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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]

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]

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 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 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]

This correspondence paper addresses linear precoding design for sum rate maximization in low-latency orthogonal frequency-division multiplexing systems. In order to mitigate the overhead of cyclic prefix (CP) originating from shortened symbol duration for low-latency communications, 5G wireless systems need to adopt short CP lengths. As channel delay spread must be less than the CP length, we first derive the effective root-mean-square (RMS) delay spread and the achievable rate using the zero-forcing assumption. We construct a sum rate optimization problem for each user subject to delay spread constraints and then convert the problem into a solvable convex problem along with a semi-definite relaxation technique. The precoding matrix is finally obtained by solving optimization problems for all users. Numerical results reveal that the proposed scheme attains superior performance to the conventional sum rate optimization, as well as small RMS delay spread. [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]

Physical layer security has drawn significant attention in recent years because of its advancement in preventing confidential information leakage to eavesdroppers. In this paper, we focus on secure beamformer designs in multiuser multi-input multi-output (MU-MIMO) systems with a multi-antenna eavesdropper attempting to overhear the confidential information of a particular user. Unlike the existing work, we aim to exploit the inherent multi-user interference to disrupt the reception of the eavesdropper and enhance the security of wireless communications. Particularly, utilizing practical signal-to-interference-noise metrics, the objective of the secure beamformer design is to minimize the eavesdropper's SINR, while providing legitimate users with required prespecified SINRs to guarantee the qualify of service. We propose secure beamformer designs for both downlink and uplink transmissions, under the conditions of known and unknown eavesdropper's channels, respectively. With the proposed secure beamformers, the multiuser signal behaves like the artificial noise or distributed friendly jamming, which can further degrade the reception of the eavesdropper. Extensive simulation studies confirm our analytical performance predictions and illustrate the advantages of proposed beamformer designs for secure MU-MIMO transmissions. [ABSTRACT FROM AUTHOR]

This paper investigates simultaneous wireless information and power transfer (SWIPT) in the ad hoc network, where access points (APs) with multiple antennas can transfer energy as well as information using a common spectrum resource. The receiving nodes decode the incoming information data (information decoding, ID) and/or harvest the RF energy (energy harvesting, EH), where two different receiving node architectures—time switching (TS) and power splitting (PS)—are considered. By using a stochastic geometry approach, we aim to analyze the transmission capacity and the harvested energy per unit area as performance measures of the SWIPT in the ad hoc network. From the analytical results, we can derive the optimal node densities of ID nodes and EH nodes for TS architectures and, furthermore, optimize the power splitting ratio jointly with the node density for the PS architectures such that the harvested energy per unit area is maximized when the target transmission capacity is given. The proposed node density optimization gives us a useful insight into the design of SWIPT-based ad hoc network, where we can show how densely the APs/nodes can be deployed in a given area and furthermore, find that the ad hoc network with PS receiving nodes outperforms that with TS receiving nodes for a large target transmission capacity, and vice versa. [ABSTRACT FROM AUTHOR]

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]

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, we study the uplink in a single-cell massive multiple-input–multiple-output system. The base station (BS) is equipped with three antenna arrays, each covering one third of the cell area. Each antenna array comprises a large yet finite number of antennas. The single-antenna users are randomly and uniformly distributed in the cell, transmitting to the BS utilizing full channel inversion power control. All users experience Rician fading. Receiver maximum-ratio-combining is performed at the BS. Under such a setting, we focus on one cell sector and analyze the intrasector interference in a realistic situation where the number of BS antennas is not extremely large compared with the user number. In particular, we show that, due to the line-of-sight (LoS) component of the channel, the interference is partially determined by the angles of arrival of the signals. We approximate the LoS component interference by a Beta mixture. The interference in Rician fading is then modeled as a noncentral chi-square distribution with a random noncentrality parameter, corresponding to the LoS component. The approximate interference distribution can be used to compute signal-to-interference-ratio-dependent metrics such as outage probability and average throughput. [ABSTRACT FROM AUTHOR]

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]

In this paper, the problem of mode switching in multiple-input–multiple-output (MIMO) broadcast channels utilizing the Per-User Unitary Rate Control (PU2RC) transmission scheme is considered. Since there is no mathematical expression for the achievable rate of the PU2RC systems, it is proposed to approximate them using proper bounds. It is shown that certain simple feedback distributions will lead to tight bounds on the achievable rates of the PU2RC systems. The proposed bounds are used for the calculation of mode-switching points and maximization of the system rate under different multiplexing order conditions. The asymptotic behavior of the preferred modes is also studied under high-signal-to-noise-ratio (SNR) and low-SNR conditions, and it is shown that the single-user transmission mode is the preferred mode for both regimes. [ABSTRACT FROM PUBLISHER]

In this paper, we study the performance of space-shift keying (SSK) modulation for multiple-input–multiple-output (MIMO) wireless systems in the presence of multiple-access interference. More specifically, a synchronous multiuser scenario is considered. The main technical contributions of this paper are given as follows: Two receiver structures based on the maximum-likelihood (ML) criterion of optimality are developed and analytically studied, i.e., single- and multiuser detectors. Accurate frameworks for computing the average bit error probability (ABEP) over independent identically distributed (i.i.d.) Rayleigh fading channels are proposed. Furthermore, simple and easy-to-use lower and upper bounds for performance analysis and system design are introduced. The frameworks account for the near–far effect, which significantly affects the achievable performance in multiple-access environments. In addition, we extend the analysis to generalized SSK (GSSK) modulation, which foresees multiple active antennas at the transmitter. With respect to SSK modulation, GSSK modulation achieves higher data rates at the cost of increased complexity at the transmitter. The performance of SSK and GSSK modulations is compared with that of conventional phase-shift keying (PSK) and quadrature amplitude modulation (QAM) schemes, and it is shown that SSK and GSSK modulations can outperform conventional schemes for various system setups and channel conditions. In particular, the performance gain of SSK and GSSK modulations increases for increasing values of the target bit rate and of the number of antennas at the receiver. Finally, we put forth the concept of coordinated multipoint (or network MIMO) SSK (CoMP-SSK) modulation as a way of exploiting network cooperation and the spatial-constellation diagram to achieve high data rates. Analytical derivations and theoretical findings are substantiated through extensive Monte Carlo simulations for many setups. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a novel relaying technique employing scheduling, precoding, beamforming, and power allocation for a multiuser multiple-input–multiple-output (MU-MIMO) relay network. In the proposed scheme, the interference is canceled by using a combination of transmit–receive weights and Tomlinson–Harashima precoding (THP). To achieve data rate fairness among different users and further improve the performance of MU-MIMO relay networks, we propose a low-complexity power allocation (LC-PA) to allocate power to each user. In addition, an algorithm to select a subset of users that has maximum sum rate performance is proposed. The performance of the proposed scheme is investigated by examining the sum rate of the system for different user selection algorithms and different power allocation schemes. [ABSTRACT FROM PUBLISHER]

Millimeter wave (mmWave) has been widely considered as a promising technology in the next generation wireless communication systems. Various beam-based directional transmission techniques have been proposed to compensate high pathloss caused by mmWave properties. However, mobility effect of users potentially causes severe inter-beam interferences, which has not been fully-investigated in existing studies. In this paper, we have analyzed different types of mobility-aware beam interference models. Additionally, the theoretical SINR is derived based on channel statistics and the trajectories of users. We propose a mobility-aware subband and beam resource allocation (MSBA) scheme for the mmWave subband-beam massive multi-input multi-output (SB-MMIMO) systems. The proposed MSBA benefits from reduced computation complexity for maximizing system throughput constrained by quality-of-service (QoS) demands of users. The first phase of MSBA scheme is responsible for resource block assignment; while the second phase allocates beamwidth and beam directions according to the analytical derivations. Numerical results show that the proposed MSBA scheme can effectively achieve the highest system throughput and the lowest complexity compared to existing schemes in open literatures. [ABSTRACT FROM AUTHOR]

Deploying a large number of distributed access points (AP)s to serve a smaller number of users is one of the promising network architectures for future wireless communication systems. Such network architecture can be operated as a distributed massive multiple-input multiple-output (MIMO) system or as a small-cell (SC) system to satisfy the anticipated high rate requirements for beyond-5G networks. However, in a practical scenario with non-ideal hardware components and high-velocity users, the network experiences an inevitable performance degradation. This paper aims at analyzing the network performance under the operation of distributed massive MIMO and SC systems, taking into account the impairments of real and dynamic systems. Considering multiple-antennas APs, we derive novel closed-form expressions for the downlink (DL) spectral efficiency of both systems. We reveal that limiting the number of served users per AP in distributed massive MIMO systems leads to a corresponding loss in the performance, especially under max-min power control. Besides, despite the SC system provides the largest per-user average DL rate under the deployment of ideal APs, distributed massive MIMO systems become superior in the presence of non-ideal APs. Notably, while increasing the number of deployed non-ideal APs can reduce the introduced loss in distributed massive MIMO systems, this leads to an extra performance loss in SC systems. Finally, we show that the presence of high-velocity users is more harsh in SC systems. In addition, our results show that the SC system operation is more suitable for low-velocity users, however, it is better to operate networks with high velocities users under the distributed massive MIMO systems operation. [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]

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]

This paper addresses the problem of coordinated beamforming across a group of base stations (BSs) and frequency slots in the downlink of a multiple-input multiple-output (MIMO) orthogonal frequency-division multiple-access (OFDMA) cellular network. Three figures of merit are considered for system design under a per-BS power constraint: 1) the weighted sum of the rates (WSR) on the frequency slots of the coordinated BSs; 2) the global energy efficiency (GEE), defined as the ratio between the network sum rate and the corresponding consumed power; and 3) the weighted sum of the energy efficiencies (WSEE) on the frequency slots of the coordinated BSs. The Karush–Kuhn–Tucker (KKT) conditions of the considered optimization problems are first derived to gain insight into the structure of the optimal beamformers. Then, we propose a suboptimal design method that can be applied to all considered figures of merit. Numerical results are provided to assess the performance of the proposed beamforming strategies. [ABSTRACT FROM PUBLISHER]

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]

For massive multiuser multiple input multiple output (MIMO) (MU-MIMO) systems, pilot contamination (PC) and data interference (DI) are two main factors that affect the accuracy of the superimposed pilot (SP) based channel estimation, provided that the channel coherence time is less than the total number of users. In this paper, to tackle the effect of the PC, we propose a block-diagonal Grassmannian line packing (GLP) approach, in which the specific sequences for different cells are first designed based on the GLP, and then are block-diagonally extended to form the SP matrices for the users in different cells. To also alleviate the effect of DI on the channel estimation, with the designed SP matrices, an iterative channel estimation (ICE) method based on Tikhonov regularization is presented. The impact that the proposed ICE method has on the signal-to-interference-plus-noise ratio with matched filtering receiver is theoretically analyzed. Moreover, the optimal power allocation factor to the SP by maximizing the spectral efficiency (SE) of the target cell is also derived. Numerical results show that the proposed ICE method with the designed SP matrices effectively mitigates the effects of the PC and DI, and hence, improves the accuracy of channel estimation and further the SE of the massive MU-MIMO systems. [ABSTRACT FROM AUTHOR]

A major challenge in designing a spectral co-existence between radar and communication systems is how to simultaneously provide efficient utilization of the shared spectrum while maintaining a reliable performance for both systems. Due to its flexibility in using linear independent waveforms and superiority in terms of target detection and estimation, the collocated multiple-input-multiple-output (MIMO) radars provide a paramount capability in realizing spectrum sharing with communication systems. In this paper, we consider the use of joint transmit and receive beamformers for both the MIMO radar and MIMO communication systems. Specifically, we design a two-tier alternating optimization spectrum sharing framework that is based on interference alignment (IA) approach. The effectiveness of spectrum sharing between radar and communication systems is guaranteed by mitigating the mutual interference signals in the shared spectral band. Subsequently, motivated by the excellent performance provided by IA in different wireless network scenarios, we propose a spectrum sharing framework that consists of a main iterative algorithm with two subalgorithms included within its operation. The first subalgorithm is used to maximize the signal-to-interference-plus-noise ratio of the radar system, whereas the second one is utilized to maximize the average sum-rate of the communication system. The main iterative algorithm is proposed to jointly optimize the transmit and receive beamforming filters of both systems by performing alternating optimization between the two subalgorithms. The convergences of the proposed algorithm and its subalgorithms are numerically verified. Simulation results are provided to confirm the superiority of the proposed framework for both systems. [ABSTRACT FROM AUTHOR]

The fifth generation communication systems aim to achieve higher capacity and more user access. Full-duplex (FD) communication can achieve twice the spectral efficiency of the conventional half-duplex systems under ideal conditions, and FD relay is a common application of FD technology. In this paper, we propose a modified signal-to-leakage-and-noise ratio (SLNR) precoding scheme for the FD multiuser MIMO relay system, in which the self-interference (SI) of the relay is considered. In contrast to block diagonalization (BD) precoding and zero-forcing (ZF) precoding, SLNR precoding does not have an antenna dimension limitation, which enables it to support more antennas and users. In addition, SLNR precoding balances the interference and noise of a system, whereas BD precoding and ZF precoding only consider the interference. The numerical results show that the proposed SLNR precoding scheme can achieve better performance with low SI. With a reasonable sum capacity loss, the SLNR precoding scheme provides more user access despite a limited number of transmit antennas. [ABSTRACT FROM AUTHOR]

In a massive multiple-input multiple-output (MIMO) system, the serious pilot contamination problem severely restricts its ability to boost the spectrum utilization. To tackle this problem, the conventional concept of softly reusing the spectrum resources for the inner regions of the neighboring cells has been extended to reuse the pilot resources so as to accommodate more users. Alternatively, properly selecting the users to reuse the pilots among the neighboring cells can alleviate the pilot contamination problem as well. In this paper, we delicately integrate these two concepts to properly reuse the pilots allocated to the outer regions of the cells. By well designing the hazard- and secure-edge regions to manage the pilot reuse, the increment of interference can be effectively suppressed, and, consequently, the more accommodated users can contribute to the remarkably higher sum data rates. Furthermore, via some adaptive power adjustment for the users within different regions, the user data rates can further be significantly enhanced. [ABSTRACT FROM AUTHOR]

Due to the use of an appropriately designed pulse shaping prototype filter, filter bank multicarrier (FBMC) system can achieve low out of band (OoB) emissions and is also robust to the channel and synchronization errors. However, it comes at a cost of long filter tails, which may reduce the spectral efficiency significantly when the block size is small. Filter output truncation (FOT) can reduce the overhead by discarding the filter tails but may also significantly destroy the orthogonality of FBMC system, by introducing intercarrier interference (ICI) and intersymbol interference (ISI) terms in the received signal. As a result, the signal-to-interference ratio (SIR) is degraded. In addition, the presence of intrinsic interference terms in FBMC also proves to be an obstacle in combining multiple-input multiple-output (MIMO) with FBMC. In this paper, we present a theoretical analysis on the effect of FOT in an MIMO-FBMC system. First, we derive the matrix model of MIMO-FBMC system, which is subsequently used to analyze the impact of finite filter length and FOT on the system performance. The analysis reveals that FOT can avoid the overhead in the time domain but also introduces extra interference in the received symbols. To combat the interference terms, we then propose a compensation algorithm that considers odd and even overlapping factors as two separate cases, where the signals are interfered by the truncation in different ways. The general form of the compensation algorithm can compensate all the symbols in a MIMO-FBMC block and can improve the SIR values of each symbol for better detection at the receiver. It is also shown that the proposed algorithm requires no overhead and can still achieve a comparable bit error rate (BER) performance to the case with no filter truncation. [ABSTRACT FROM AUTHOR]

This paper presents a generalized closed-form beamforming technique that can achieve the maximum degrees of freedom in compounded multiple-input multiple-output (MIMO) broadcast channels with mixed classes of multiple-antenna users. The contribution is first described within the context of a three-cell network and later extended to the general multicell scenario where we also show how to determine the conditions required to align the interference in a subspace that is orthogonal to the one reserved for the desired signals. This is then followed by an analysis of the impact of antenna correlation for different channel state information acquisition models. The proposed scheme is examined under both conventional and large-scale MIMO systems. It will be shown that the proposed technique enables networks with any combination of user classes to achieve superior performance even under significant antenna correlation, particularly in the case of the large-scale MIMO systems. [ABSTRACT FROM AUTHOR]

The nested array, implemented by nonuniform antenna placement, is an effective approach to achieve $O(N^2)$ degrees of freedom (DOF) with an antenna array of $N$ antennas. Such DOF refers to the number of directions of incoming signals that can be resolved. With the increased number of DOF, an important application of nested array is to nullify interference signals from multiple directions. In this paper, we apply nested array in a massive multiple input multiple output (MIMO) heterogeneous network (HetNet) for interference management. With a nested array, a base station (BS) can nullify a certain number of interference signals based on their directions. Then, a key design issue is how to select the set of interference sources to be nullified at each BS. As the DOF of each BS is used to resolve both desired signals and interference, the number of interference signals that can be nullified depends on the number of users served by the BS. Thus, user association is another factor that impacts the system performance and should be jointly considered with interference nulling. We formulate the joint interference nulling scheduling and user association problem as an integer programming problem, aiming to maximize the sum rate of all users subject to BS DOF constraints. We first investigate the case of interference nulling with a given user association, and propose a scheme to solve a relaxed problem as well as derive a performance upper bound. Then, we propose a distributed joint interference nulling and user association scheme based on a poly matching between users and BSs. Simulation results show that the proposed schemes effectively improve the sum rate and achieves a near optimal performance. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the resource allocation problem in two-tier heterogenous networks (HetNets) with massive MIMO, where two frequency bands, cellular frequency band and millimeter wave frequency band, are used for wireless backhaul links. To coordinate the interference among small cells (SCs), SCs are grouped into multiple SC clusters (SCCs), where SC users are jointly served by SC base stations (BSs) (SBSs) belonging to the same SCC. To eliminate the multi-user and inter-tier interference, we propose a block diagonalization based precoding scheme at macro-BS and each SCC, where the transmit precoding matrix for users is projected onto the null space of interference channels. Following this, we formulate a power allocation optimization problem to maximize the downlink sum rate of the system subject to per-SCC power and users’ quality of service requirements. Since the formulated problem is nonconvex, we transform it into a convex one by appropriate approximation, and a constrained concave convex procedure based iterative algorithm is proposed to obtain the solution. Furthermore, we prove that the obtained solution converges to the local optimum. Meanwhile, according to the structure of the original formulated problem, we divide it into multiple subproblems and propose an optimal iterative water-filling algorithm. Next, we extend the original problem with per-SBS power constraint, which results in that the precoding of each SCC has to be redesigned. On this basis, we propose an iterative water-filling algorithm to obtain the optimal power allocation and precoding. Numerical results are presented to verify the performance of our proposed algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, we present a novel matrix decomposition method, called generalized multi-unitary decomposition (GMUD), and use it to achieve robust multi-antenna multi-user multiple-input–multiple-output (MIMO) precoding with limited and partial channel information feedback. GMUD transforms complex matrix {H} into \bf H = \bf P\theta,\, r{\bf R}r{\bf Q}\theta,\, r^{H}, where \bf Rr is a lower triangular matrix, and \bf P\theta,\, r and \bf Q\theta,\, r are unitary matrices. A unique feature of GMUD is that it gives multiple solutions of the unitary matrices \bf P\theta,\, r and \bf Q\theta,\, r based on two parameters, namely the direction parameter \theta and magnitude parameter r. This property enables the GMUD precoder to steer the precoding vectors of different users to jointly optimize their performance. Compared with regularized-inverse precoding (an existing multi-user MIMO precoding technique that we have extended to handle multiple receive antennas), the advantages of GMUD precoding are that it requires only partial channel state information (CSI) from the users, and its performance is robust to CSI quantization. [ABSTRACT FROM PUBLISHER]

Interference alignment (IA) has been recognized as a promising technique to obtain large multiplexing gain in multiple-input–multiple-output (MIMO) interference channels. Most existing IA schemes require global channel state information (CSI) at the transmitter to design precoding vectors and, thus, result in significant capacity overhead in the feedback link. To reduce the feedback overhead, in this paper, we investigate the IA scheme employing differential CSI feedback over time-correlated MIMO channels. Specifically, we analyze the achievable sum-rate performance using differential feedback and derive the minimum differential feedback rate to achieve the maximum multiplexing gain. We also provide the upper bound of the sum-rate performance loss due to the limited differential feedback rate. Finally, the analytical results are verified by simulations in a practical IA scheme with differential CSI feedback using Lloyd's quantization algorithm. [ABSTRACT FROM PUBLISHER]

We consider linear precoding in the downlink of a multiuser multiple-input–single-output (MISO) overlay cognitive radio (CR) network, wherein a primary base station (PBS) and a cognitive base station (CBS) share the same frequency band to transmit to a number of primary users (PUs) and secondary users. Conventionally, linear precoding techniques in a CR network aim to limit or completely cancel interference to the PUs while achieving maximum downlink throughput of the CR system. In this paper, we investigate novel adaptive linear precoding techniques at the CBS to exploit the interference to the primary and secondary systems, instead of its cancellation, by exploring the potential of making use of interference energy when the interference between the two systems is mutually constructive on an instantaneous basis. By doing so, the received signal-to-noise ratio (SNR) is enhanced by the signal energy gleaned from the constructive interference. In this direction, constructive-interference-based adaptive linear precoding techniques are proposed for the CR network, assuming a simple zero-forcing precoder at the PBS and noncausal knowledge of the primary message at the CBS. The presented analysis and simulations show that the proposed precoding techniques outperform conventional techniques, as the CR transmission actively enhances the performance of the PUs through constructive interference while achieving significant throughput for its own transmission. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a sequential and incremental precoder design for downlink joint transmission (JT) network multiple-input–multiple-output (MIMO) systems with imperfect backhaul links. The objective of our design is to minimize the maximum of the substream mean square errors, which dominates the average bit error rate (BER) performance of the system. In the proposed scheme, we first optimize the precoder at the serving base station (BS) and then sequentially optimize the precoders of nonserving BSs in the JT set according to the descending order of their probabilities of participating in the JT. The BS-wise sequential optimization process can improve system performance when some BSs have to temporarily quit the JT operations because of poor instant backhaul conditions. In addition, the precoder of an additional BS is derived in an incremental way, i.e., the sequentially optimized precoders of the previous BSs are fixed, and thus, the additional precoder plays an incremental part in multi-BS JT operations. An iterative algorithm is designed to jointly optimize the substream precoder and substream power allocation for each additional BS in the proposed sequential and incremental optimization scheme. Simulations show that, under the practical backhaul link conditions, our scheme significantly outperforms the autonomous global precoding scheme in terms of BER performance. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the performance analysis of the maximum eigenmode beamforming (MEB) scheme with equal power allocation (EPA) over practically coded multiple-input multiple-output (MIMO) multiple-access channels (MACs). Both the scenarios of perfect and imperfect channel state information (CSI) at the transmitters (CSIT) are considered. Analytical and numerical results show that MEB with EPA can achieve significant power savings and is less sensitive to CSIT error than other alternatives. [ABSTRACT FROM PUBLISHER]

This paper analyzes the average bit error rate (BER) of multiple-input–multiple-output (MIMO) systems in transmit-correlated Rayleigh flat-fading channels. The receiver scheme is based on the minimum mean square error (MMSE) criterion, and the input may be precoded to optimize the communication. Accurate closed-form formulations for the average BER are derived. [ABSTRACT FROM PUBLISHER]

Multicell cooperative processing (MCP) has been recognized as a promising technique for increasing the spectral efficiency of future wireless systems. Unfortunately, the provided benefits of MCP come at the cost of increased radio feedback and backhaul overhead; for downlink transmission in frequency-division duplexing (FDD) systems, users need to feed back their channel-state information (CSI) to the MCP scheduler, and user data need to be exchanged between all cooperating base stations (BSs) through the backhaul network. In the context of conventional noncooperative networks, it has been suggested that radio feedback load could be reduced by preventing users with low-quality channels from feeding back their CSI (concept of selective feedback), at the cost of a small fraction of the multiuser diversity gain. In this paper, we investigate the translation of this selective feedback concept to MCP systems. According to this technique, users with weak interference links are prevented from feeding back their full CSI to the MCP scheduler. Although efficient, this technique alone cannot mitigate the backhaul overhead related to routing user data possibly to several BSs. To overcome this condition, we propose two schemes: one scheme based on Media Access Control (MAC)-layer scheduling and the other scheme based on physical-layer precoding. These schemes, combined with feedback load reduction, allow for a substantial mitigation of the MCP overheads related to feedback and backhaul load. We analyze the improvements in terms of both user-to-BS feedback reduction and backhaul load reduction, and we show that this framework results in a good tradeoff between performance and overhead for multicell cooperative networks. [ABSTRACT FROM PUBLISHER]

Channel estimation is critical to the performance of a multiple-input multiple-output and orthogonal frequency-division-multiplexing (MIMO-OFDM) communication system. Current MIMO-OFDM channel estimation techniques suffer from either high complexity or poor performance. In fact, this issue has become one of the bottlenecks of a practical MIMO-OFDM system. This paper solves the problem by introducing a new technique that has minimum complexity and yet provides superior channel tracking performance close to a minimum mean square error (MMSE) estimate over a wide range of channel selectivity and noise variance. The performance was evaluated via numerical simulations. [ABSTRACT FROM PUBLISHER]

We consider the scenario in which multiple transmitters send signals to a receiver in the asynchronous multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) mode. A receiver structure that can perform joint synchronization and space-time equalization for the asynchronous MIMO-OFDM systems is proposed. We first introduce a novel space-time equalization algorithm based on the channel state information. This algorithm aims to null the cochannel interference and combat asynchronism, as well as minimize a lower bound to the symbol error rate in the asynchronous MIMO-OFDM system. In the second part of this paper, we propose a training-based minimizing mean-square-error (MMSE) algorithm to jointly obtain frequency offsets and equalization delays. We compensate for the effects of the frequency offsets and the propagation delays with these estimated parameters and then use the proposed direct training-based equalizer design algorithm to obtain the equalizer coefficients. The simulation section illustrates the desirable bit-error-rate (BER) performance of our proposed algorithms. [ABSTRACT FROM AUTHOR]

Full-duplex (FD) multiple-input multiple-output relaying has been considered an effective scheme to increase the spectral efficiency for wireless communications. As known, the main problem for the FD system is the cancellation of loop interference (LI). In this paper, we propose using the joint source/relay precoding to reduce the influence of LI. Therein, linear precoders are used at the source and relay, while the minimum mean-squared-error receiver is adopted at the destination. The joint precoder design is complicated when spatial multiplexing is exploited for signal transmission. To solve the problem, we propose an iterative method in which the original problem is split into two subproblems. With some matrix properties, we then show that each subproblem can be formulated as a convex optimization. Finally, a closed-form solution can be obtained with the Karush–Kuhn–Tucker conditions. Using a mean-squared-error upper bound, we also propose a low-complexity method to reduce the computational complexity. The proposed precoders have closed-form expressions, which is a great advantage in real-world implementation. Simulation results show that the proposed methods significantly outperform existing ones. [ABSTRACT FROM AUTHOR]

Cognitive radio (CR) in conjunction with multiple-input multiple-output (MIMO) orthogonal frequency-division multiple access is a candidate technology for future mobile radio networks. The short communication range of underlay CR systems is commonly a major limiting factor. In this paper, we propose a computationally and spectrally efficient resource allocation scheme for multiuser MIMO orthogonal-frequency-division-multiplexing-based underlay CR networks to provide good spectral efficiency gain and, therefore, increased communication range. Since the formulated optimization problem defines a mixed-integer programming (combinatorial task) that is hard to solve, we propose a two-phase scheme to produce efficient solutions for both the downlink and the uplink. Particularly, the first procedure elaborates on an adaptive precoding that is characterized by spectral efficiency due to the degrees of freedom it can provide. The second procedure develops a fast subcarrier mapping algorithm, which can be worked out through optimal power distribution among the CR users. The proposed scheme is optimal for the downlink but, however, near-optimal for the uplink. Simulation results demonstrate the bandwidth and computational efficiencies of the proposed scheme compared with the state of the art. [ABSTRACT FROM AUTHOR]

This paper considers a multipair two-way amplify-and-forward (AF) relaying system, where multiple pairs of full-duplex users are served via a full-duplex relay with massive antennas, and the relay adopts maximum-ratio combining/maximum-ratio transmission (MRC/MRT) processing. The orthogonal pilot scheme and the least square method are first exploited to estimate the channel state information (CSI). When the number of relay antennas is finite, we derive an approximate sum rate expression which is shown to be a good predictor of the ergodic sum rate, especially with a large number of antennas. Then, the corresponding achievable rate expression is obtained by adopting another pilot scheme which estimates the composite CSI for each user pair to reduce the pilot overhead of channel estimation. We analyze the achievable rates of the two pilot schemes and then show the relative advantages of the two methods. Furthermore, power allocation strategies for users and the relay are proposed based on sum rate maximization and max-min fairness criterion, respectively. Finally, numerical results verify the accuracy of the analytical results and show the performance gains achieved by the proposed power allocation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework to evaluate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in cognitive radio networks (CRNs). The proposed framework is discussed in three typical CRN paradigms: underlay CRNs (UCRNs), overlay CRNs (OCRNs), and interweave CRNs (ICRNs). The EE–SE relation for three CRNs is expressed in the closed-form formulation, in which the optimal (suboptimal) EE solution as the function of SE is deduced with the corresponding limits. The theoretical analysis and numerical results indicate that the EE–SE relation in CRNs is not contrary, i.e., an optimal EE–SE tradeoff can be achieved. The proposed framework provides a useful guidance in the design of practical green CRNs. [ABSTRACT FROM AUTHOR]