Recently, the multiple-input–multiple-output (MIMO) nonorthogonal multiple-access (NOMA) transmission, denoted as MIMO- NOMA, has been widely applied for Internet of Things (IoT) systems due to its spectral efficiency. As a promising precoding method, the generalized singular value decomposition (GSVD)-based precoding scheme has been studied in MIMO- NOMA. In this study, we apply the GSVD-based precoding scheme to a downlink MIMO- NOMA communication system with an amplify-and-forward (AF) relay and two IoT users. A closed-form expression of the probability density function (PDF) of two channel matrices’ generalized singular values (GSVs) is obtained in order to facilitate the performance analysis for cooperative MIMO- NOMA transmission. In particular, by this distribution characteristic result, the users’ rates and outage probabilities achieved by MIMO- NOMA are studied for the insightful performance evaluation. In addition, the asymptotic approximations for outage probabilities at the high signal-to-noise-ratio (SNR) condition are presented. In addition to characterize the performance achieved by cooperative MIMO- NOMA, resource allocation for the addressed NOMA system is also investigated in this article, where a suboptimal power allocation algorithm to maximize the sum rate is given. The solution obtained by the proposed algorithm is studied, where the optimality condition of the solution is obtained. Finally, simulation results are presented to show the superiority of the scheme and verify these analytical results.

This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC) is considered. This problem is hard to solve due to its nonconvexity and the existence of multiple quadratic constraints. Conventional methods to tackle this problem, such as the iterative weighted minimum mean squared error (WMMSE) algorithm, typically consist of two nested loops and thus suffer from high computational complexity. By leveraging the inherent separability of the PAPC constraint set, we propose a low-complexity single-loop algorithm for solving the WSR maximization problem under PAPC, in which each updating step is done efficiently with closed form. Theoretically, we prove the convergence of the proposed algorithm to stationary solutions. Then we extend the proposed algorithm to the multi-carrier scenario where the power constraints are shared over the subcarriers. Complexity analysis and numerical results show that the proposed single-loop algorithm maintains the same WSR performance as existing methods but dramatically reduces the computational complexity.

In recent years, the multiple-input multiple-output (MIMO) non-orthogonal multiple-access (NOMA) systems have attracted a significant interest in the relevant research communities. As a potential precoding scheme, the generalized singular value decomposition (GSVD) can be adopted in MIMO-NOMA systems and has been proved to have a good trade-off for complexity and performance. In this paper, the performance of the GSVD-based MIMO-NOMA communications with Rician fading is studied. In particular, the distribution characteristics of generalized singular values (GSVs) of channel matrices are analyzed. Two novel mathematical tools, the linearization trick and the deterministic equivalent method, which are based on operator-valued free probability theory, are exploited to derive the Cauchy transform of GSVs. An iterative process is proposed to obtain the numerical values of the Cauchy transform of GSVs, which can be exploited to derive the average data rates of the communication system. In addition, the special case when the channel is modeled as Rayleigh fading, i.e., the line-of-sight propagation is trivial, is analyzed. In this case, the closed-form expressions of average rates are derived from the proposed iterative process. Simulation results are provided to validate the derived analytical results.

The application of network non-orthogonal multiple access (N-NOMA) technique to coordinated multi-point (CoMP) systems has attracted significant attention due to its superior capability to improve connectivity and maintain reliable transmission for CoMP users simultaneously. Based on the concept of quasi-degraded channel for N-NOMA, this paper studies the precoding design for downlink N-NOMA scenarios with two base stations (BSs) equipped with multiple antennas. In specific, under quasi-degraded channels, simple linear precoding based N-NOMA can achieve the same minimal total transmission power as theoretically optimal but complicated dirty paper coding (DPC) scheme, when the users’ target rates and minimal transmission power of each BS are given. In this paper, the channel quasi-degradation (QD) condition is first rigorously derived for the scenario with single CoMP user and two NOMA users. The closed-form optimal precoders for N-NOMA under quasi-degraded channels are also provided. Then, based on QD condition, a novel hybrid N-NOMA (H-N-NOMA) scheme is proposed, which is a mixture of N-NOMA and conventional zero-forcing beamforming (ZFBF) scheme. Further, for the scenarios with more users, a low-complexity QD based user pairing (QDUP) algorithm is proposed, which is then combined with H-N-NOMA to make a novel scheme termed H-N-NOMA/QDUP into being. Numerical results are presented to reveal the impact factors on QD channels, and also demonstrate the superior performance of the proposed H-N-NOMA/QDUP scheme. It is shown that the proposed H-N-NOMA/QDUP scheme can effectively exploit the benefit of multi user diversity.

In this study, a simple two‐user multiple‐input multiple‐output (MIMO) relaying scenario is considered. To efficiently exploit the spectrum resources, a generalised singular value decomposition (GSVD) based precoding scheme with non‐orthogonal multiple access (NOMA) is proposed, which converts the multiple channels into several parallel single channels. The performance of the proposed GSVD‐MIMO relaying scheme is evaluated by using the distribution characteristics of squared generalised singular values of two users' channel matrices and the eigenvalues of the relay's channel matrix to obtain the expressions of the average data rate and outage probabilities. Both the asymptotic case and a practical scenario with nodes equipped with finite numbers of antennas are analysed because the distribution characteristics of squared generalised singular values in the two cases are different. Two special cases, single‐input multiple‐output and multiple‐input single‐output are considered. Simulation experiments are carried out to verify the effectiveness and accuracy of the obtained analytical results.

This paper studies the application of the unmanned aerial vehicles (UAVs) to a malfunction area. Note that the ground base stations (GBSs) inside the malfunction area are broken, whereas the GBSs outside work well and are distributed according to a homogeneous Poisson point process (HPPP). A user-centric cooperative scheme is proposed to serve the user equipments(UEs) in the malfunction area. Specifically, based on the UEs' connections to the UAV and nearest GBS, the users in the malfunction area can be served by the UAV only, both the UAV and the nearest GBS or the nearest GBS only. The proposed scheme can be tuned by a parameter δ. Analytical framework is developed to obtain the expression for the coverage probability achieved by a UE in the malfunction area, which is verified by computer simulations.

In this study, the authors consider the secrecy communication of one source–destination pair in a wireless multi‐hop relay network, where each node is equipped with multiple antennas. They use the method of interference alignment for secrecy transmission in the presence of an eavesdropper. Firstly, they propose a decode‐and‐forward (DF) relaying protocol and give a new result on the joint probability density function of the first, second, …, k th ( ) largest eigenvalues of the complex Wishart matrices , where is an matrix whose elements are independent identically distributed complex Gaussian variables with zero mean and unit variance. They then utilise this result to characterise the legitimate outage probability and the diversity order of the proposed DF protocol. The case where the relay works in the amplify‐and‐forward (AF) mode is considered at last, and the diversity order of the proposed AF protocol is given.

A promising application of unmanned aerial vehicles (UAVs) to the future communication networks is to address emergency communications. This paper considers such a scenario where a UAV is employed to a malfunction area (modeled as a circular disc) in which all ground base stations (BSs) break down. The ground BSs outside the malfunction area are modelled as a homogeneous Poisson point process (HPPP). Particularly, a user-centric cooperative scheme is proposed to serve the UEs in the malfunction area. According to the user equipment's (UE's) connections to the UAV and the nearest ground BS, the malfunction area is divided into three regions, namely the UAV region, the cooperation region and the nearest ground BS region, in which the UEs are served by the UAV only, both the UAV and the nearest ground BS, and the nearest ground BS, respectively. The region size of each type can be adjusted by a cooperation parameter $\delta$. Through rigorous derivations, an expression for the coverage probability achieved by the UE in the malfunction area is obtained. In order to provide a fair comparison, the normalized spectral efficiency (NSE) which is defined by taking both system throughput and the number of serving BSs into consideration, is used as a criterion for the performance evaluation. Numerical results are presented to verify the accuracy of the analytical results and also to demonstrate the superior performance of the proposed scheme.

To improve the system throughput, this paper proposes a network non-orthogonal multiple access (N-NOMA) technique for the uplink coordinated multi-point transmission (CoMP). In the considered scenario, multiple base stations collaborate with each other to serve a single user, referred to as the CoMP user, which is the same as for conventional CoMP. However, unlike conventional CoMP, each base station in N-NOMA opportunistically serves an extra user, referred to as the NOMA user, while serving the CoMP user at the same bandwidth. The CoMP user is typically located far from the base stations, whereas users close to the base stations are scheduled as NOMA users. Hence, the channel conditions of the two kinds of users are very distinctive, which facilitates the implementation of NOMA. Compared to the conventional orthogonal multiple access-based CoMP scheme, where multiple base stations serve a single CoMP user only, the proposed N-NOMA scheme can support larger connectivity by serving the extra NOMA users, and improve the spectral efficiency by avoiding the CoMP user solely occupying the spectrum. A stochastic geometry approach is applied to model the considered N-NOMA scenario as a Poisson cluster process, based on which insightful closed-form or quasi closed-form analytical expressions for outage probabilities and ergodic rates are obtained. Numerical results are presented to show the accuracy of the analytical results and also demonstrate the superior performance of the proposed N-NOMA scheme.

This paper considers a multiple-input multipleoutput (MIMO) downlink communication scenario with one base station and two users, where each user is equipped with m antennas and the base station is equipped with n antennas. To efficiently exploit the spectrum resources, we propose a transmission protocol which combines generalized singular value decomposition (GSVD) and non-orthogonal multiple access (NOMA). The expected data rates achieved by the two users are adopted as performance metrics for the evaluation of the proposed GSVD-NOMA scheme. In particular, we first characterize the limiting distribution of the squared generalized singular values of the two users' channel matrices for the asymptotic case, where the numbers of transmit and receive antennas approach infinity. Then, we calculate the expected normalized individual rates of the users in the considered asymptotic regime. Furthermore, we extend the proposed GSVD-NOMA scheme to the general MIMO downlink communication scenario with more than two users. To this end, we propose a hybrid multiple access approach, where the base station divides the users into different groups, the proposed GSVD-NOMA scheme is implemented within each group, and different groups are allocated orthogonal bandwidth resources. Finally, numerical results are provided to validate the effectiveness of the proposed GSVD-NOMA protocol and the accuracy of the developed analytical results.

To study the feasibility of network non-orthogonal multiple access (N-NOMA) techniques, this paper proposes a N-NOMA scheme for a downlink coordinated multipoint (CoMP) communication scenario, with randomly deployed users. In the considered N-NOMA scheme, superposition coding (SC) is employed to serve cell-edge users as well as users close to base stations (BSs) simultaneously, and distributed analog beamforming by the BSs to meet the cell-edge user's quality of service requirements. The combination of SC and distributed analog beamforming significantly complicates the expressions for the signal-to-interference-plus-noise ratio at the receiver, which makes the performance analysis particularly challenging. However, by using rational approximations, insightful analytical results are obtained in order to characterize the outage performance of the considered N-NOMA scheme. Computer simulation results are provided to show the superior performance of the proposed scheme as well as to demonstrate the accuracy of the analytical results.

In this paper, we consider the design of a new secure transmission scheme for a four-node relay-eavesdropper channel, where user cooperation is used to facilitate secure communications. The key idea of the proposed achievable scheme is to apply the compression relaying concept of noisy network coding (NNC) to the secrecy communication scenario. But different from the original non-secrecy NNC, the compression rate at the relay is adaptively chosen according to the eavesdropping channel. Particularly, helping interference information is injected into the compression codebook at the relay by simply enlarging the compression rate, which is to effectively suppress the eavesdropping channel. Closed-form expressions of the secrecy rates achieved by the proposed NNC-based secure scheme are characterized for both the discrete memoryless and Gaussian relay-eavesdropper channels, where the optimal compression rate and the optimal transmit power at the relay are also determined. The proposed secure scheme can be viewed as a general framework, which naturally combines the NNC compression relaying scheme with the interference-assisted scheme. Analytical and numerical results demonstrate that the proposed secure scheme offers constant performance gains over typical existing cooperative secure schemes.

This paper considers the secrecy communication of a wirelessly powered network, where an energy-constrained legitimate transmitter (Alice) sends message to a legitimate receiver (Bob) with the energy harvested from a dedicated power beacon, while an eavesdropper (Eve) intends to intercept the information. A simple time-switching protocol with a time-switching ratio α is used to supply power for the energy-constrained legitimate transmitter. To improve the physical layer security, we first propose a protocol that combines maximum ratio transmission with zero-forcing (ZF) jamming for the case without Eve's channel state information (CS!), i.e., Alice has access to Bob's CSI only. Then, we propose a protocol that uses a ZF transmitting strategy to minimize the signal-to-noise ratio (SNR) at Eve for the case that Alice is capable of obtaining partial CSI related to Eve. Closed-form expressions and simple approximations of the connection outage probability and secrecy outage probability are derived for both protocols. Furthermore, the secrecy throughput as well as the diversity orders achieved by our proposed protocols are characterized, and the optimal time-switching ratio α and power allocation coefficient β for secrecy throughput maximization are derived in the high SNR regime. Finally, numerical results validate the effectiveness of the proposed schemes.

This paper investigates group secret key generation problems for different types of wireless networks, by exploiting physical layer characteristics of wireless channels. A new group key generation strategy with low complexity is proposed, which combines the well-established point-to-point pairwise key generation technique, the multisegment scheme, and the one-time pad. In particular, this group key generation process is studied for three types of communication networks: 1) the three-node network; 2) the multinode ring network; and 3) the multinode mesh network. Three group key generation algorithms are developed for these communication networks, respectively. The analysis shows that the first two algorithms yield optimal group key rates, whereas the third algorithm achieves the optimal multiplexing gain. Next, for the first two types of networks, we address the time allocation problem in the channel estimation step to maximize the group key rates. This non-convex max-min time allocation problem is first reformulated into a series of geometric programming, and then, a single-condensation-method-based iterative algorithm is proposed. Numerical results are also provided to validate the performance of the proposed key generation algorithms and the time allocation algorithm.

This paper studies the problem of simultaneously generating a secret key (SK) and a private key (PK) between Alice and Bob, in a cooperative pairwise-independent network (PIN) with two relays. In the PIN, the pairwise source observed by every pair of terminals is independent of those sources observed by any other pairs. The SK needs to be protected from Eve, while the PK needs to be protected not only from Eve but also from the two relays. Two cooperative SK-PK generation algorithms are proposed: both of them first generate common randomness, based on the well-established pairwise key generation technique and the application of the one-time pad; but then, the two algorithms utilize the XOR operation and a specific random-binning-based SK-PK codebook to generate the expected keys, respectively. The achievable SK-PK rate regions of both the two proposed algorithms are analyzed. Of particular interest is the second algorithm with random-bing based codebook, whose achievable key rate region is demonstrated to be exactly the same as the derived outer bound, a crucial step for establishing the key capacity of this PIN model. Finally, the two proposed SK-PK generation algorithms are extended to a cooperative wireless network, where the correlated source observations are obtained from estimating wireless channels during a training phase.

We study the problem of private key generation in a cooperative pairwise independent network (PIN), with M + 2 terminals (Alice, Bob, and M relays), M ≥ 2. In the PIN, the correlated source observed by every pair of terminals is independent of the sources observed by any other pairs of terminals. Moreover, all terminals can communicate with each other over a public channel, which is also observed by Eve, noiselessly. The objective is to generate a private key between Alice and Bob with the help of the M relays; such a private key needs to be protected not only from Eve but also from all relays. A single-letter expression for the private key capacity of this PIN model is obtained, where the achievability part is established by proposing a random binning (RB)-based key generation algorithm, and the converse part is established by deriving upper bounds of M enhanced source models. Next, we consider a cooperative wireless network and use the estimates of fading channels to generate private keys. It has been shown that the proposed RB key generation algorithm can achieve a multiplexing gain of M - 1, which is an improvement compared with the existing XOR algorithm, whose achievable multiplexing gain is IM/2J.

In this paper, the outage performance of downlink non-orthogonal multiple access (NOMA) is investigated for the case where each user feeds back only one bit of its channel state information (CSI) to the base station. Conventionally, opportunistic one-bit feedback has been used in fading broadcast channels to select only one user for transmission. In contrast, the considered NOMA scheme adopts superposition coding to serve all users simultaneously in order to improve user fairness. A closed-form expression for the common outage probability (COP) is derived, along with the optimal diversity gains under two types of power constraints. Particularly, it is demonstrated that the diversity gain under a long-term power constraint is twice as large as that under a short-term power constraint. Furthermore, we study dynamic power allocation optimization for minimizing the COP, based on one-bit CSI feedback. This problem is challenging, since the objective function is non-convex; however, under the short-term power constraint, we demonstrate that the original problem can be transformed into a set of convex problems. Under the long-term power constraint, an asymptotically optimal solution is obtained for high signal-to-noise ratio.

Recently, lattice-reduction-aided detection in multiple-input multiple-output (MIMO) systems has attracted significant research efforts for its capability of achieving full diversity performance with low complexity. However, most lattice reduction algorithms are not designed directly to enhance the bit error ratio (BER) performance. In this paper, a fast lattice reduction (FLR) algorithm for complex-valued matrices, which aims at maximizing the minimal signal to noise ratios (SNR) of all layers, is proposed for V-BLAST (Vertical Bell Laboratories Layered Space-Time) systems, employing presorting technique and complex Givens rotation to reduce its computational complexity. The SNRs of all layers are related to the diagonal elements of the triangular matrix via QR decomposition of the channel matrix, and can be optimized by a series of iterations which can be efficiently implemented by exploiting the complex Givens rotation, while the average number of iterations is significantly diminished by utilizing the low complexity pre-sorting technique. Our analysis reveals that the proposed SIC-FLR decoder can significantly reduce the computational complexity without sacrificing any performance. Simulation results show that the proposed algorithm achieves the same performance as the state-of-art complex LLL (Lenstra-Lenstra-Lovász) algorithm only with a fraction of complexity.

This paper studies the private key generation of a cooperative pairwise-independent network (PIN) with M + 2 terminals, where Alice and Bob wish to generate a private key under the help of the M relays, M ≥ 2; such a private key needs to be protected not only from Eve but also from individual relays simultaneously. In this PIN, the correlated source observed by every pair of terminals is independent of those sources observed by any other pair of terminals. All the terminals can communicate with each other over a public channel which is also observed by Eve noiselessly. The private key capacity of this PIN model is established, whose lower bound is obtained by proposing a novel random binning (RB) based key generation algorithm, and the upper bound is obtained based on the construction of M enhanced source models. The two bounds are shown to be exactly the same. Then, we consider a cooperative wireless network and use the estimates of fading channels to generate private keys. Compared to the existing XOR-based algorithm whose achievable multiplexing gain is ⌊M/2⌋, the proposed RB-based algorithm is demonstrated to achieve the optimal multiplexing gain M - 1.

This paper considers a general framework of the wiretap channel with helping interference and state information (WT-HI-SI), where a transmitter-receiver pair wishes to keep the message secret from a passive eavesdropper in the presence of an interferer and a random state. The interferer is to help the legitimate transceivers to enhance their security level, and the state information is available at the transmitter, but not at the eavesdropper. For the discrete memoryless WT-HI-SI, an achievable scheme is proposed by combining the noise forward scheme and the double binning coding scheme. Some previously proposed schemes can be viewed as special cases of the proposed scheme. Then, the achievable scheme is applied to two special channels, the Gaussian WT-HI-SI and the Gaussian WT-HI, respectively. For the Gaussian WT-HI-SI, there exists an external random state noncausally available to the transmitter in advance. But for the Gaussian WT-HI, there does not exist any external random state. In this case, we propose a novel achievable scheme that requires the transmitter to artificially generate the random state whose power can be adjusted adaptively according to dynamic channel conditions. Both the analytic and numerical results are provided to demonstrate that the use of the state information can generally improve the secrecy performance. A more important contribution of this paper is that even for the scenario where no external state information is available to the transmitter, the proposed scheme with the artificial state can still achieve a strictly larger secrecy rate in comparison with existing interference assisted schemes.

This paper study information-theoretic security for a four-node relay-eavesdropper channel. We propose a new achievable scheme whose key idea is to combine noisy network coding for relay channels and the interference assisted strategy for wiretap channel with a helping interferer. The corresponding achievable secrecy rate is characterized for both discrete memoryless and Gaussian channels. The previous interference assisted schemes such as noise-forwarding and cooperative jamming are shown to be special cases of the proposed scheme. Moreover, in some very strong eavesdropping case where these interference assisted schemes can only achieve zero secrecy rate, the proposed secrecy scheme can still achieve a positive secrecy rate.

An efficient analog network coding transmission protocol is proposed in this letter for a MIMO two way cellular network. Block signal alignment is first proposed to null the inter-user interference for multi-antenna users, which makes the dimensions of aligned space larger compared with the existing signal alignment. Two algorithms are developed to jointly design the precoding matrices at the relay and BS for outage optimization. The performance of this transmission protocol is also verified by simulations.

This paper studies the impact of partial encoder cooperation on the secrecy of the multiple access channel (MAC) with an external eavesdropper. In particular, two encoders, connected by two communication links with finite capacities, wish to send secret messages to the common intended decoder in the presence of a passive eavesdropper. The inner and outer bounds on the secrecy capacity are derived for the discrete memoryless channel. The derived inner bound rate region is achievable by combining Willems's coding for the MAC with partially cooperating encoders and Wyner's random binning for the wiretap channel. Then, both the inner and outer bounds are extended to the Gaussian case and the corresponding rate regions are established. Several simple achievable transmission schemes are proposed for the Gaussian channel and the numerical results show that the partial encoder cooperation can increase the achievable rate regions.

Consider a MIMO multicast channel where a multi-antenna base station (BS) sends common messages to K multi-antenna users. Assuming that the channel state information (CSI) of the K users are known at the BS, we study the optimal downlink rank-one beamforming which maximizes the postprocessing SNRs of the bottleneck users. We first study the special case where the BS has two transmit antennas. Denoting γ ∊ Rkas a vector consisting of the SNRs of the K users, we derive the closed-form expression of the feasible set of γ as a two-dimension ellipsoid embedded in a K-dimension space. Based on this observation, we develop a prune and search algorithm (PASA) which guarantees to find a global optimal Tx beamforming vector and meanwhile is computationally faster than the existing suboptimal algorithms. For the general case where the BS has an arbitrary number of Tx antennas, we leverage the two-antenna result and propose an iterative 2-dimensional optimization (I2DO) method, which at each iterative step transforms the original problem into the two-antenna one and improves the solution using PASA. The simulation results show that the proposed methods outperform the existing ones in both performance and complexity.

A novel cooperative transmission protocol is proposed for multiple access scenarios, where multiple users communicate with a common destination with the assistant of multiple half-duplex relays. The proposed alternative relaying decode-and-forward (ARDF) protocol can achieve the full diversity gain by applying superposition coding at each transmitter, which also utilizes the linear zero-forcing detection at each relay to combat a serious inter-relay interference. Different to the previous uplink protocols, the proposed protocol can exploit the cooperation involving both the relays and sources, which guarantees the proposed scheme to approach the optimal multiple-input singleoutput upper bound even with general inter-relay interference. Analytical and numerical results have been provided to demonstrate the performance of the proposed protocol.

While various cooperative protocols have been developed for the simple scenario with one source-destination pair, most of them still suffer a significant loss compared with the optimal multiple-input single-output (MISO) upper bound. The diversity-multiplexing tradeoff will be used as the criterion for performance evaluation. In this paper, we propose two new half-duplex decode-forward cooperative transmission protocols, whose performance can approach the optimal MISO bound, and achieve a better diversity-multiplexing tradeoff when compared with existing cooperative protocols, particularly for large multiplexing gains. Firstly, a simple protocol of cooperative transmission is devised by combining opportunistic strategies with non-orthogonal transmission. When the number of relays is large, the proposed opportunistic decode-forward cooperative protocol can approach the optimal MISO upper bound. Due to the inter-relay interference constraint, each relay can only be used once, which limits the achievable diversity gain. Such an observation motivates our second transmission protocol which can further push the performance of cooperative transmission close to the optimal upper bound. Secondly, a relaying protocol is proposed for a four-node network where two multiple-antenna relays alternately forward messages to the destination when they can successfully cancel the inter-relay interference using the zero forcing method. Monte-Carlo simulation has also been provided to demonstrate the performance of both protocols and comparable ones.