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This paper presents a multiple-input–multiple-output (MIMO) precoder with a compensated QR decomposition (CQRD) combination for coordinated multipoint (CoMP) downlink transmission. Unlike conventional QR decomposition (QRD) combination, CQRD combination adopts compensated channel matrix orderings. This paper first proposes CQRD combination for CoMP scenarios. The statistics for combined spatial subchannel gains with a CQRD combination of two coordinated base stations (BSs) are derived, and these statistics show that more balanced subchannel gains are generated with a CQRD combination than with a QRD combination. Furthermore, this paper proposes a generalized CQRD combination scheme with a joint sorting strategy that can be applied to scenarios with more than two coordinated BSs. Unlike the unsorted strategy, the joint sorting strategy determines an enhanced compensated combination to further increase spatial subchannel gains; therefore, the performance can be upgraded. Because conventional Tomlinson–Harashima precoding (THP) cannot be used in the CQRD combination, interference presubtraction and vector precoding (VP) is adopted. Theoretical analysis and simulation results are both provided to demonstrate the advantages of balanced spatial subchannel gains and enhanced bit-error-rate (BER) performance in the proposed CQRD-based schemes. Compared with existing QRD-based MIMO precoders in CoMP scenarios, the proposed CQRD-based schemes have substantial signal-to-noise ratio (SNR) improvements of 2–5 dB. [ABSTRACT FROM PUBLISHER]

This paper concerns the uplink of multicell multiuser multiple-input multiple-output (MIMO) systems. To tackle the effect of pilot contamination that is generally viewed as a bottleneck in previous work, this paper presents a superimposed pilot (SP)-aided uplink channel estimation scheme and mathematically characterizes the impact that an SP has on the performance of such a very large MIMO system. It is shown that there are two types of interference components that do not vanish, even when the number of antennas $M$ grows to infinity. The first type, which is referred to as cross-contamination, is due to the correlation between the SP and data among different cells. The second type, which is referred to as self-contamination, is due to the dependence between channel estimation and estimation error. Cross-contamination is, in principle, similar to pilot contamination in a conventional pilot-based multicell MIMO system, whereas self-contamination is unique for the SP-aided scheme. Both theoretical and simulation results demonstrate that the SP-aided scheme can effectively reduce the estimation contamination by increasing the data frame size and, in turn, achieve a significant improvement over the spectral efficiency, in comparison with conventional pilot-based methods. [ABSTRACT FROM AUTHOR]

This paper focuses on precoding design for sum-rate maximization while considering the effects of residual self-interference for multiuser multiple-input–multiple-output (MU-MIMO) full-duplex (FD) systems. The problem formulation leads to a nonconvex matrix-variable optimization problem, where we develop two efficient sum-rate maximization algorithms using sequential convex programming (SCP), namely, the difference of convex functions (DC)-based and the sequential convex approximations for matrix-variable programming (SCAMP) algorithms. In addition, we derive the achievable sum rate under the effect of residual self-interference. Simulation results show that, even in cases of high self-interference and high estimation error, the SCAMP algorithm provides approximately 20%–30% sum-rate improvements over both conventional optimized half-duplex (HD) transmission and the existing state-of-the-art FD algorithm in a wide range of scenarios. Finally, the convergence results indicate that the DC-based algorithm tends to initially give the best performance; however, at convergence, the SCAMP algorithm tends to significantly outperform the other algorithms. [ABSTRACT FROM AUTHOR]

Interference alignment (IA) is a precoding technique that aligns interfering signals at receivers. It is known that IA achieves the maximum degrees of freedom over an interference channel under ideal assumptions. The real-world performance of IA depends on a range of practical issues, such as imperfect synchronization, channel estimation, and feedback. Practical issues have been studied in simulations and prototypes, but fully distributed operation of IA network nodes has not been considered. In this paper, we present the first investigation of real-time IA performance on a fully distributed 2 $\times$ 2 multiple-input–multiple-output (MIMO) prototype system with three physically independent user pairs. Over-the-air algorithms for time and frequency synchronization, as well as analog feedback, are studied and implemented. Sum rates are illustrated as a function of complexity and accuracy of different alignment, synchronization, and feedback algorithms. Corresponding tradeoffs are evaluated using an iterative IA method, the injection of residual frequency offset into synchronization, and analog versus quantization-based limited feedback approaches. We demonstrate that, while considering all possible error sources in estimation, synchronization, and feedback, the theoretical multiplexing gain of IA can be reached in practical systems with a constant sum rate loss that remains within 5 bits/Hz/s compared with an ideal simulation. [ABSTRACT FROM PUBLISHER]

In this paper, we study the downlink resource assignment problem of maximizing the total data rate subject to minimum satisfaction guarantees in multiservice scenarios assuming the use of multiuser (MU) multiple-input–multiple-output (MIMO) techniques. With the use of MU MIMO techniques, the same frequency resource can be shared by different terminals at the same time by assigning different spatial channels to each terminal. Different from single-user (SU) access per frequency resource where the resource assignment problem consists of searching for the best association between frequency resources and terminals, with MU access per resource, we aim at finding which space-division multiple-access (SDMA) group should be associated with each frequency resource. The first contribution of this paper is the formal presentation of this generalized problem as an optimization problem. Then, after some mathematical manipulations, we managed to convert this problem from a nonlinear integer to an integer linear problem (ILP) that can be optimally solved by standard techniques instead of resorting to brute-force methods. Motivated by the high computational complexity of the optimal solution, we propose a low-complexity algorithm. By analyzing outage rate and total data rate performance metrics, we show that the proposed solution presents a good performance–complexity tradeoff compared with the method for obtaining the optimal solution. [ABSTRACT FROM PUBLISHER]

Current and future mobile network access technologies increasingly rely on multiantenna transmission techniques and on cell miniaturization to achieve orders-of-magnitude gains in capacity. In this paper, we propose and evaluate the idea of multiuser multiple-input–multiple-input-based (MU-MIMO) cell reassignments. Dense small-cell deployments make it possible to pair user equipment units (UEs), which were originally assigned to different cells, enabling multiuser MIMO (MU-MIMO) and resulting in performance improvements to both UEs. We discuss how such pairings can be accomplished, and we assess the potential gains in the resulting spectral efficiency and MU-MIMO usage. These are assessed through both discussion of performance bounds and detailed system-level simulation in a realistic outdoor small-cell scenario. [ABSTRACT FROM PUBLISHER]

In this paper, the downlink of a clustered coordinated multicell multiuser multiple-input multiple-output (MIMO) system is considered, and various low-complexity user scheduling algorithms to maximize the sum rate are proposed. The users' data signals are transmitted cooperatively via the base stations (BSs) of a cluster within the sectorized multicell heterogeneous cellular network. Exhaustive search as the optimal scheduling method is extremely complex, particularly for large numbers of users requesting service. We therefore propose suboptimal scheduling algorithms based on the lower complexity metaheuristic stochastic optimization techniques of simulated annealing (SA) and particle swarm (PS). Moreover, a hybrid algorithm combining the traits of PS and a greedy scheduler is also proposed. The performance and complexity of these algorithms are evaluated for a heterogeneous system model employing different precoding methods. Assessing the algorithms' performance via computer simulations, the effectiveness of the proposed schemes in terms of sum rate is demonstrated, yielding performance very close to that of the exhaustive search at much lower complexity. For each precoding method used in the employed system model, the best corresponding approach to scheduling from our proposed algorithms is determined. [ABSTRACT FROM AUTHOR]

Multicell coordinated beamforming (CB) can mitigate intercell interference (ICI). However, existing work on CB focuses on systems that maximize overall throughput. This paper considers CB for systems with multiple receive antennas and further extends the CB to multiuser and multistream transmission. We consider fairness and pay close attention to cell-edge users. CB that maximizes the harmonic sum of signal-to-interference-plus-noise ratio (SINR) can be derived into a low-complexity algorithm that favors cell-edge users. Two iterative algorithms are developed. From the simulation results, the proposed algorithms can provide a better fifth-percentile user throughput compared with the CB algorithms minimizing mean square error, maximizing uplink SINR, and maximizing weighted sum rate. Furthermore, the computational complexity of the proposed algorithms is significantly lower than that maximizing the minimum SINR of users. [ABSTRACT FROM AUTHOR]

In this paper, we study user selection (US) strategies for a multiple-input–multiple-output (MIMO) cognitive radio (CR) downlink network, where the r-antenna underlay CR secondary users (SUs) coexist with a primary user (PU), and all terminals are equipped with multiple antennas. Two main scenarios are considered: 1) The t-antenna cognitive base station (CBS) has perfect or partial channel state information at the transmitter (CSIT) from the CBS to the PU receiver (RX), and 2) the CBS has absolutely no PU CSIT. For these scenarios, we propose and evaluate multiple SU selection schemes that are applicable to both best-effort PU interference mitigation and hard interference temperature (IT) constraints. The computational complexity of the proposed schemes can be significantly smaller than that of an exhaustive search with negligible performance degradation. For the selection of C SUs out of K, whereas an exhaustive search is on the order of \mathcal{O}(\binom{K}{C}C^4r^3). When t$ and r$ are of the same order, the computational complexity of the proposed scheme can be \binom{K}{C}C^4/K times smaller. Mathematical complexity analysis and numerical simulations are provided to show the advantage of our schemes. [ABSTRACT FROM PUBLISHER]

This paper presents a coherent scheme to optimize an in-band full-duplex multiple-input–multiple-output (MIMO) relay via beamforming and transmit power allocation in a two-hop single-input–single-output (SISO) link under full channel knowledge and perfect hardware assumptions. First, we derive in closed form the optimal pair of transmit power and receive filter for a fixed transmit filter by unifying the minimum-mean-square-error (MMSE) filtering with the SISO-equivalent power allocation, as an iterative approach is not guaranteed to converge to global optimum. Second, we propose a heuristic algorithm to approximate the optimal transmit filter for a fixed receive filter. Furthermore, we study the well-known null-space projection constraint and derive a singular value decomposition (SVD)-based solution for the arbitrary-rank self-interference channel by generalizing the optimal solution under the assumption of rank-1 self-interference channel. Finally, we combine these solutions into a partially iterative algorithm in order to address the global optimization as our observations justify that some of the aforementioned schemes converge to the optimal solution under certain criteria. The numerical analysis of the proposed iterative algorithm demonstrates close-to-optimal performance relative to the theoretical upper bound of the end-to-end link in terms of maximum achievable throughput. [ABSTRACT FROM PUBLISHER]

The main focus of this paper is on multistream multiantenna (multiple-input multiple-output) communications in large-scale heterogeneous random networks. Previous work in this area mainly studies the outage probability from the perspective of a given stream, which is inaccurate as it generally overlooks possible interference-driven cross stream signal-to-interference correlation in each communication link. To tackle this issue, in this paper, we focus on a link-level performance evaluation by characterizing the complementary cumulative distribution function (CCDF) of random mutual information (RMI) under heterogeneous interference. We focus on the scenarios that no coordination among transmitters is persuaded, and the receivers do not attempt to cancel out part of interuser interference. Assume that channel state information is known at both the transmitter and receiver of each communication pair, Rayleigh fading, that the singular value decomposition (SVD) is applied to construct pre-coding/post-coding filters for single-user detection, and that transmitted signals of antennas are i.i.d. Gaussian. We first provide accurate expression for the achievable data rate (ADR) of each link, and show that, regardless of the interference power, when transceivers are equipped with equal number of antennas it grows sublinearly with the number of antennas. We then approximate RMI via Gaussian distribution that its mean is the ADR and its variance is derived based on network's parameters. It is seen that the Gaussian approximation is credible even when two streams of data are transmitted. This paper provides various insights regarding the impact of system parameters, including density of transmitters, path-loss exponent, and the number of antennas, on the ADR and CCDF of RMI. We finally spot tremendous benefits of the SVD scheme over other prominent multiplexing systems, including maximum ratio combining, zero-forcing, and diagonal BLAST superstructure with minimum mean square error receivers. [ABSTRACT FROM PUBLISHER]

This paper considers multicell scheduling for coordinated multiple-input multiple-output cellular networks. In a multicell scenario, intercell interference, which is the major challenge degrading system performance, can be suppressed via multicell coordination. However, when the number of users is larger than that can be served, user/multimode selection is necessary, and can significantly enhance the performance in such interference-limited environment. Nevertheless, user selection in a multicell scenario incurs high computational complexity and overhead signalling. To this end, in this paper, low complexity greedy algorithms are proposed for user selection. The algorithms are based on the concept of angle between subspaces and intersection of null spaces, and work in partially distributed fashion with limited information exchange. By these algorithms, channel feedback can be greatly reduced with reasonable computational complexity. In addition, multimode scheduling schemes are proposed for this multicell set up, where the spatial streams are adaptively selected. The proposed algorithms are analysed and compared with the optimal solution obtained by exhaustive search. Simulation results show that the algorithms achieve most of the throughput achievable by the optimal solution. [ABSTRACT FROM AUTHOR]

This paper considers limited feedback for a two-cell interfering multiple-input–multiple-output multiple-access channel (MIMO-MAC). We propose a QR decomposition-based interference alignment (QRD-IA) scheme for efficient limited feedback and investigate the conditions for the antenna configuration. We characterize the interference leakage caused by quantization error as a function of the number of feedback bits. To minimize the interference leakage, we further propose a quantized-precoder-based IA (QP-IA) scheme by modifying the proposed QRD-IA scheme. By characterizing the interference leakage of the QP-IA scheme, we investigate the number of feedback bits to maintain the degrees of freedom (DOFs) in the two-cell interfering MIMO-MAC and a feedback bit allocation algorithm to improve the sum rate. From simulation results, we demonstrate that our proposed schemes can provide better sum-rate performance than the existing scheme using the same number of feedback bits, and our feedback bit allocation algorithm provides a higher sum rate compared with equal feedback bit allocation. [ABSTRACT FROM PUBLISHER]

In multiple-input–multiple-ouput (MIMO) interference channels (IFCs), interference alignment (IA) with zero-forcing (ZF) linear detection can be used to achieve the maximum degrees of freedom (DoFs). However, ZF linear detection usually degrades the performance due to the noise enhancement in practical systems. In this paper, we propose lattice reduction (LR)-aided successive interference cancelation (SIC) in conjunction with IA over lattice for three-user (and extendable to $K$-user) MIMO IFCs in which the interfering signals aligned over the lattices are detected and canceled rather than nulled out. To complete the proposed LR-aided SIC method, the detection ordering and the precoding matrix that minimize the mean square error are also determined. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the problem of spectrum leasing in cognitive radio (CR) networks, while incorporating two advanced physical-layer technologies, i.e., multiple-input multiple-output (MIMO) and distributed interference alignment. We present a cooperative spectrum leasing scheme for primary and secondary users to balance the tension between data transmission and revenue collection/payment. A Stackelberg game is formulated, where the primary user is the leader, and secondary users are followers. With backward induction, we derive the optimal strategies for primary and secondary users that can achieve the unique Stackelberg equilibrium, where no player can gain by a unilaterally changing strategy. We find that spectrum leasing is always beneficial to enhancing the utilities of primary and secondary users. The proposed scheme outperforms a no-spectrum-leasing scheme and a cooperative scheme presented in the literature with considerable gains, which demonstrate the benefits of spectrum leasing and distributed interference alignment and validates the efficacy of the proposed scheme. [ABSTRACT FROM PUBLISHER]

The channel feedback overhead for massive multiple-input multiple-output systems with a large number of base station (BS) antennas is very high since the number of feedback bits of traditional codebooks scales linearly with the number of BS antennas. To reduce the feedback overhead, an effective codebook based on channel statistics has been designed, where the required number of feedback bits only scales linearly with the rank of the channel correlation matrix. However, this attractive conclusion was only proved under a particular channel assumption in the literature. To provide a rigorous theoretical proof under a general channel assumption, in this paper, we quantitatively analyze the performance of the channel-statistics-based codebook. Specifically, we first introduce the rate gap between the ideal case of perfect channel state information at the transmitter and the practical case of limited channel feedback, where we find that the rate gap depends on the quantization error of the codebook. Then, we derive an upper bound of the quantization error, based on which we prove that the required number of feedback bits to ensure a constant rate gap only scales linearly with the rank of the channel correlation matrix. Finally, numerical results are provided to verify this conclusion. [ABSTRACT FROM AUTHOR]

Convergence and density evolution of a low-complexity iterative multiple-input multiple-output detection based on belief propagation over a ring-type pairwise graph are presented for binary data. The detection algorithm to be considered is effectively a forward–backward recursion and was originally proposed by Yoon and Chae in a work published in 2014, in which link-level performance, computational complexity, and convergence for Gaussian input were analyzed in detail. This paper presents the convergence proof and the density evolution framework for binary input to give an asymptotic performance in terms of average signal-to-interference-plus-noise ratio and bit error rate (BER) without channel coding. The BER curve obtained via density evolution shows a good match with the simulation results for uncoded BER in the paper by Yoon and Chae verifying the effectiveness of the analysis provided and the performance of the detection algorithm. [ABSTRACT FROM AUTHOR]

Multiple-input–multiple-output (MIMO) full-duplex relaying (FDR) has been considered an efficient technique to provide coverage to users where their direct links from the base station (BS) are too weak for reliable signal reception. However, when multiple MIMO full-duplex relays are deployed in a network, the signal reception quality relies on the effective suppression of multiple types of interference. In this paper, the distributed beamforming is studied for the MIMO FDR network by formulating a power minimization problem with a nonstrict convex objective function (total transmit power of both the BS and all the relays in the network) under individual user rate constraints. We come up with two iterative distributed beamforming algorithms, Algorithm 1 for relays equipped with single receive antenna and Algorithm 2 with multiple receive antennas. The former can yield a global optimal solution of the power minimization problem, whereas the latter can yield only a local optimal solution due to conservative successive convex approximations (SCAs) performed at each iteration, and a rigorous analysis on the upper bounds of step sizes is proposed to guarantee their convergence. The proposed two algorithms only require local information exchange between relays and hence are scalable for different network sizes and topologies. An “early termination” strategy in the operation of the proposed two algorithms is also presented to acquire an acceptable transmit power solution with less computation time consumption and thus suitable for realistic applications. Finally, some simulation results are provided to demonstrate that the proposed two algorithms perform well and significantly better than the existing state-of-the-art scheme reported in the work of Lee and Shin. [ABSTRACT FROM PUBLISHER]

Low-complexity linear precoders are known to be close to optimal for massive multiple-input multiple-output (M-MIMO) systems. However, the large number of antennas at the transmitter imposes a high computational burden and high hardware overloads. In line with this, in this paper, we propose a low-complexity antenna selection (AS) scheme that selects the antennas that maximize constructive interference between the users. Our analyses show that the proposed AS algorithm, in combination with a simple matched-filter (MF) precoder at the transmitter, is able to achieve better performances than systems equipped with a more complex channel inversion (CI) precoder and computationally expensive AS techniques. First, we give an analytical definition of constructive and destructive interference, based on the phase of the received signals from phase-shift-keying-modulated transmissions. Then, we introduce the proposed AS algorithm, which identifies the antenna subset with the highest constructive interference, maximizing the power received by the user. In our study, we derive the computational burden of the proposed technique with a rigorous and thorough analysis, and we identify a closed-form expression of the upper bound received power at the user side. In addition, we evaluate in detail the power benefits of the proposed transmission scheme by defining an efficiency metric based on the achieved throughput. The results presented in this paper prove that AS and green radio concepts can be jointly used for power-efficient M-MIMO, as they lead to significant power savings and complexity reductions. [ABSTRACT FROM AUTHOR]

This paper proposes an amplify-and-forward-based massive multiple-input–multiple-output full-duplex relaying (AF-MM-FDR) protocol, where multiple source–destination pairs communicate simultaneously with a common full-duplex relay. A zero-forcing (ZF)-based relay transceiver design with semiblind gain control is presented, considering the problem of relay oscillation. The asymptotic expression of end-to-end signal-to-interference-plus-noise power (SINR) is derived under the general power scaling scheme. The scaling behaviors of echo interference (EI) and effective channel estimation error are determined. Scaling results show that the deployment of very large antenna arrays at the relay has the potential to eliminate the effect of EI due to the full-duplex operation, if the power scaling scheme is selected properly. Moreover, based on the asymptotic analysis, a low-complexity power control scheme is proposed to optimize the spectral efficiency of AF-MM-FDR. Simulation results show that the proposed power control scheme improves the spectral–energy efficiency tradeoff of AF-MM-FDR significantly. [ABSTRACT FROM AUTHOR]

In this paper, we consider time-domain vector perturbation (TDVP) in a large-system limit when channel state information (CSI) is imperfect due to pilot contamination, and we derive the system's achievable sum rate per cell. We use random matrix methods to avoid time-consuming Monte Carlo simulations. Numerical results show that, in general, linear precoding ensures a higher sum rate than TDVP in the massive multiple-input–multiple-output (MIMO) regime. [ABSTRACT FROM AUTHOR]

This paper considers a two-cell uplink cochannel multiple-input–multiple-output (MIMO) network with users sequentially arriving at the network. We study the problem of sequential base-station (BS) selection for the users, with the selection criterion based on the degrees of freedom (DoFs) available for the new arriving user. We find that different sequential BS selections affect individual and network performance in terms of the individual and network sum DoF, as well as the number of admissible users in the network. We propose a method to build the tree structure for sequential BS selection, which carries trellis information for individual and system-wide selections. The properties of the tree are analytically studied. It turns out that by adopting an interference coordination strategy based on the concept of interference alignment (IA), better individual and network performance can be achieved. Simulation compares the proposed DoF-based BS selection and traditional BS selection schemes and highlights the advantages of the proposed scheme. [ABSTRACT FROM PUBLISHER]

Tomlinson–Harashima precoded (THP) multiple-input–multiple-output (MIMO) systems are developed to cancel the intersymbol interference (ISI) at the transmitter. However, the THP at least requires perfect channel direction information (CDI) to completely mitigate the interference at the transmitter, which is not practical in the real world. The limited feedback systems are then practically developed to convey the quantized CDI to the transmitter. Using the quantized CDI to conduct the THP, an unavoidable interference degrades the performance at the receiver. In this paper, we investigate the performance degradation resulted from the random vector quantization (RVQ), which is a kind of CDI-based limited feedback mechanism. Here, we measure the performance degradation as the excess mean-squared error (EMSE). Since the formulation of the EMSE is a complicated function of the quantization error, we proposed using the second-order Taylor expansion to derive an analytical result. Simulation results have also verified our proposed analysis, showing that the derived analysis can match the actual EMSE. [ABSTRACT FROM PUBLISHER]

This paper presents a non-orthogonal multiple access (NOMA) scheme with group detection for uplink multiple-input multiple-output (MIMO) systems, for which an effective precoder design is developed. In the scheme, users are divided into groups in accordance with their locations for detection at the base station. The inter- and intra-group interferences are mitigated by successive interference cancellation (SIC) and transceivers, respectively. Based on a derived approximate signal-to-interference-plus-noise ratio (SINR) for using zero-forcing detection, an iterative power and beamforming update procedure is developed for obtaining the user precoders. The precoder design effectively mitigates the intra-group-inter-user correlation making the adopted approximate SINR represent the original SINR accurately. The proposed multi-group MIMO-NOMA scheme can work under more practical transmit-receive antenna configurations and is shown to outperform upon existing cluster-based MIMO-NOMA schemes in terms of total transmit power for various system configurations. The impact of SIC residuals on the multi-group MIMO-NOMA scheme is investigated. Feasibility conditions for the design under imperfect SIC based on the fractional cancellation error model are developed. [ABSTRACT FROM AUTHOR]

The number of commercial and civilian vehicles equipped with automotive radars is expected to rise rapidly in the forthcoming years and with that comes the problem of increased mutual interference between the radar sensors, which can result in severely reduced radar sensitivity and increased false alarm rates. The difficulty and complexity of the problem increase with MIMO radar systems and multiply even further with a growing number of vehicles present on the scene. A system of connected vehicles can efficiently address this problem by sharing information amongst themselves. In this paper, we propose an efficient waveform design algorithm that seeks to minimize a collective cross-ambiguity function. Vehicles that can talk to each other, can perform the design online in a collaborative manner, or offline, in which case the radar codes can be designed and stored in a codebook for future use. The proposed coding scheme is computationally efficient for practical use and the incorporation of such schemes requires only a slight modification of the existing systems. Our numerical examples indicate that the proposed scheme can significantly reduce the interference power level in a desired area of the radar cross-ambiguity functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the codebook size design strategies in the multiple-input–multiple-output (MIMO) broadcast channel (BC) systems. We adopt the nonlinear Tomlinson–Harashima precoder (THP), which is designed by the imperfect channel direction information (CDI) acquired from the random vector quantization (RVQ) feedback mechanism. Under the limitation of the total feedback rate, we flexibly allocate the size of each user's codebook so that the overall channel capacity is maximized. Since the design problem is not convex, directly finding out the optimum allocation of codebook size is not attainable. However, by sophisticatedly using the discrete majorization theory, we can derive the codebook size allocation strategies for the high- and the low-signal-to-noise-ratio (SNR) regions. Interestingly, the results show that the equal size codebook is preferable in the low-SNR region, whereas the codebook allocates the whole available codebook size to a single user in the high-SNR region. Simulations certify the theoretical result of our design. [ABSTRACT FROM PUBLISHER]

We consider the uplink transmission in multiuser wireless systems with multiple single-antenna transmitting users and a multiantenna receiver. We address two problems in this paper. The first problem is user admission, i.e., given a large number of users, how to admit the maximum number of users that can simultaneously satisfy quality of service (QoS) and power constraints. The second problem is how to distribute the data among the users when they are allowed to share data before transmission. The aim is to minimize the total data exchange cost. Such a problem is called user clustering. We formulate those problems into sparsity-maximization problems, which are NP-hard. Inspired by compressive sensing techniques, we propose a common framework to tackle those problems by first applying the \ell1 -norm relaxation and then solving them with convex optimization methods. Simulations show that the proposed algorithms achieve excellent performance. For user admission, the numbers of admitted users by the proposed algorithms are close to the optimum numbers of admitted users obtained by exhaustive search (ES) . For user clustering, the total data exchange cost is reduced by more than 10% after only a few iterations. When the QoS requirement is low, the user data exchange can be avoided using the proposed method, which achieves the optimum result obtained by ES. [ABSTRACT FROM PUBLISHER]

This paper investigates an outage-constrained secrecy rate maximization (OC-SRM) problem based on the statistical channel uncertainty assumption in an underlay multiple-input multiple-output (MIMO) cognitive radio network, where the secondary transmitter provides simultaneous wireless information and power transfer to receivers. Our objective is to design the transmit covariance matrix and artificial noise aided covariance matrix through maximizing the secrecy rate of the secondary user while satisfying the given outage probability requirements. The designed problem is nonconvex and challenging. We employ the existing theory to reformulate the original problem into two equivalent subproblems by introducing auxiliary variables in order to overcome the difficulty arising from the Shannon capacity expression. The Bernstein-type inequality approach is resorted to conservatively approximate the probabilistic constraints. The merit of the transformation and conversion is that the tractable solutions of the original OC-SRM problem can be easily obtained through solving two convex conic subproblems alternately. Furthermore, we extend the proposed algorithm to solve full uncertainty model design. Numerical results demonstrate the efficacy of the proposed designs. [ABSTRACT FROM AUTHOR]

We investigate the performance of multiuser multiple-input-single-output (MU-MISO) downlink in the presence of the mutual coupling effect at the transmitter. Contrary to traditional approaches that aim at eliminating this effect, in this paper we propose a joint analog–digital (AD) beamforming scheme that exploits this effect to further improve the system performance. A jointly optimal AD beamformer is first obtained by iteratively maximizing the minimum received signal-to-interference-plus-noise ratio in the digital domain, followed by an optimization on the load impedance of each antenna element in the analog domain. We further introduce a decoupled low-complexity approach, with which existing closed-form beamforming schemes can also be efficiently applied. For the consideration of hardware imperfections in practice, we study the case where the analog load values are quantized, and propose a sequential search scheme based on greedy algorithm to efficiently obtain the desired quantized load values. Moreover, we also investigate the imperfect channel state information (CSI) scenarios, where we prove the optimality for closed-form beamformers, and further propose the robust schemes for two typical CSI error models. Simulation results show that with the proposed schemes the mutual coupling effect can be exploited to further improve the performance for both perfect CSI and imperfect CSI. [ABSTRACT FROM PUBLISHER]

The evaluation of the coverage probability of multistream multiple-input multiple-output (MIMO) communications in HetNets subject to noise, fading, and intercell interference is undoubtedly intricate. Unfortunately, the current literature misses its comprehensive evaluation, as the effects of noise and cross-stream correlation are often overlooked. Furthermore, computationally friendly expressions of the coverage probability allowing engineering insights and adaptive system design are lacking. For multistream MIMO zero-forcing beamforming, in this paper we tackle these issues by considering scenarios where a receiver is in the coverage if all of its data-streams are successfully decoded. Assuming the max signal-to-interference-plus-noise ratio (SINR) cell association (CA), we adopt the stochastic geometry tools to provide an upper bound and an easy-to-compute closed-form lower bound on the coverage probability, while their accuracies are confirmed against extensive simulations. Our contributions are as follows. We prove that full correlation of data streams of a given link slightly reduces the coverage performance. We show that from a coverage probability perspective, the single stream communication is preferable. We exploit our analysis to explore several pertinent design issues, which have not fully discussed in the literature. Our results demonstrate tradeoffs between densification and multiplexing gains. We, further, see that by appropriately designating feedback channel with modest capacity 8 bits per frame per user, the spatial throughput grows by nearly 180 $\%$ over the conventional 1-bit feedback scenario. Finally, We present important extensions of our analysis to underlay spectrum sharing, practical aspects of the max-SINR CA, and a nonhomogeneous path loss environment. [ABSTRACT FROM PUBLISHER]

In this paper, a low-complexity detection scheme is proposed for an underdetermined multiple-input–multiple-output (UD-MIMO) wireless communication system that employs $N$ transmit antennas and M < N$ receive antennas. The proposed scheme combines a simplified parallel interference cancelation (S-PIC) with the block decision feedback equalization (BDFE) algorithm. To account for the extra (N - M)$-dimension in the transmitted signal, the UD-MIMO system is partitioned into two subsystems: one with (N - M)$ transmit antennas and the other one with M sequences in the first subsystem, with $Q$ being the constellation size, the proposed scheme explores only a small number of candidate sequences in the first subsystem; thus, it achieves significant complexity reduction. Two new candidate sequence selection methods are proposed. In the first iteration, the candidate sequences used for PIC are selected by exploring the statistical properties of the received signals. In the second iteration and beyond, the set containing the candidate sequences is constructed by utilizing the soft information generated from the previous iteration. The proposed scheme provides a balanced tradeoff between computational complexity and bit error rate (BER) performance. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel low-complexity beamforming algorithm for multiuser successive maximum ratio transmission (MS-MRT) toward space-division multiplexing to achieve video quality maximization in the downlink of a multiuser (MU) multiple-input–multiple-output (MIMO) orthogonal frequency-division multiple-access (OFDMA)-based fourth-generation (4G) wireless network. We compare the performance of this algorithm in terms of system throughput and video quality with the two popular precoding techniques, namely, block diagonalization (BD) and successive optimization (SO). We also compare its performance with the generalized versions of these two algorithms termed coordinated transmit–receive processing (CTR)-BD and CTR-SO algorithms, respectively. Further, we propose an extension of the MS-MRT scheme to broadcast scenarios, termed broadcast successive maximum ratio transmission (BS-MRT), which computes the optimal broadcast beamforming vector to maximize the video quality at each of the broadcast group members while maintaining orthogonality to the previously scheduled user groups. We also demonstrate that the proposed MS-MRT and BS-MRT schemes can be naturally adapted to the context of various MU OFDMA scheduling algorithms such as proportional fairness (PF) and round robin (RR), to name a few, to maximize video quality through optimal scheduling in the presence of a large number of users. We discuss implementations of the proposed MS-MRT scheme in association with these scheduling algorithms for MU unicast and broadcast video transmission scenarios. The simulation results presented in this work rely on the rate models derived using the Joint Scalable Video Model (JSVM) software developed by the Joint Video Team (JVT) and are, thus, readily applicable in practice. The presented results clearly demonstrate the ability of the proposed algorithm to maximize the video quality in comparison with the other competing MU MIMO precoding techniques. Further, employing the proportional fair scheduling algorithm in conjunction with the MS-MRT results in an overall enhancement in the received video quality compared with the RR and max-rate algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, system design for a multiple-input–multiple-output (MIMO) relay broadcast channel with individual signal-to-interference-plus-noise ratio (SINR) constraints at mobile stations (MSs) is considered. By exploring the structure of downlink–uplink duality at either the base station (BS) or the relay station (RS), we propose two schemes of joint power allocation and beamforming design at the BS and the RS. The problem of the existence of feasible solutions under practical power constraints at the BS and the RS with given SINR targets is considered first. Then, the problem of sum power minimization is considered. Each design problem can be efficiently solved using optimal joint power allocation and beamforming under the framework of convex optimization. We also show that with subchannel pairing at the RS, the transmission power can be further reduced. Finally, a generalization to the multihop scenario is provided to further improve power efficiency. [ABSTRACT FROM PUBLISHER]

This paper studies robust interference mitigation against the imperfectness of channel knowledge involved in the interference link of a multiple-input–multiple-output (MIMO) cognitive radio (CR) system that coexists with a primary radio (PR) system via opportunistic spectrum-sharing (OSS) scheme. The robust design leads to a seemingly complicated matrix-valued problem. Nevertheless, we show that it can be equivalently converted into two convex semidefinite programs (SDPs). One of them is identified as a null-forcing approach with closed-form power allocation, and the other can be reduced to a convex scalar power allocation subproblem by properly relaxing the interference constraint. Numerical results demonstrate significant performance gain of the robust design over previous nonrobust strategies. [ABSTRACT FROM PUBLISHER]

Interrelay interference (IRI) is known to limit the performance of virtual full-duplex (VFD) relaying schemes. Available interference cancelation schemes are unable to simultaneously improve the diversity and maintain the multiplexing gain of VFD relaying schemes in multiple antennas scenarios. In this paper, we propose a technique to improve the reliability of multiantenna VFD relaying scheme, while maintaining the multiplexing gain in the presence of IRI. In the proposed scheme, the source and interrelay channels are concatenated and their signals are jointly decoded at the relay. A superposition of the decoded messages is forwarded to the destination. To reduce the effect of IRI on the receiving relay, two suboptimal relay transmit antenna selection schemes, namely, random antenna selection and maximum capacity antenna selection, are investigated. The system capacity and outage probability bounds of the proposed scheme are derived in closed form. The diversity and multiplexing tradeoff is also characterized. The analytical and numerical results show that the proposed scheme can achieve full diversity and maintain the multiplexing gain of the full-duplex relaying scheme. Also, the proposed scheme can outperform conventional VFD relaying scheme in terms of reliability even in the presence of IRI. [ABSTRACT FROM PUBLISHER]

A multicell massive multiple-input multiple-output (MIMO) system, which utilizes a large number of base-station antennas to simultaneously serve a set of users, suffers from pilot contamination (PC) due to unavoidable reuse of pilots in adjacent cells. In this paper, a weighted-graph-coloring-based pilot decontamination (WGC-PD) scheme is proposed to mitigate PC for multicell massive MIMO systems. Specifically, based on limited cooperation among cells, an edge-weighted interference graph (EWIG) is first constructed to depict the potential PC relationship among users, whereby two users in different cells are connected by a weighted edge, indicating the strength of potential PC when they reuse the same pilot. Then, inspired by classical graph coloring algorithms, we develop the WGC-PD scheme by denoting each color as a pilot and each vertex as a user in the EWIG, which is able to mitigate PC by assigning different pilots to connected users with a large weight in a greedy way with insufficient pilot resource. Compared with exhaustive search among numerous pilot assignment solutions, the proposed WGC-PD scheme is able to mitigate PC with significantly reduced complexity, which is verified by numerical results. [ABSTRACT FROM PUBLISHER]

Due to the unique physical-layer characteristics associated with multiple-input multiple-output (MIMO) and cognitive radio (CR), the network performance is tightly coupled with mechanisms at the physical, link, network, and transport layers. In this paper, we consider an energy-efficient cross-layer optimization problem in multihop MIMO CR networks (CRNs) and provide a new formulation to balance the weighted network utility and the weighted power consumption of secondary users (SUs), with the minimum transmission rate constraint of primary users (PUs) and the SU power consumption constraint. However, this formulation is highly challenging due to the nonconvexity of the PU rate constraint. We propose a solution that features a linearization-based alternative optimization method and a heuristic primal recovery method. We further develop a distributed algorithm to jointly optimize the covariance matrix of the transmitted signal vector at each SU node, bandwidth allocation at each SU link, rate control at each session source, and multihop/multipath routing. Extensive simulation results demonstrate that the performance of the proposed distributed algorithm is very close to that of the centralized algorithm, and the proposed formulation provides an efficient way to save power consumption significantly, while achieving the network utility very close to that achieved with full power consumption. [ABSTRACT FROM PUBLISHER]

In this paper, resilient transmission in a multicell multiple-input multiple-output (MIMO) interference wiretap channel model is studied. Each base station (BS) transmits confidential messages to its intended legitimate user with multiple antennas in the presence of eavesdroppers that can overhear the transmission. We study the problem of finding the optimal transmit covariance matrices at the BSs to maximize the secrecy sum rate, which is typically nonconvex and intractable to obtain a globally optimal solution. A distributed iterative optimization algorithm based on a novel decomposition framework across all users is proposed. The decomposition framework preserves the convexity of the objective function and linearizes the nonconvex part. At each iteration, the BSs simultaneously solve a sequence of problems that are decoupled convex approximations of the original secrecy sum-rate function. Moreover, the complexity of the algorithm is analyzed. Numerical results are presented to validate the effectiveness of the proposed distributed algorithm. [ABSTRACT FROM PUBLISHER]

This paper studies the impact of a multiple-input–multiple-output (MIMO) relay on the $K$- user multiple-input–single-output (MISO) interference channel (IC) when the relay has delayed feedback (i.e., delayed channel state information (CSI) or delayed channel output feedback) from each receiver, yet each transmitter has no knowledge about CSI. We first develop a new relay-aided retrospective interference alignment (r-RIA) and characterize the optimal sum degrees of freedom (DoFs) for the $K$- user MISO IC with a MIMO relay by providing a new matching outer bound. It is shown that the sum DoF does not decrease, even in the absence of direct links between transmitters and receivers, as long as $K$ is sufficiently large. We next show that a MIMO relay can provide a sum-DoF gain in the $K$- user MISO IC with delayed feedback to the relay in the absence of CSI at transmitter (CSIT), whereas relaying is shown to be not useful with instantaneous CSIT from the DoF perspective. [ABSTRACT FROM PUBLISHER]

Massive multiple-input multiple-output (MIMO) is a key technology in fifth-generation (5G) networks. By using a large number of antenna elements placed in a 2-D array, an evolved Node B (eNB) can form multiple vertical beams in the elevation domain and adaptively track moving vehicles. Thus, the throughput and spatial multiplexing efficiency in vehicle-to-infrastructure (V2I) access can be significantly increased. However, multipath spatial propagation in wireless channels results in the angular spread of the power arrival profile, which causes intersector interference in massive-MIMO beamforming and becomes a limiting factor for the system capacity. In this paper, we investigate the channel propagation characteristics and the intervehicle interference in the elevation-domain spatial multiplexing for V2I mobile access and develop a packet-level channel model that can be used for system design and network protocol simulations. First, a measurement campaign for the urban macrocell street uplink channels was performed using a 3-D MIMO channel sounder, and the elevation power spectra (EPSs) on the eNB side were measured. Then, the intersector interference in the vertical beamforming is evaluated based on the antenna array pattern and channel EPS. Finally, a packet-level channel model in the form of a finite-state Markov chain (FSMC) is proposed for the V2I elevation multiplexing uplinks. The model describes the received signal-to-interference ratio (SIR) variation when a vehicle is moving toward an eNB. The steady-state distribution of the FSMC is analytically derived and verified by simulations. Based on the stochastic process of the SIR, the concepts of “large/small-scale multiplexing fading” are proposed. The field measurement results in this work have revealed the spatial power arrival profiles of the V2I street channels that are critical for the MIMO system design, and the proposed packet-level channel model provides an enabling tool for the analysis and simulation of the V2I elevation multiplexing links in the 5G networks. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the spectral efficiency of multicell massive multiple-input–multiple-output (MIMO) systems with downlink training and a new pilot contamination precoding (PCP) scheme. First, we analyze the spectral efficiency of the beamforming training (BT) scheme with maximum-ratio transmission (MRT) precoding. Then, we derive an approximate closed-form expression of the spectral efficiency to find the optimal lengths of uplink and downlink pilots. Simulation results show that the achieved spectral efficiency can be improved due to channel estimation at the user side, but in comparison with a single-cell scenario, the spectral efficiency per cell in multicell scenario degrades because of pilot contamination. We focus on the practical case where the number of base station (BS) antennas is large but still finite and propose the BT and PCP (BT-PCP) transmission scheme to mitigate the pilot contamination with limited cooperation between BSs. We confirm the effectiveness of the proposed BT-PCP scheme with simulation, and we show that the proposed BT-PCP scheme achieves higher spectral efficiency than the conventional PCP method and that the performance gap from the perfect channel state information (CSI) scenario without pilot contamination is small. [ABSTRACT FROM AUTHOR]

In this paper, we examine orthogonal space–time block coding with receiver maximal ratio combining (OSTBC/MRC) and selection combining (OSTBC/SC) in multiple-input–multiple-output (MIMO) decode-and-forward (DF) relay networks with underlay spectrum sharing, considering optimal and suboptimal cases. The secondary network under consideration is equipped with multiple correlated antennas at the source, the relay, and the destination. On the other hand, the primary network is composed of $L$ primary users (PUs), each of which is equipped with multiple correlated antennas. For the considered underlay spectrum sharing, the transmit power condition is related by an interference limit on the primary network and the maximum transmission power in the secondary network. In particular, new exact expressions for the outage probability of the adopted system models are obtained. Moreover, simple asymptotic expressions for the outage probability are provided to enable the characterization of the achievable diversity orders and coding gains. To enhance the secondary network performance, optimal power allocation (PA) between the secondary source and the secondary relay is obtained based on the asymptotic outage probability under the constraints of total allowable transmit power at the secondary user (SU) and maximum allowable interference power limit at the PU. The derived analytical formulas herein are supported by numerical results to clarify the main contributions. [ABSTRACT FROM AUTHOR]

Interference alignment (IA) is a promising transmission technology enabling, essentially, the maximum achievable degrees of freedom (DOF) in $K$-user multiple-input–multiple-output (MIMO) interference channels. The ideal DOF of IA systems have been obtained using independent MIMO channels, which is, usually rarely observed in reality, particularly in indoor environments. Therefore, the data sum rate and symbol error-rate of IA are dramatically degraded in real-world scenarios since the correlation between MIMO channels decreases the signal-to-noise ratio (SNR) of the received signal after alignment. For this reason, an acceptable sum rate of IA in real MIMO-orthogonal frequency-division multiplexing (MIMO-OFDM) interference channels was obtained in the literature by modifying the distance between network nodes and the separation between the antennas within each node to minimize the spatial correlation. In this paper, we propose to apply transmit antenna selection to MIMO-OFDM IA systems either through bulk or per-subcarrier selection, aiming at improving the sum-rate and/or error-rate performance under real-world channel circumstances, while keeping the minimum spatial antenna separation of 0.5 wavelengths within each node. Two selection criteria are considered: maximum sum rate (Max-SR) and minimum error rate (Min-ER). To avoid subcarrier imbalance across the antennas of each user, which is caused by per-subcarrier selection, a constrained per-subcarrier antenna selection is operated. Furthermore, a suboptimal antenna selection algorithm is proposed to reduce the computational complexity of the optimal algorithm. An experimental validation of MIMO-OFDM IA with antenna selection in an indoor wireless network scenario is presented. The experimental results are compared with deterministic channels that are synthesized using hybrid electromagnetic (EM) ray-tracing models. Our performance evaluation shows that the practical feasibility of MIMO-OFDM IA systems is significantly increased by antenna selection in real-world scenarios. [ABSTRACT FROM AUTHOR]

Multiuser orthogonal frequency-division multiplexing (OFDM) and multiple-output multiple-output (MIMO) have been widely adopted to enhance the system throughput and combat the detrimental effects of wireless channels. Interference alignment has been proposed to exploit interference to enable concurrent transmissions of multiple signals. In this paper, we investigate how to combine these techniques to further enhance the system throughput. We first reveal the unique characteristics and challenges brought about by using interference alignment in diagonal channels. We then derive a performance bound for the multiuser (MIMO) OFDM interference alignment system under practical constraints and show how to achieve this bound with a decomposition approach. The superior performance of the proposed scheme is validated with simulations. [ABSTRACT FROM PUBLISHER]

Massive multiple-input–multiple-output (MIMO) antenna system implies the use of a large number of base station (BS) antennas to serve a relatively small number of user terminals (UTs) for extraordinary spectral efficiency. However, its performance is limited by pilot contamination due to unavoidable reuse of pilot sequences from UTs in different cells. In this paper, we analyze the performance of massive MIMO zero-forcing (ZF) systems using the time-shifted pilot scheme, which was known to combat pilot contamination effectively using conjugate beamforming if there is a very large number of antennas. We derive expressions for achievable sum rates and the signal-to-interference-plus-noise ratios (SINRs) of forward and reverse links if the number of BS antennas is finite. Then, the impact of system parameters, such as cell radius, transmit power, group number (a parameter related to the time-shifted pilot scheme), BS antenna number, etc., on the system performance are revealed. Our model embraces a series of previous works as special cases. Moreover, we compare the performance of conjugate and ZF precoders, from which a simple but effective large-scale fading-based UT scheduling scheme is proposed to enhance the system throughput. [ABSTRACT FROM PUBLISHER]

In this paper, we consider unicast/multicast multicell cooperative transmission with interference among users/user groups. In this context, we derive the optimal minimum variance distortionless response (MVDR)-based successive minimum variance beamforming (SMVB) scheme that achieves a superior sum-rate performance compared with the block diagonalization scheme. Subsequently, we derive an optimal joint power allocation and broadcast beamforming scheme for multicell cooperative broadcast transmission for a pooled power constraint at the base stations. This scheme is extended to include per base station power constraints by formulating it as a relaxed semi-definite program (SDP). We also consider the multicell cooperative uplink scenario and derive a successive multiuser (MU) uplink beamforming (SMUB) scheme that maximizes the signal-to-interference-plus-noise ratio (SINR) of each user. Next, we consider imperfect channel state information (CSI) and derive a robust beamforming scheme for the downlink, based on minimizing the worst-case interference by formulating it as a second-order cone program. It is demonstrated that the corresponding robust beamformer for the uplink transmission can be derived by employing the multidimensional covariance fitting approach. Simulation results are presented to demonstrate the superior sum-rate performance of the proposed multicell transmission schemes. The performance is also compared with several bounds for cooperative multicell scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we develop beamforming (BF) schemes to minimize the total transmitted power of both uplink (UL) and downlink (DL) in two-tier network with in-band wireless backhaul (WB) while the target rates of user equipment (UE) are satisfied under the backhaul constraints. We propose a centralized BF scheme with an alternate update algorithm optimizing the BF matrices and power allocation vectors. Then the UL-DL feasible target rate region of the proposed scheme is analyzed, which can be enlarged in both UL and DL by increasing the number of antennas of small cell base stations (SBSs). Simulation results show that the proposed in-band WB system for two-tier network can save the power consumption by 33.5% and 82.1% compared with the out-of-band WB system and conventional one-tier network, respectively, at the UE target rates of 80 Mb/s in DL and 40 Mb/s in UL. In addition, we propose a distributed BF scheme to locally optimize the variables at each SBS, which can achieve above 90% of the feasible target rate region of the centralized scheme without the instantaneous information exchange. [ABSTRACT FROM AUTHOR]

Recently, heterogeneous network (HetNet) has been introduced as an appropriate strategy to cope with the explosive growth of wireless traffic. To address the issue of severe interference in the HetNet, we can consider interference alignment (IA), which achieves the maximum degrees of freedom (DOFs) in multiple-input–multiple-output (MIMO) interference channels (ICs). However, an anticipated performance of the MIMO IA is difficult to be clarified, particularly with different numbers of antennas across the nodes when designing an appropriate system. In this paper, we thus study antenna configurations for the three-user MIMO IA with respect to the intended data stream tuple, i.e., DOF. For simple analysis, we consider two-tier network with two types of data stream numbers in a system. First, the dimension of the subspace occupied by interference is derived by aligning the interference in the signal space of the MIMO IA. After this, the suitable numbers of antennas are computed depending on the transmitted data stream numbers. Our obtained results provide an insight on how the performance of the MIMO IA is affected as the system configurations change. Furthermore, we discuss how to maximize the performance of such systems when the available numbers of antennas are finite. The actual simulations with an iterative IA confirm the validity of our derived results. [ABSTRACT FROM PUBLISHER]

In this paper, a novel unified transmission framework in the context of both decode-and-forward (DF) and amplify-and-forward (AF) protocols was proposed for a two-hop multiple-input–multiple-output (MIMO) alternate half-duplex (HD) relaying system with $M$ antennas for each node, which can achieve the maximum M$ degrees of freedom (DoFs) of the system, compared with the existing interference alignment (IA) schemes that can only get \3M/\4 DoF. Furthermore, the proposed schemes require only two relays against three relays invoked in the existing IA schemes. Moreover, the proposed schemes are valid for the cases where the number of antennas $M$ can be either even or odd, whereas the existing IA schemes can only apply for an even number of antennas $M$. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new three-user network information flow model, referred to as the triangular multiple-input–multiple-output (MIMO) relay (TMR) channel, which consists of three users and three relays equipped with nU and nR antennas, respectively. Each user sends two independent messages to the other two users via the adjacent relays in two time slots, which are referred to as the multiple-access and broadcast stages. We derive a novel simultaneous signal and interference alignment for the proposed TMR channel in a scenario where there are fewer antennas at each relay than at each user (nR < nU ) . An optimized pseudo-inverse scheme based on an efficient gradient projection algorithm is proposed to solve the simultaneous alignment problem. By deriving a gradient over weighted sum-rate maximization and applying a gradient descent method, the optimal beamforming vectors are obtained to maximize the effective signal-to-noise ratios. Furthermore, to obtain rapid convergence speed and reduce computational complexity, we introduce a quasi-Newton method, which is referred to as the Broyden–Fletcher–Goldfarb–Shanno algorithm, by approximating the Hessian matrix of a pure Newton method. The convergence of the proposed gradient algorithm is guaranteed by proposing a line search algorithm. Finally, a performance evaluation shows that the proposed scheme offers a higher sum rate, produces a better outage probability, and achieves a higher multiplexing gain than the existing schemes. [ABSTRACT FROM PUBLISHER]