Utilizing complex-valued neural networks (CVNNs) in wireless communication tasks has received growing attention for their ability to provide natural and effective representation of complex-valued signals and data. However, existing studies typically employ complex-valued versions of simple neural network architectures. Not only they merely scratch the surface of the extensive range of modern deep learning techniques, theoretical understanding of the superior performance of CVNNs is missing. To this end, this paper aims to fill both the theoretical and practice gap of employing CVNNs in wireless communications. In particular, we provide a comprehensive description on the various operations in CVNNs and theoretically prove that when the output dimension is large, the CVNN requires fewer layers than its real-valued counterpart to achieve a given approximation error of a continuous complex-valued function. Furthermore, to advance CVNNs in the field of wireless communications, this paper focuses on the transformer model, which represents a more sophisticated deep learning architecture and has been shown to have excellent performance in wireless communications but only in its real-valued form. In this aspect, we propose a fundamental paradigm of complex-valued transformers for wireless communications, including the complex-valued embedding module, encoding module, decoding module, and output projection module. Leveraging this structure, we develop customized complex-valued transformers for three representative applications in wireless communications: channel estimation, user activity detection, and joint design of pilot, feedback quantization, and precoder. These applications utilize transformers with varying levels of sophistication and span a variety of tasks, ranging from regression to classification, supervised to unsupervised learning, and specific module design to end-to-end design. Experimental results verify the theoretical advantage and effectiveness of the complex-valued transformers for the above three applications compared to other traditional real-valued neural network-based methods.

Joint activity detection and channel estimation is a crucial task in grant-free random access for massive machine-type communications. To enhance communication quality, intelligent reflecting surfaces (IRSs) have been proposed as a promising technology by controlling the propagation environment with passive reflecting elements. However, due to their passive nature and the non-Gaussian device-IRS-BS composite channels, IRSs introduce significant challenges for joint activity detection and channel estimation. To this end, this paper establishes an accurate statistical model for the composite channel, demonstrating that it follows a variance-gamma (VG) distribution. Based on the exact channel statistics, this paper employs a Bernoulli-VG prior and extends the standard approximate message passing algorithm to learn the Gamma-distributed channel variance within an expectation-maximization framework. Additionally, this paper introduces a novel approach to enforce consistency in device activity status across all base station antennas by transforming the activity detection task into the estimation of a dedicated active probability for each device. Extensive simulations validate the proposed VG channel model and demonstrate significant improvement due to imposing consistent activity probability across multiple antennas.

The recently emerged movable antenna (MA) shows great potential in leveraging spatial degrees of freedom for enhancing the performance of wireless systems. However, resource allocation in MA-aided systems faces unique challenges due to the non-convex and coupled constraints on antenna positions. This paper systematically reveals the challenges brought by the minimum MA separation constraints, and proposes a penalty framework for resource allocation under such new constraints in MA-aided systems. By introducing auxiliary variables, the proposed framework separates the non-convex and coupled antenna distance constraints from the movable region constraint. This enables the resulting problem be efficiently solved by alternating optimization, where the optimization of the original variables resembles that in conventional resource allocation problem while the optimization with respect to the auxiliary variables is achieved in closed-form solutions. To illustrate the effectiveness of the proposed framework, we present three case studies: capacity maximization, latency minimization, and regularized zero-forcing precoding. Simulation results demonstrate that the proposed optimization framework consistently outperforms state-of-the-art schemes.

A great amount of endeavor has recently been devoted to activity detection for massive machine-type communications in cell-free multiple-input multiple-output (MIMO) systems. However, as the number of antennas at the access points (APs) increases, the Rayleigh distance that separates the near-field and far-field regions also expands, rendering the conventional assumption of sole far-field propagation impractical. To address this challenge, this paper establishes a covariance-based formulation that can effectively capture the statistical property of hybrid near-far field channels. Based on this formulation, we theoretically reveal that increasing the proportion of near-field channels enhances the detection performance. Furthermore, we propose a distributed algorithm, where each AP performs local activity detection and only exchanges the detection results to the central processing unit, thus significantly reduces the computational complexity and the communication overhead. Not only with convergence guarantee, the proposed algorithm is unified in the sense that it can handle single-cell or cell-free systems with either near-field or far-field devices as special cases. Simulation results validate the theoretical analyses and demonstrate the superior performance of the proposed approach compared with existing methods.

This paper studies the device activity detection problem in a massive multiple-input multiple-output (MIMO) system for near-field communications (NFC). In this system, active devices transmit their signature sequences to the base station (BS), which detects the active devices based on the received signal. In this paper, we model the near-field channels as correlated Rician fading channels and formulate the device activity detection problem as a maximum likelihood estimation (MLE) problem. Compared to the traditional uncorrelated channel model, the correlation of channels complicates both algorithm design and theoretical analysis of the MLE problem. On the algorithmic side, we present the classical exact coordinate descent (CD) algorithm for solving the MLE problem, which suffers from numerical instability when applied to correlated channels. We propose a computationally efficient inexact CD algorithm by approximating the objective function, which approximately solves the one-dimensional subproblem and improves both computational efficiency and numerical stability. Additionally, we analyze the detection performance of the MLE problem under correlated channels by comparing it with the case of uncorrelated channels. The analysis shows that when the overall number of devicesNis large or the signature sequence lengthLis small, the detection performance of MLE under correlated channels tends to be better than that under uncorrelated channels. Conversely, whenNis small orLis large, MLE performs better under uncorrelated channels than under correlated ones. Finally, we study the MLE model in the joint device activity and data detection context. Simulation results demonstrate the computational performance of the presented algorithms and verify the correctness of the analysis.

A great amount of endeavor has recently been devoted to activity detection for massive machine-type communications in cell-free massive MIMO. However, in practice, as the number of antennas at the access points (APs) increases, the Rayleigh distance that separates the near-field and far-field regions also expands, rendering the conventional assumption of far-field propagation alone impractical. To address this challenge, this paper considers a hybrid near-far field activity detection in cell-free massive MIMO, and establishes a covariance-based formulation, which facilitates the development of a distributed algorithm to alleviate the computational burden at the central processing unit (CPU). Specifically, each AP performs local activity detection for the devices and then transmits the detection result to the CPU for further processing. In particular, a novel coordinate descent algorithm based on the Sherman-Morrison-Woodbury update with Taylor expansion is proposed to handle the local detection problem at each AP. Moreover, we theoretically analyze how the hybrid near-far field channels affect the detection performance. Simulation results validate the theoretical analysis and demonstrate the superior performance of the proposed approach compared with existing approaches.

Wireless resource allocation is a critical component in modern communication systems, and deep neural networks (DNNs) have shown great promise in addressing this challenge. However, the conventional DNNs assume that testing data follows the same distribution as that of the training data, which is incongruent with the dynamic nature of real-world wireless environments. This paper introduces a new training algorithm designed specifically for dynamic wireless environments where channel distribution exhibits variability. This method helps DNNs adapt to new environments while preserving previously learned information. The proposed approach distinguishes itself by updating the DNN parameters in the null space of the low-rank covariance of previous data, which reduces memory needs and boosts training efficiency. Additionally, to counter the problem of DNNs hitting their model capacity during continuous adaptation, a selective forgetting mechanism is proposed. This mechanism allows DNNs to discard the unimportant knowledge over time, freeing up model capacity for more effective adaptation. The effectiveness of the algorithm is validated by integrating it with graph neural networks and multilayer perceptrons for weighted sum-rate maximization. Through a comprehensive evaluation that includes synthetic and ray-tracing-based datasets, superior performance is demonstrated compared to existing methods.

In continual learning, networks confront a trade-off between stability and plasticity when trained on a sequence of tasks. To bolster plasticity without sacrificing stability, we propose a novel training algorithm called LRFR. This approach optimizes network parameters in the null space of the past tasks’ feature representation matrix to guarantee the stability. Concurrently, we judiciously select only a subset of neurons in each layer of the network while training individual tasks to learn the past tasks’ feature representation matrix in low-rank. This increases the null space dimension when designing network parameters for subsequent tasks, thereby enhancing the plasticity. Using CIFAR-100 and TinyImageNet as benchmark datasets for continual learning, the proposed approach consistently outperforms state-of-the-art methods.

Activity detection is an important task in the next generation Internet-of-things (IoT) networks. Existing algorithms mostly require precise information about the network, such as large-scale fading, noise variance, and small-scale fading statistics. Acquiring such information would take a significant overhead and their estimated values might not be accurate. This problem is even more severe in cell-free networks as more parameters are acquired. Therefore, this paper sets out to investigate this problem without the above mentioned information. In order to handle so many unknown parameters, this paper employs a Bayesian approach, where they are endowed with prior distributions as regularizations. Together with the likelihood function, a maximum a posteriori (MAP) estimator is derived. Simulations demonstrate that the proposed method outperforms state-of-the-art methods especially under imprecise information.

This paper studies the quality-of-service (QoS) constrained multi-group multicast beamforming design problem, where each multicast group is composed of a number of users requiring the same content. Due to the nonconvex QoS constraints, this problem is nonconvex and NP-hard. While existing optimization-based iterative algorithms can obtain a suboptimal solution, their iterative nature results in large computational complexity and delay. To facilitate real-time implementations, this paper proposes a deep learning-based approach, which consists of a beamforming structure assisted problem transformation and a customized neural network architecture named hierarchical permutation equivariance (HPE) transformer. The proposed HPE transformer is proved to be permutation equivariant with respect to the users within each multicast group, and also permutation equivariant with respect to different multicast groups. Simulation results demonstrate that the proposed HPE transformer outperforms state-of-the-art optimization-based and deep learning-based approaches for multi-group multicast beamforming design in terms of the total transmit power, the constraint violation, and the computational time. In addition, the proposed HPE transformer achieves pretty good generalization performance on different numbers of users, different numbers of multicast groups, and different signal-to-interference-plus-noise ratio targets.

This paper investigates a novel deep learning framework for the general nonconvex quality-of-service (QoS)-constrained beamforming design problems in multi-user systems. While existing deep learning-based approaches have shown great success for various power allocation and beamforming design problems, most of the considered problems are equipped with simple constraints (e.g., power budget constraints), which can be satisfied by a simple projection operation. However, it is still a challenge to tackle the more complicated QoS constraints, in which the beamformers and the wireless channels are commonly coupled. To fill this gap, this paper proposes an augmented Lagrangian based penalty-dual training algorithm, which trains two individual neural networks for inferring the beamformers and the corresponding Lagrange multipliers alternatingly. Furthermore, we apply the proposed penalty-dual learning framework to optimize the energy-efficient unicast beamformers and the power-minimized multicast beamformers, respectively. The neural network architectures are judiciously designed based on the solution structures of the two problems. Simulation results on the two applications demonstrate that the proposed penalty-dual approach outperforms state-of-the-art learning approaches and optimization-based algorithms in terms of the constraint violation and the computational time, respectively.

A great amount of endeavour has recently been devoted to activity detection for cell-free massive multiple-input multiple-output (MIMO) systems, where multiple access points (APs) jointly identify the active devices from a large number of potential devices. In practice, the APs and the central processing unit (CPU) are connected by capacity-limited fronthauls and the signals at the APs need to be compressed/quantized before they are forwarded to the CPU. However, existing approaches treat the compression/quantization and activity detection as separate tasks, which makes it difficult to achieve global system optimality. To tackle the above problem, this paper proposes an augmented model-driven end-to-end learning framework which jointly optimizes the compression modules, quantization modules at the APs, and the decompression module and detection module at the CPU. Specifically, deep unfolding is leveraged for designing the detection module in order to inherit the domain knowledge derived from the optimization algorithm, and other modules are constructed by judiciously designed neural network architectures for improving the learning capability. Furthermore, we design an enhanced scheme so that the proposed framework is adaptable to different compression rates. We demonstrate numerically that the proposed framework significantly reduces the computational complexity and achieves better detection performance than the conventional approaches. Moreover, it costs a much smaller number of bits on the fronthauls while still maintaining the detection performance.

This paper investigates a covariance-based approach for intelligent reflecting surface (IRS) aided activity detection in massive machine-type communications (mMTC). In the conventional scenario without IRS, the covariance-based approach, which exploits the probability density function (PDF) of the received signals at the base station (BS), has been demonstrated to outperform the compressed sensing approach. However, when taking the impact of the IRS into account, due to the newly introduced cascaded channels, it is difficult to obtain the exact PDF of the received signals at the BS. To tackle this challenge, we propose an approximation for the intended PDF with tunable parameters in the covariance matrix of the received signals. Based on the proposed tractable reformulation, an analytic framework is established to reveal the guideline for the phase shift design. Moreover, to determine the optimal correlation parameters, a deep unfolding approach is further leveraged by regarding them as trainable parameters. Simulation results validate the theoretical analysis and demonstrate the superior performance of the proposed learning approach.

In order to achieve high data rate and ubiquitous connectivity in future wireless networks, a key task is to efficiently manage the radio resource by judicious beamforming and power allocation. Unfortunately, the iterative nature of the commonly applied optimization-based algorithms cannot meet the low latency requirements due to the high computational complexity. For real-time implementations, deep learning-based approaches, especially the graph neural networks (GNNs), have been demonstrated with good scalability and generalization performance due to the permutation equivariance (PE) property. However, the current architectures are only equipped with the node-update mechanism, which prohibits the applications to a more general setup, where the unknown variables are also defined on the graph edges. To fill this gap, we propose an edge-update mechanism, which enables GNNs to handle both node and edge variables and prove its PE property with respect to both transmitters and receivers. Simulation results on typical radio resource management problems demonstrate that the proposed method achieves higher sum rate but with much shorter computation time than state-of-the-art methods and generalizes well on different numbers of base stations and users, different noise variances, interference levels, and transmit power budgets.

This paper proposes a deep learning-based approach for the quality-of-service (QoS) constrained multi-group mul-ticast beamforming design. The proposed method consists of a beamforming structure assisted problem transformation and a customized neural network architecture named hierarchical permutation equivariance (HPE) transformer. The proposed HPE transformer is proved to be permutation equivariant with respect to the users within each multicast group, and also permutation equivariant with respect to different multicast groups. Simulation results demonstrate that the proposed HPE transformer outperforms state-of-the-art optimization-based and deep learning-based approaches for multi-group multicast beamforming design in terms of the total transmit power, the constraint violation, and the computational time. In addition, the proposed HPE transformer achieves pretty good generalization performance on different numbers of users and multicast groups.

This paper investigates a covariance-based learning approach for intelligent reflecting surface (IRS) aided activity detection in massive machine-type communications (mMTC). In the conventional scenario without IRS, the covariance-based approach has been demonstrated to outperform the compressed sensing approach, as the covariance-based approach can well exploit the probability density function (PDF) of the received signals at the base station (BS). However, when taking the impact of the IRS into account, due to the newly introduced cascaded channels, it is quite difficult to obtain the exact PDF of the received signals at the BS. To tackle this challenge, we propose an approximation for the intended PDF by modeling a correlation parameter in the covariance matrix of the received signals. Based on the covariance-based formulation, a learning approach is further proposed to automatically learn the correlation parameter. Simulation results demonstrate the performance of the covariance-based activity detection, and the superiority of the proposed covariance-based learning approach.

Device activity detection in the emerging cell-free massive multiple-input multiple-output systems has been recognized as a crucial task in machine-type communications, in which multiple access points jointly identify the active devices from a large number of potential devices based on the received signals. Most of the existing works addressing this problem rely on the impractical assumption that different active devices transmit signals synchronously. However, in practice, synchronization cannot be guaranteed due to the low-cost oscillators, which brings additional discontinuous and nonconvex constraints to the detection problem. To address this challenge, this paper reveals an equivalent reformulation to the asynchronous activity detection problem, which facilitates the development of a distributed algorithm that satisfies the highly nonconvex constraints in a gentle fashion as the iteration number increases. To reduce the capacity requirements of the fronthauls, we further design a communication-efficient accelerated distributed algorithm. Simulation results demonstrate that the proposed two distributed algorithms outperform state-of-the-art approaches. Moreover, the accelerated distributed algorithm requires a very small number of quantization bits to approach the ideal detection performance.

A great amount of endeavour has recently been devoted to device activity detection in massive machine-type communications. This paper targets at a practical issue: communication-efficient joint signal compression and activity detection in cell-free massive MIMO with capacity-limited fronthauls. To this end, we propose a novel deep learning framework which jointly optimizes the compression modules, quantization modules at the access points, and the decompression module and detection module at the central processing unit. Specifically, deep unfolding is leveraged for designing the detection module in order to inherit the domain knowledge derived from the optimization algorithm, and the other modules are constructed by generic layers for increasing the learning capability. A joint training strategy is proposed to optimize all the modules in an end-to-end manner. Numerical results demonstrate the superiority of the proposed end-to-end learning framework compared with classical optimization methods.

Cooperative beamforming has been recognized as an effective approach to meet the dramatically increasing demand of various wireless data traffics. Conventionally, the beamforming design problem is posed as an optimization problem and solved through iterative algorithms, which are difficult for real-time implementations. Recent advances in the field have witnessed the emergence of learning-based methods for beamforming design in real-time. Graph Neural Networks (GNNs) have been demonstrated to leverage the graph topology in wireless networks and generalize to unseen problem sizes. However, the current implementations of GNNs suffer from a limitation in modeling more complex cooperative beamforming, where the beamformers are on the graph edges. To address this shortcoming, this paper presents a novel Edge-Graph-Neural-Network (Edge-GNN) which incorporates an edge-update mechanism, thus allowing for the learning of cooperative beamforming on graph edges. Simulation results affirm the superiority of the proposed Edge-GNN over state-of-the-art approaches. The Edge-GNN achieves a higher sum rate with reduced computation time and exhibits excellent generalization to different numbers of base stations and user equipments.

In massive machine-type communications, data transmission is usually considered sporadic, and thus inherently has a sparse structure. This paper focuses on the joint activity detection (AD) and channel estimation (CE) problems in massive-connected communication systems with low-resolution analog-to-digital converters. To further exploit the sparse structure in transmission, we propose a maximum posterior probability (MAP) estimation problem based on both sporadic activity and sparse channels for joint AD and CE. Moreover, a majorization-minimization-based method is proposed for solving the MAP problem. Finally, various numerical experiments verify that the proposed scheme outperforms state-of-the-art methods.

Employing graph neural networks (GNNs) for learning the multiuser multi-input multi-output precoder has gained significant attention recently. By modeling the precoder optimization problem in a graph format, GNN can effectively capture the representation of the precoder by leveraging the information aggregated and propagated across the graph. In this paper, we strive to design the information aggregation mechanism of GNN. By analyzing the behavior of the numerical gradient descent algorithm for precoder optimization, we identify the relevant information and the appropriate form for aggregation, enabling us to develop new update equations for GNNs. Simulation results demonstrate the advantages of the proposed GNNs in learning and generalization performance.

To support modern machine-type communications, a crucial task during the random access phase is device activity detection, which is to identify the active devices from a large number of potential devices based on the received signal at the access point. By utilizing the statistical properties of the channel, state-of-the-art covariance based methods have been demonstrated to achieve better activity detection performance than compressed sensing based methods. However, covariance based methods require to solve a high dimensional nonconvex optimization problem by updating the estimate of the activity status of each device sequentially. Since the number of updates is proportional to the device number, the computational complexity and delay make the iterative updates difficult for real-time implementation especially when the device number scales up. Inspired by the success of deep learning for real-time inference, this paper proposes a learning based method with a customized heterogeneous transformer architecture for device activity detection. By adopting an attention mechanism in the architecture design, the proposed method is able to extract features reflecting relevance among device pilots and received signal, permutation equivariant with respect to devices, and its training parameter number is independent of the device number. Simulation results demonstrate that the proposed method achieves better activity detection performance with much shorter computation time than state-of-the-art covariance approach, and generalizes well to different numbers of devices and BS-antennas, different pilot lengths, transmit powers, and cell radii.

Device activity detection in the emerging cell-free massive multiple-input multiple-output (MIMO) systems has been recognized as a crucial task in machine-type communications, in which multiple access points (APs) jointly identify the active devices from a large number of potential devices based on the received signals. Most of the existing works addressing this problem rely on the impractical assumption that different active devices transmit signals synchronously. However, in practice, synchronization cannot be guaranteed due to the low-cost oscillators, which brings additional discontinuous and nonconvex constraints to the detection problem. To address this challenge, this paper reveals an equivalent reformulation to the asynchronous activity detection problem, which facilitates the development of a centralized algorithm and a distributed algorithm that satisfy the highly nonconvex constraints in a gentle fashion as the iteration number increases, so that the sequence generated by the proposed algorithms can get around bad stationary points. To reduce the capacity requirements of the fronthauls, we further design a communication-efficient accelerated distributed algorithm. Simulation results demonstrate that the proposed centralized and distributed algorithms outperform state-of-the-art approaches, and the proposed accelerated distributed algorithm achieves close detection performance to that of the centralized algorithm but with a much smaller number of bits to be transmitted on the fronthaul links.

Grant-free random access is a promising mechanism to support modern massive machine-type communications in which devices are sporadically active with small payloads. Under this random access, a unique challenge is the detection of device activity without the cooperation from devices. Furthermore, for only a few bits of data, it is more efficient to embed the data to the signature sequences so that the activity and data detection can be jointly carried out. However, compared with the vanilla device activity detection, joint activity and data detection has an extra discontinuous sparsity constraint, which makes the detection problem more challenging. In contrast to the prevalent way of first neglecting the discontinuous sparsity constraint and reinforcing it at the end, this paper proposes a novel approach to incorporate the discontinuous sparsity constraint into the optimization procedure. In particular, we first establish the equivalence between the discontinuous sparsity constraint and a continuous difference-of-norms (DN) form. Then, by introducing a DN penalty term in the objective function, an iterative DN penalty method with an increasing penalty weight is adopted. We prove theoretically that by solving each penalized problem to a stationary solution, the discontinuous sparsity constraint can be exactly satisfied when the penalty weight is sufficiently large, and the resulting solution is guaranteed to be at least a stationary point of the original problem. Due to the superior theoretical guarantee, simulation results demonstrate that the proposed method achieves around 10 times better detection performance than state-of-the-art approaches.

Cloud radio access network (C-RAN) has been recognized as a promising architecture for next-generation wireless systems to support the rapidly increasing demand for higher data rate. However, the performance of C-RAN is limited by the backhaul capacities, especially for the wireless deployment. While C-RAN with fixed BS caching has been demonstrated to reduce backhaul consumption, it is more challenging to further optimize the cache allocation at BSs with multi-cluster multicast backhaul, where the inter-cluster interference induces additional non-convexity to the cache optimization problem. Despite the challenges, we propose an accelerated first-order algorithm, which achieves much higher content downloading sum-rate than a second-order algorithm running for the same amount of time. Simulation results demonstrate that, by simultaneously delivering the required contents to different multicast clusters, the proposed algorithm achieves significantly higher downloading sum-rate than those of time-division single-cluster transmission schemes. Moreover, it is found that the proposed algorithm allocates larger cache sizes to the farther BSs within the nearer clusters, which provides insight to the superiority of the proposed cache allocation.

Activity detection in machine-type communication (MTC) has been recognized as an effective way to support massive connectivity of the Internet-of-Things (IoT) devices. However, due to the sporadic traffic pattern of the MTC, only a small portion of the massive potential devices are active, making the activity detection a challenging large-scale sparsity-constrained problem. On the other hand, since the low-cost IoT devices are commonly equipped with cheap crystal oscillators, the resulting frequency offsets would intensify the multi-user interference during the activity detection and invalidate existing detection methods that are designed under ideal frequency synchronization. To fill this gap, this paper proposes two methods for activity detection under unknown frequency offsets: a Lasso-based method and a sparsity-constrained method. Both the methods are first-order algorithms, making them suitable for large-scale IoT systems. Furthermore, the sparsity-constrained method can be executed in parallel and is proved to converge to a set of critical points. The simulation results show that both the proposed methods achieve much better detection performance than a two-stage approach that separately performs frequency synchronization and activity detection. Moreover, the proposed sparsity-constrained method is shown to perform better than two competing algorithms exploiting hierarchical sparsity.

As the demand for supporting hybrid multicast and unicast services is rapidly increasing, a non-orthogonal multiplexing transmission scheme called layered-division multiplexing (LDM) has been recognized as an effective way to provide high spectrum efficiency (SE). However, high SE is not necessarily equivalent to high energy efficiency (EE). In fact, it is still unclear how much benefit LDM would provide for hybrid multicast and unicast services under EE maximization, which belongs to the more challenging class of fractional programs. To fill this gap, we formulate the problem of energy-efficient precoding design for the LDM-based multi-user multi-input-multi-output downlink system, under both multicast and unicast multi-stream data rate constraints of each user. Although the problem is nonsmooth and nonconvex, we propose a first-order algorithm for finding both the initial point and the final solution. Since the proposed first-order algorithm involves only gradient information, it achieves very low complexity. The simulation results demonstrate that, compared with the orthogonal transmission schemes, the LDM transmission under the proposed precoding can provide a much higher EE. Moreover, the proposed first-order algorithm achieves the same EE as that of a second-order based approach, but requires much shorter computation time.

In multimedia-rich communication scenarios, popular contents are requested by many users. This calls for the communication system design perspective transferring from user-centric to content-centric. To realize the content-centric paradigm, one of the dominant approaches is the multi-group multicast transmission. However, different content groups may cause interference with each other, and the quality of service is difficult to be guaranteed without coordination. Fortunately, a cloud radio access network (C-RAN) perfectly fills this gap as all the computations in the network are off-loaded to the computation center, making the central coordination possible. But a major challenge that C-RAN faces is that the resultant problem size could be extremely large, invalidating many existing second-order algorithms. In this paper, content-centric sparse multicast beamforming in a large-scale C-RAN is studied. In addition to the large-scale nature, this problem is further complicated by the discontinuity and non-convexity of the cost function and constraints. Despite the challenges, a first-order algorithm is proposed. Not only is the proposed algorithm guaranteed to converge to a critical point, but its complexity order is only linear with respect to the problem size. This is in sharp contrast to the cubic order of an existing solution, making the proposed algorithm indispensable for large-scale C-RAN with hundreds or thousands of users.

In heterogeneous cellular networks, cross-tier inter-cell interference is often in mixed interference scenario where the macro-cell causes strong interference to pico-cells while pico-cells only cause weak interference to the macro-cell. In this scenario, the popular interference coordination schemes using power control or time/frequency division multiplexing are far from achieving the spectrum efficiency potential. Exploiting the difference of transmit powers and channel gains in heterogeneous networks, the transmission schemes based on interference cancelation have great opportunity to gain more throughput benefit. In this paper, we propose a coordinated precoding and proactive interference cancelation scheme, where the precoding design is based on the known decoding order and is to maximize the sum-rate of two interfering users. Since the optimization problem is non-convex, we find a local maximum by constructing a concave lower bound of the objective function and iteratively tightening it. Simulation results show that the network throughput is remarkably improved in mixed interference scenarios relative to orthogonal division scheme and coordinated multipoint transmission scheme with zero forcing precoding.

Coordinated beamforming has been optimized to maximize the sum rate under the transmit power constraints, or to minimize the transmit power under the data rate constraints. In this paper, we study coordinated beamforming to maximize the energy efficiency (EE) of multi-cell multi-antenna systems meanwhile ensuring the individual data rate requirement of each user. To find a solution of the non-convex optimization problem for the precoding design, we construct a convex subset of the original constraint set and a quasi-concave lower bound of the EE. Then, we propose an iterative algorithm to maximize the lower bound of the EE within the convex subset. We evaluate the EE of the proposed algorithm through simulations under different data rate requirements, user locations, and cell-edge signal-to-noise ratios. The results demonstrate that the proposed precoder is much more energy-efficient than the transmit power minimization precoder when the circuit power consumption dominates, and always outperforms two interference-free transmission schemes with the optimized transmit power toward maximizing the EE.