. In this paper, using stochastic geometry, we fill the current research gap in system-level theoretical models for the analysis of beam misalignment and network spatial throughput by considering the effects of beamwidth, mobility, blockage, and molecular absorption. Our analyses show that an increase in nodes density or user mobility often results in severe beam misalignment, which in turn requires more signaling overhead and degrades THz network reliability and throughput. Although using wider beams reduces this impact, it increases THz network sensitivity to molecular absorption. To maximize spatial throughput, optimal beamwidth needs to be adjusted according to communication demand priority and network status. Our work provides useful insights into beamwidth adaptation according to parameters trade-off that helps THz network achieve higher reliability and throughput in different applications.

In mobile edge computing (MEC) systems, users offload computationally intensive tasks to edge servers at base stations. However, with unequal demand across the network, there might be excess demand at some locations and underutilized resources at other locations. To address such load-unbalanced problem in MEC systems, in this paper we propose virtual machines (VMs) sharing across base stations. Specifically, we consider the joint VM placement and pricing problem across base stations to match demand and supply and maximize revenue at the network level. To make this problem tractable, we decompose it into master and slave problems. For the placement master problem, we propose a Markov approximation algorithm MAP on the design of a continuous time Markov chain. As for the pricing slave problem, we propose OPA - an optimal VM pricing auction, where all users are truthful. Furthermore, given users' potential untruthful behaviors, we propose an incentive compatible auction iCAT along with a partitioning mechanism PUFF, for which we prove incentive compatibility and revenue guarantees. Finally, we combine MAP and OPA or PUFF to solve the original problem, and analyze the optimality gap. Simulation results show that collaborative base stations increases revenue by up to 50%.

This paper considers a scenario in which an access point (AP) is equipped with a server of finite computing power, and serves multiple resource-hungry users by charging users a price. This price helps to regulate users' behavior in offloading jobs to the AP. However, existing works on pricing are based on abstract concave utility functions, giving no dependence on physical layer parameters. To that end, we first introduce a novel utility function, which measures the cost reduction by offloading as compared with executing jobs locally. Based on this utility function we then formulate two offloading games, with one maximizing individuals interest and the other maximizing the overall systems interest. We analyze the structural property of the games and admit in closed-form the Nash Equilibrium and the Social Equilibrium for the homogeneous user case, respectively. The proposed expressions are functions of user parameters such as the weights of time and energy, the distance from the AP, thus constituting an advancement over prior economic works that have considered only abstract functions. Finally, we propose an optimal price-based scheme, with which we prove that the interactive decision-making process with self-interested users converges to a Nash Equilibrium point equal to the Social Equilibrium point.

Multi-access Edge Computing (MEC) is an emerging paradigm which allows users to offload their computationally intensive tasks to the network edge. In this paper, we analyze resource allocation in MEC from the market and economic perspective. Due to extremely heterogeneous usage demands across users in the future IoE market, current coarse-grained pricing schemes result in partial wastage: some users would have excess un-utilized resource quota while others might have reserved insufficient resources. Therefore, we introduce a novel sharing economy-inspired business model, where a platform facilitates the sharing of resource quota among users, increasing resource efficiency. The goal is to maximize the overall welfare of users who join the sharing platform. As the platform lacks control and has imperfect knowledge of users' payoff functions and distributions, a distributed pricing mechanism is proposed. In our mechanism, the platform and users jointly arrive at an equilibrium. We prove that the equilibrium point of the mechanism is the socially optimal point. Simulations illustrate convergence, the robustness of our mechanism to changes in demand and supply, and that sharing increases the welfare of users.

In the era of Internet of Things (IoT), watching videos on mobile devices has been a popular application in our daily life. How to recommend videos to users is one of the most concerned problem for Internet video service providers (IVSPs). In order to provide better recommendation service to users, they deploy cloud servers in a geo-distributed manner. Each server is responsible for analyzing a local area of user data. Therefore, these cloud servers form information islands and the characteristics of data present nonindependent and identically distribution (non-i.i.d). In this scenario, it is difficult to provide accurate video recommendation service to the minority of users in each area. To tackle this issue, we propose JointRec, a deep learning-based joint cloud video recommendation framework. JointRec integrates the JointCloud architecture into mobile IoT and achieves federated training among distributed cloud servers. Specifically, we first design a dual-convolutional probabilistic matrix factorization (Dual-CPMF) model to conduct video recommendation. Based on this model, each cloud can recommend videos by exploiting the user's profiles and description of videos that users rate, thereby providing more accurate video recommendation services. Then, we present a federated recommendation algorithm which enables each cloud to share their weights and train a model cooperatively. Furthermore, considering the heavy communication costs in the process of federated training, we combine low-rank matrix factorization and 8-bit quantization method to reduce uplink communication costs and network bandwidth. We validate the proposed approach on the real-world data set, and the experimental results indicate the effectiveness of our proposed approach.

This paper considers a scenario in which an access point (AP) is equipped with a mobile edge server (MEC) of finite computing power, and serves multiple resource-hungry mobile users by charging users a price. This price helps to regulate users' behavior in offloading computation jobs to the AP. To that end, first we introduce an economics model for MEC bearing physical layer offloading intuition. We then propose a learning based pricing mechanism, in which with no direct control and no knowledge of users' private information, the AP learns the optimal price. Under our mechanism, the AP induces self-interested users to make socially optimal offloading decisions, thus maximizing the system-wide welfare.

This paper investigates the optimal secure beam steering design of millimeter wave (mmWave) communications, where an Alice-Bob pair wishes to communicate in secret in the presence of Eve, with each node equipped with large-scale antenna arrays. Owing to the reduced peak-to-average power ratio and hardware cost, beam steering design emerges as an attractive technique in mmWave communications recently. However, from the physical layer perspective, the beam steering design subject to security requirement has not been investigated yet. In this paper, we consider a secrecy rate maximization problem with respect to beam steering design, i.e., analog beam selection of radio frequency (RF) chains and power allocation over the selected RF chains, which turns out to be an intractable mixed integer nonlinear optimization problem. To tackle it, we first determine a set of optimal analog beam candidates, based on which the considered multi-input multi-output (MIMO) wiretap channel is decoupled into a sequence of parallel single-input single-output (SISO) wiretap channels. Then, it is shown that the optimal power allocation over the parallel wiretap channels can be derived in a semi-closed-form. Numerical results illustrate that the proposed design offer better secrecy performance than traditional beam steering design in the presence of wiretapping as long as the channel has more than two propagation paths.

This paper investigates and quantifies the advantages of a Full-Duplex (FD) transmitter/receiver pair in improving the secrecy rate of the system. We consider a linear precoder design for a multiple-input multiple-output Gaussian wiretap channel, which comprises two legitimate nodes, i.e., Alice and Bob, operating in FD mode and exchanging confidential messages in the presence of a passive eavesdropper. Using the sum secrecy degrees of freedoms (sum SDoFs) as metric, we formulate an optimization problem with respect to Alice's and Bob's precoding matrices. In order to solve this problem, we first propose a cooperative secrecy transmission scheme, whose feasible set is sufficient to achieve the maximum sum SDoF. Based on that feasible set, we then determine in closed form the maximum achievable sum SDoF and also provide a method for constructing the precoding matrix pair, which achieves the maximum sum SDoF. The latter pair would be near-optimal in terms of the achievable secrecy sum rate in the high signal-to-noise ratio (SNR) regime. By providing the maximum achievable sum SDoF as a function of the number of antennas, one could select the optimal system parameters to further maximize the achievable sum SDoF. We use simulations to evaluate the performance of the proposed precoding matrices in realistic channel scenarios and at various levels of the SNR.

This paper considers a scenario in which an Alice-Bob pair wishes to communicate in secret in the presence of an active Eve, who is capable of jamming as well as eavesdropping and operates in full-duplex (FD) mode. As countermeasure, Bob operates in FD mode, using a subset of its antennas to receive, and the remaining antennas to transmit jamming noise. Alice and Bob employ linear precoding, and all nodes use Gaussian code books. In that context, our goal is to maximize the achievable secrecy degrees of freedom (S.D.o.F.) of the system. We provide the optimal receive/transmit antennas allocation at Bob, based on which we determine in closed form the maximum achievable S.D.o.F. We also provide a method for constructing the precoding matrices of Alice and Bob, based on which the maximum S.D.o.F. can be achieved. We further investigate the adverse scenario in which Eve knows Bob's transmission strategy and optimizes its transmit/receive antennas allocation in order to minimize the achievable S.D.o.F. For that case, we find the worst case achievable S.D.o.F. Numerical results validate the theoretical findings and demonstrate the performance of the proposed method.

We consider the problem of scheduling multi-task jobs on identical machines in parallel.Each multi-task job consists of one or more tasks.Each job has a release date and a due date.A task of a job can be processed by any one of the machines.Multiple machines can process the tasks of a job concurrently.The completion time of a job is the time at which all its individual tasks have been completed.A job is late if it is completed after its due date.We study the problem of minimizing the total number of late jobs.We show that while some special cases are solvable, the general problem is NP-hard and there exists no polynomial time ρ-approximation algorithm, for any ρ > 1.We present a general algorithm for the problem and derive from it six heuristics whose performance is evaluated by experimental results.

This paper considers secrecy communication from a signal processing point of view, and studies the maximal achievable secrecy degrees of freedoms (S.D.o.F.) of a helper-assisted Gaussian wiretap channel, consisting of a source, a legitimate receiver, an eavesdropper and an external helper. Each terminal is equipped with multiple antennas. We first propose a cooperative secrecy transmission scheme, and show that it achieves the maximal secrecy degrees of freedom. We then propose a heuristic method, through which, we solve analytically the optimization problem associated with the proposed cooperative secrecy transmission scheme. By this way, we obtain the maximal achievable S.D.o.F. and also the precoding matrices which achieve the maximal S.D.o.F. in closed-form.

This paper considers an artificial noise (AN)-aided transmit design for multi-user MISO systems in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for all receivers and one confidential message intended for only one authorized receiver. The confidential message is kept perfectly secure from all the unauthorized receivers. Assuming imperfect channel state information (CSI) of unauthorized receivers at the transmitter, our goal is to jointly design the input covariances of the multicast message, confidential message and AN such that the outage secrecy rate is maximized for a given outage probability, while keeping the outage probability of multicast message for each user below a certain threshold. Due to the intrinsical complexity of this problem, a safe and convex albeit suboptimal reformulation, based on two advanced convex restriction approaches, is applied to generate a tractable approximation for this problem. By this means, a computationally efficient lower bound on the outage secrecy rate can be determined. We also prove the feasibility of beamforming to achieve the obtained secrecy rate. Numerical results are presented to verify the efficacy of our proposed method.

This paper considers an energy-efficient transmit design in a three-node MISO wiretap channel in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for both receivers and one confidential message intended for only one authorized receiver. The confidential message must be kept perfectly secure from the unauthorized receiver. Our goal is to jointly design the input covariance matrices of the multicast message and confidential message such that the secrecy energy efficiency (SEE) is maximized, subject to the multicast rate, secrecy rate and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the feasibility of transmit beamforming to achieve the maximum SEE. Numerical results are finally presented to verify the efficacy of our proposed method.

This letter considers secrecy communication from an information-theoretic perspective, and studies the secrecy capacity of a multi-input multi-output (MIMO) Gaussian wiretap channel with a source (Alice), an eavesdropper (Eve) and a Full-Duplex (FD) legitimate receiver (Bob). Bob can allocate part of his antennas to transmit jamming signals to impair Eve’s channel. Our goal is to identify the secrecy capacity behavior in the high signal-to-noise ratio (SNR) regimes, i.e., the maximal achievable secure degrees of freedom (S.D.o.F). Such S.D.o.F maximization is generally difficult to solve since it requires to face a nonlinear fractional problem. To deal with this issue, we first propose a cooperative secrecy transmission scheme, and prove its optimality in the sense of achieving the maximal S.D.o.F.. By studying this proposed transmission scheme, we obtain the maximal achievable S.D.o.F. in closed form for any given antenna allocation at Bob. Based on this closed-form result, we further analytically derive the optimal antenna allocation at Bob. To the best of our knowledge, this is the first time that the benefit brought by using the FD jamming Bob has been quantified.

We investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with Na, Njand Neantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if Nea+Nj-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where Nea+Nj-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.

In this paper, we consider a massive MIMO wiretap system where the transmitter, the receiver and the eavesdropper are equipped with a large number of antennas. Being different from the previous works using asymptotic random matrix theory, our analysis relies on the concentration measure of non-asymptotic random matrix theory which allows us to obtain tight bounds for secrecy capacity of massive MIMO system with finite antenna number. The analytical and simulation results reveal the following, in the massive MIMO system employing equal power allocation at each transmit antenna: 1) the secrecy capacity falls within a bounds with a probability growing exponentially with the number of transmit antenna, while the ergodic secrecy capacity falls within a deterministic bounds; 2) the gap between the upper and the lower bound on secrecy rate is proportional to the square root of the SNR at legitimate receiver and the SNR at eavesdropper, respectively; 3) when the entry of legitimate channel matrix and eavesdropping channel matrix satisfies Gaussian distribution, the gap between the upper and the lower bound on secrecy rate is a linear reciprocal function of the number of transmit antennas.

We study the transmit design at relay nodes for secure amplify-and-forward (AF) networks. Two joint cooperative relaying and jamming schemes, namely Secrecy Rate Maximization Scheme and Null-Space Jamming Scheme, are proposed. In the first scheme, optimal relaying weight vector and optimal covariance matrix associated with the artificial noise (AN) are obtained, which involves doing a one-dimensional search and solving a sequence of semidefinite programs(SDPs). In the second scheme, which is suboptimal but computationally much cheaper, AN is designed to decrease the rate at the eavesdropper while the relaying weight vector is determined to increase the rate at the destination. In addition, Power Allocation based on secrecy rate maximization provides a balance between these two goals. Numerical results show that the proposed Secrecy Rate Maximization Scheme outperforms the existing cooperative relaying without jamming scheme. Especially, when the power is large enough, the secrecy rate achieved by the proposed schemes approaches the maximal achievable rate for the no-eavesdropper case.

In this paper, we consider the transmit design for multi-input multi-output (MIMO) wiretap channel including a malicious jammer. We first transform the system model into the traditional three-node wiretap channel by whitening the interference at the legitimate user. Additionally, the eavesdropper channel state information (ECSI) may be fully or statistically known, even unknown to the transmitter. Hence, some strategies are proposed in terms of different levels of ECSI available to the transmitter in our paper. For the case of unknown ECSI, a target rate for the legitimate user is first specified. And then an inverse water-filling algorithm is put forward to find the optimal power allocation for each information symbol, with a stepwise search being used to adjust the spatial dimension allocated to artificial noise (AN) such that the target rate is achievable. As for the case of statistical ECSI, several simulated channels are randomly generated according to the distribution of ECSI. We show that the ergodic secrecy capacity can be approximated as the average secrecy capacity of these simulated channels. Through maximizing this average secrecy capacity, we can obtain a feasible power and spatial dimension allocation scheme by using one dimension search. Finally, numerical results reveal the effectiveness and computational efficiency of our algorithms.

We consider a physical layer security problem where there is a source, an external helper, a legitimate receiver, and an eavesdropper, each equipped with one antenna. We assume that an additional out-of-band link from the source to the helper is available to improve the transmission security rate. A two-stage cooperative scheme is proposed. The proposed scheme consists of an information sharing stage and a cooperative transmission stage. Specifically, in the information sharing stage the source informs the helper of the signal to be transmitted, while in the cooperative transmission stage the source and the helper cooperate to transmit the signal to the legitimate receiver. Under this framework, we determine the optimal weights associated with this scheme and examine the secrecy capacity of the helper-assisted wiretap channel. The optimal weight design problem is generally nonconvex. To deal with this issue, an algorithm involving a one-dimensional search is developed. On the other hand, an analytical lower bound on the secrecy capacity is derived. Based on this lower bound, we further analyze the sufficient and necessary condition to ensure a positive secrecy capacity and derive the maximal achievable secure degrees of freedom, which are shown to be exactly the same as those of the multi-input single-output (MISO) wiretap channel.

This paper exploits co-channel interference (CCI) to secure the multi-antenna wiretap IFC consisting of two source-destination-eavesdropper triples, where each source-destination link is wiretapped by an external eavesdropper. To this end, we first propose a cooperative secrecy beamforming scheme, which is proved to be sufficient and necessary to achieve the secure degrees of freedom (S.D.o.F.) pair (1,1). By investigating the feasibility of the proposed beamforming scheme, we obtain the sufficient and necessary condition and also the beamforming vectors in closed-form to achieve the S.D.o.F pair (1,1). To the best of our knowledge, this is the first time that the benefit brought by CCI has been quantified.

This paper studies robust transmit design to maximize the worst-case secrecy rate in AF networks under both total and individual relay power constraints. Channel state information (CSI) in the network is assumed to be perfectly known except for that associated with the eavesdroppers whose imperfection is modeled as deterministic bounded errors. To use the power at the relay nodes more efficiently, a joint cooperative relaying and jamming scheme is considered. Through some matrix manipulations, we recast the original nonconvex optimization problem as a sequence of semidefinite programs (SDPs), which enables us to obtain the optimal relay weights and the optimal covariance matrix of the jamming signal. Numerical results are presented to show the efficacy of the proposed scheme.

We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped with$M$and$N$antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rate${R_N}$. The relationship between the average secrecy capacity${\bar C_N}$of Gaussian wiretap channel and the average secrecy rate${\bar R_N}$achieved by the null-space jamming scheme is investigated, and we prove that${\bar R_N} \leq {\bar C_N} \leq {\bar R_{N + 1}}$. Based on this inequality and the derived lower and upper bounds on${R_N}$, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that when$N > M$, the average secrecy capacity increases linearly with the total transmit power; while when$N \leq M - 1$, there exists a performance ceiling on it.

We consider the problem of interference alignment (IA) for the K-user constant multiple-input multiple-output interference channel (K-user MIMO IFC) over correlated channels with imperfect channel state information (CSI). Recent performance evaluations show that most of the existing IA algorithms suffer serious sum rate degradations when the available CSI is imperfect. To deal with this issue, an uplink-downlink (UL-DL) Average-Mean-Square-Error(AMSE) duality is firstly established for the K-user MIMO IFC. Based on this duality, a robust IA algorithm is developed. Numerical results show that the proposed algorithm not only achieves better sum rate performance than other existing algorithms, but can also accommodate to the case when the perfect CSI is not available.

In this paper, a joint source and relay optimization problem is studied for a multiuser multiple-input multiple-output (MIMO) relay system. Assuming that the channel state information (CSI) at the source and relay is available, two amplify and forward (AF) relaying schemes are proposed under the criterion of maximizing the sum-rate. First, a scheme which iteratively searches the optimal source and relay matrices by deriving the partial derivatives of the sum-rate and applying the gradient search algorithm is proposed. Next, in order to reduce the computational complexity, an alternating method utilizing the equivalent channel method is developed. This method also resorts to a so called maximum-signal-leakage-and-noise-ratio (SLNR) that can suppress the co-channel interference (CCI) and noise at the users effectively. Theoretical analysis and Monte Carlo simulation illustrate the performance of the both schemes.