Multicast Beamforming Research Articles

Corrections to “Deep Learning Enabled Multicast Beamforming With Movable Antenna Array”

Corrections to “Deep Learning Enabled Multicast Beamforming With Movable Antenna Array”

Completion Time Minimization for Multi-Antenna UAV-Enabled Multicasting With Rank-Two Multicast Beamforming

Completion Time Minimization for Multi-Antenna UAV-Enabled Multicasting With Rank-Two Multicast Beamforming

Multi-Antenna Coded Caching for Location-Dependent Content Delivery

Human-computer interaction continuously evolves towards a genuinely immersive experience, submerging users in a three-dimensional (3D) virtual world. A realistic, immersive experience necessitates a highly reliable and agile wireless connection to support immense data transmission. Yet, there are abundant but underutilized memory resources available at the devices which can be harnessed as supplementary assets to reduce the excessive burden on the wireless medium. What is more, the use of Coded Caching (CC) techniques enables the cumulative cache memory of users in the network to be used as an additional communication resource. To this end, a location-dependent multi-antenna CC-based content delivery scheme tailored specifically for wireless extended reality applications is proposed in this paper. First, a novel memory allocation process is developed, enabling an appropriate trade-off between local and global caching gains. In this regard, the local caching gain is maximized when the memory is mostly dedicated to locations with poor connectivity conditions (absolute fairness). In contrast, the global caching gain is maximized when the memory is uniformly allocated among all the locations. As a result of the memory allocation process, unequal fractions of location-dependent multimedia content are cached by each user. Given the asymmetric cache placement, a novel algorithm is proposed to create suitable codewords for each user during the subsequent delivery phase, which simultaneously achieves a global and local caching gain. The proposed delivery scheme also combines global caching and spatial multiplexing gains using a weighted max-min multicast beamformer design with multi-rate modulation. Numerical experiments and mathematical analysis demonstrate significant performance gains, in terms of the 95-percentile expected delivery time, compared to unicast and multicast scenarios where either the local or global caching gain is maximized.

Low-Complexity Joint Antenna Selection and Robust Multi-Group Multicast Beamforming for Massive MIMO

Low-Complexity Joint Antenna Selection and Robust Multi-Group Multicast Beamforming for Massive MIMO

Beamforming Vector Design and Device Selection in Over-the-Air Federated Learning

In this paper, we consider a beamforming vector design and device selection problem in over-the-air computation (AirComp) for federated learning. Since the learning performance improves as more devices participate in the federated learning aggregation, we formulate a beamforming vector optimization problem that maximizes the number of selected devices under a given target aggregation mean-squared error. This AirComp uplink beamforming problem with device selection is shown to have the same form as the downlink multicast beamforming problem with user selection, which establishes the AirComp-multicasting duality. We design a low-complexity algorithm based on the projected subgradient method that is orders of magnitude faster than conventional semidefinite relaxation-based algorithms and faster than local model training on the devices, which makes it possible to implement the proposed wireless federated learning in real time. Numerical results show that the proposed algorithm provides significant multiple antenna beamforming gains and achieves the performance of the ideal federated learning system with no aggregation errors.

Passive Reflection Optimization for IRS-Aided Multicast Beamforming With Discrete Phase Shifts

Intelligent reflecting surface (IRS) can bring promising advantages to enhance the communication system performance by reconfiguring wireless channels dynamically. The design of passive IRS reflection has attracted high attention and most existing works have considered continuous phase shift for IRS reflection. However, this is difficult to realize in practice due to hardware limitations and discrete phase shifts are applied for practical IRSs instead. In this letter, the information multicast beamforming problem in an IRS-aided multi-user system is considered, where the minimum receive signal-to-noise-ratio among the users is maximized by optimizing the IRS reflections with discrete phase shifts. By leveraging semi-definite relaxation (SDR) and gradient descent/ascent (GDA), two solutions are presented with high/low computational complexity, respectively. Simulation results show the efficacy of the proposed GDA-based algorithm as compared to the SDR-based and other benchmark schemes.

Robust Beamforming Design for Cache-Enabled C-RAN With Fronthaul Multicast

In this article, we study a robust beamforming design problem in the cached-enable cloud radio access network, where the imperfect channel state information of the access links are considered. Two transmission schemes, nonsimultaneous transmission (NST) scheme and simultaneous transmission (ST) scheme, are developed. To improve the system performance, the cooperative transmission technique is applied. In NST scheme, the base stations (BSs) obtain the uncached required files from the central processor (CP) and then transmit all required files to users. Based on this, we design an effective transmission model based on cache files and the qualities of the fronthaul link channels, and formulate a transmission delay minimization problem. Then, an alternative optimization algorithm is developed to solve it. In ST scheme, the BSs obtain the uncached files from the CP and transmit the cached files to users simultaneously. We divide two cases according to the access link transmission rate and cached files. For each case, we formulate an optimization problem by jointly designing the fronthaul multicast beamforming and access link transmission beamforming. Next, an iterative algorithm is developed via the L0 norm approximation, successive convex approximation and semidefinite relaxation techniques. Finally, simulation results show the proposed schemes can reduce the transmission delay better than the conventional multicast schemes.

Resource-Aware Video Delivery in Fog Radio Access Networks: A Joint QoE and QoS Perspective

In this paper, the video delivery strategy is studied under the cooperative framework of cache-enabled fog radio access networks (F-RAN), where multicast beamforming and video-quality selection are both taken into account in terms of different scenarios. In the user-centered scenario, an optimization problem regarding to the network quality of experience (QoE) improvement is first formulated under the essential quality of service (QoS) requirements of the users. Furthermore, an energy efficiency maximization scheme is proposed in the user-dense scenario to improve the resource utilization when network resources may be insufficient to guarantee the QoS requirements of all the users. In particular, a user scheduling scheme is studied in this case. More specifically, the non-convex constraints and fractional object functions in the aforementioned problems are dealt with by successive convex approximation (SCA) technique and the Dinkelbach approach. In order to solve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{0}$</tex-math></inline-formula> -norm problem caused by user scheduling, we introduce the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation to improve the sparsity of the solution. Finally, the effectiveness of the proposed schemes is validated by extensive simulations.

Multigroup Multicast Beamforming for High Throughput GEO Satellite Communications Under Power-Consumption Outage Constraints

The heat dissipation of high throughput geostationary earth orbit (GEO) satellites poses great challenges to current satellite communications, which may cause performance degradation due to the power-consumption outage (PCO). Motivated by this, we investigate the multigroup multicast beamforming design for high throughput GEO satellite communications as an energy efficiency maximization problem which considers the PCO and total power constraints in this work. To cope with this nonconvex problem, we propose a low-complexity algorithmic approach. Numerical results demonstrate that our proposed approach outperforms the conventional one.

Ultra-Low-Complexity Algorithms With Structurally Optimal Multi-Group Multicast Beamforming in Large-Scale Systems

In this work, we propose ultra-low-complexity design solutions for multi-group multicast beamforming in large-scale systems. For the quality-of-service (QoS) problem, by utilizing the optimal multicast beamforming structure obtained recently in [2], we convert the original problem into a non-convex weight optimization problem of a lower dimension and propose two fast first-order algorithms to solve it. Both algorithms are based on successive convex approximation (SCA) and provide fast iterative updates to solve each SCA subproblem. The first algorithm uses a saddle point reformulation in the dual domain and applies the extragradient method with an adaptive step-size procedure to find the saddle point with simple closed-form updates. The second algorithm adopts the alternating direction method of multipliers (ADMM) method by converting each SCA subproblem into a favorable ADMM structure. The structure leads to simple closed-form ADMM updates, where the problem in each update block can be further decomposed into parallel subproblems of small sizes, for which closed-form solutions are obtained. We also propose efficient initialization methods to obtain favorable initial points that facilitate fast convergence. Furthermore, taking advantage of the proposed fast algorithms, for the max-min fair (MMF) problem, we propose a simple closed-form scaling scheme that directly uses the solution obtained from the QoS problem, avoiding the conventional computationally expensive method that iteratively solves the inverse QoS problem. We further develop lower and upper bounds on the performance of this scaling scheme. Simulation results show that the proposed algorithms offer near-optimal performance with substantially lower computational complexity than the state-of-the-art algorithms for large-scale systems.

A Learning Approach for Efficient Multicast Beamforming Based on Determinantal Point Process

The problem of single-group multicast beamforming (SMBF) is well-known NP-hard. It motivates the pursuit of computationally efficient near-optimal solutions. Due to multicasting, the multicast group is bottlenecked by the user(s) with the minimum received signal-to-noise ratio (SNR). This paper provides an in-depth interpretation of the SMBF problem from the multicasting point of view and proposes to solve it in two steps: i) select the bottlenecking users by a machine learning approach based on determinantal point process (DPP), and ii) design the beamformer for the selected users. The DPP model jointly considers the magnitudes and directions of users’ channel vectors, and thus enables an efficient selection of the bottlenecking users. Moreover, for a specific channel model, the DPP model is only associated with network size and each takes a one-off training cost, thus can be used as a codebook. The proposed DPP-based subset selection is incorporated adaptively into two fast beamforming algorithms, i.e., the QR decomposition algorithm and the successive beamforming (SB) algorithm. They specifically design the beamformers for the selected users by leveraging channel orthogonalization therein. Numerical results demonstrate the superiority of the proposed QR-DPP and SB-DPP algorithms in terms of the performance-complexity compromise and their robustness to different scenarios.

Fast First-Order Algorithm for Large-Scale Max-Min Fair Multi-Group Multicast Beamforming

We propose a first-order fast algorithm for the weighted max-min fair (MMF) multi-group multicast beamforming problem in large-scale systems. Utilizing the optimal multicast beamforming structure obtained recently, we convert the nonconvex MMF problem into a min-max weight minimization problem and show that it is a weakly convex problem. We propose using the projected subgradient algorithm (PSA) to solve the problem directly, instead of the conventional method that requires iteratively solving its inverse problem. We show that PSA for our problem has closed-form updates and thus is computationally cheap. Furthermore, PSA converges to a near-stationary point of our problem within finite time. Simulation results show that our PSA-based algorithm offers near-optimal performance with considerably lower computational complexity than existing methods for large-scale systems.

Joint Design of Multicast Transmission and In-Network Caching for Green Internet of Things

In this paper, the joint design of energy-efficient multicast beamforming and in-network caching in Internet of Things is investigated. We propose the fractional in-network caching scheme. Specifically, parts of the sensed data resources are cached in the helpers, such as small-cell base stations and device-to-device equipments, and the caching fraction for a certain resource is the same among the helpers. The remaining data resources are kept in the sensor nodes. Employing multicast transmission at the helpers, the cached data can be cooperatively transmitted to the clients belonging to multiple multicast groups, where the data requests are identical among the clients in the same multicast group. Based on the proposed fractional caching and multicast transmission protocols, the power consumption model is established, and then we formulate the energy efficiency (EE) optimization problem, which is challenging to solve due to its non-convexity. Thereafter, by exploiting the Dinkelbach ’ s method, semi-definite relaxation, successive convex approximation and other approximation techniques, the original problem is converted into a second-order cone programming problem, which is convex and can be efficiently solved by off-the-shelf CVX solvers. Numerical results exhibit the fast convergence of the proposed algorithm, and demonstrate the superior EE performance of the proposed fractional caching scheme, compared to the benchmark strategies.

Learning-Based Branch-and-Bound for Non-Convex Complex Modulus Constrained Problems With Applications in Wireless Communications

We consider a class of non-convex complex modulus constrained problems (CMCPs), which has many important applications in signal processing for wireless communications, including multicast beamforming and multi-input multi-output detection. Due to the non-convex constraints, traditional optimization-based algorithms either obtain sub-optimal solutions or take exponential complexity to reach the optimum. In this paper, we propose a learning based branch-and-bound (LBB) algorithm for solving the considered CMCPs. LBB regards the search procedure of the global optimal argument-cut based branch-and-bound (AC-BB) algorithm as a sequential decision problem in a binary tree and learns the optimal pruning policy via supervised learning. We first propose to apply ensemble learning to train multiple classifiers and then combine them to achieve better performance. To tackle the imbalanced issue, we propose an undersampling-supervised learning method to sample several balanced subsets and train a classifier on each of them. We also show that the computational complexity of LBB is determined by the depth of the binary tree and give its expression in the worst case. Finally, we validate the proposed LBB with two classic problems in wireless communications, i.e., multicast beamforming and MIMO detection. Numerical results show that LBB runs significantly faster than AC-BB while achieving nearly the same optimal performance.

Rank-Two Multicast Beamforming for Multiuser MISO Downlink With Intelligent Reflecting Surface

Recently, intelligent reflecting surface (IRS) has received considerable attention and is seen as a promising technology for 6 G communications. This correspondence studies the IRS-aided multiuser multi-input single-output (MISO) downlink multicast beamforming. Depart from the conventional (rank-one) beamforming, the Alamouti-aided <i>rank-two</i> beamforming is employed at the base station (BS), and a joint optimization of the rank-two beamforming and the IRS phase shift is formulated to minimize the transmit power with guaranteed signal-to-noise ratio at the users. This power minimization problem is nonconvex. To tackle it, we custom-derive a proximal distance algorithm (PDA) with generalized power method (GPM) to iteratively optimize the beamformer and the phase shift. Both PDA and GPM can be performed very efficiently than the semidefinite relaxation method. Simulation results demonstrate that the rank-two beamforming attains much lower porwer than the rank-one beamforming with reduced computation complexity.

Cooperative multigroup multicast beamforming for cache‐enabled ultra‐dense low earth orbit satellite constellation networks

SummaryThe ultra‐dense low earth orbit (LEO) satellite constellation (UD‐LSC) networks are expected to be incorporated in future wireless networks, particularly 6G networks, to provide global wireless access with enhanced data rates. This paper investigates the downlink multigroup multicast transmission for UD‐LSC networks, in which LEO satellites provide the multicast service for ground users with full frequency reuse. Moreover, in‐network caching, as a key enabling technology of information‐centric networking, is brought into UD‐LSC networks to achieve both bandwidths saving and delay reduction. However, the multicast capacity is constrained by the signal to interference and noise ratio (SINR) of bottleneck users in each multicast group. Besides, the high‐speed movement of LEO satellites makes cache placement and updating more challenging than ground networks with immobile base stations. To track these problems, we first propose a cache‐enabled multi‐satellite cooperation framework and formulate the multicast transmission problem and the content caching problem. Then, to reduce the average content delivery delay (CDD) of ground users, we propose a cooperative multicast beamforming and transmission‐aware dynamic caching (CMB‐TDC) algorithm based on the sample average approach and successive convex approximation. Simulation results show that the proposed CMB‐TDC algorithm can improve the multicast capacity, and then the average CDD is reduced for UD‐LSC networks.

Joint Cache Placement and Cooperative Multicast Beamforming in Integrated Satellite-Terrestrial Networks

This paper studies joint cache placement and cooperative multicast beamforming to provide content-centric data services for mobile users in the integrated satellite-terrestrial network (ISTN). Specifically, in the ISTN, users requesting the same content are arranged into a multicast group and served by the cache-enabled base stations (BSs) and low earth orbit (LEO) satellite via cooperative beamforming. To maximize the network utility that takes network throughput and backhaul traffic into consideration, the cache placement, LEO satellite and BS clustering, and multicast beamforming are jointly designed and formulated as a two-timescale optimization problem. However, the original problem is anti-causal since the cache placement strategy and content delivery policy are coupled in different timescales. By utilizing historical information, we propose a two-step scheme to decompose the problem into a short-term content delivery subproblem and a long-term cache placement subproblem. As the former subproblem is nonconvex with mixed-integer variables and coupling constraints, we transform it into an equivalent problem and propose a penalty concave-convex procedure based algorithm to solve it. To address the latter subproblem, a centralized iterative algorithm and a distributed alternating algorithm with low complexity are developed, respectively. Simulation results validate that the proposed schemes can effectively enhance the network throughput and reduce the backhaul traffic compared with benchmark scheme.

Fast Algorithm for Joint Unicast and Multicast Beamforming for Large-Scale Massive MIMO

We consider the problem of joint unicast and multi-group multicast beamforming design for large-scale massive multiple-input multiple-output (MIMO) systems, with a potentially large number of unicast users. Focusing on minimizing the total transmit power subject to quality-of-service constraints, we propose an alternating direction method of multipliers (ADMM)-based fast algorithm to efficiently obtain the beamforming solutions for both unicast and multicast users. Exploiting the optimal beamforming structure obtained recently for multi-group multicast beamforming, we decompose the original problem into two subproblems for the unicast and multicast users and solve them using the alternating optimization technique. We obtain the solution to the unicast subproblem in closed form by exploring the unicast beamforming structure, thereby substantially reducing the computational complexity of the overall algorithm. We solve the multicast subproblem by approximating the non-convex constraints with a sequence of convex constraints using the successive convex approximation. Each convex subproblem is then reformulated into an ADMM form, which enables us to derive a closed-form update for the multicast subproblem. Simulation results show that our proposed algorithm achieves a near-optimal performance at a very low complexity for large-scale systems.

Low-Complexity ADMM-Based Algorithm for Robust Multi-Group Multicast Beamforming in Large-Scale Systems

We design an efficient robust multi-group multicast beamforming scheme for massive multiple-input multiple-output (MIMO) systems. Assuming only estimates of the channel covariance matrices are available at the base station with a bounded error, we formulate the robust quality-of-service (QoS) problem, which is to minimize the transmit power subject to the worst-case minimum signal-to-interference-plus-noise-ratio (SINR) guarantee. We directly solve the worst-case SINR problem and convert the robust QoS constraint into a number of non-convex constraints. Based on the recent convergence result of the alternating direction method of multipliers (ADMM) for non-convex problems, we develop an ADMM-based fast algorithm to directly tackle the reformulated non-convex problem with a convergence guarantee. The algorithm contains two layers of ADMM procedures. We design the outer-layer ADMM to decompose the problem into three convex subproblems and solve them alternatingly. We further develop an inner-layer consensus-ADMM-based algorithm to efficiently solve one subproblem. By exploring each subproblem structure and developing the special optimization techniques, we obtain closed-form or semi-closed-form solutions to each subproblem. These results lead to a fast iterative algorithm, which is guaranteed to converge to a stationary point of the original robust QoS problem. Simulation shows that our proposed algorithm provides a favorable performance compared with existing alternative methods with magnitudes of computational complexity reduction.

Rate Splitting Multiple Access for Multigroup Multicast Beamforming in Cache-Enabled C-RAN

This paper investigates rate splitting multiple access (RSMA) for multigroup multicast beamforming in a cache-enabled cloud radio access network (C <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^2$</tex-math></inline-formula> -RAN). To maximize the minimum weighted rate among all users and ensure the base station (BS) transmit power and backhaul capacity constraints, we jointly optimize the dynamic BS clustering, message splitting, and beamforming vectors. More specifically, users requesting the same content are collected to a multicast group and served by a cluster of BSs. Each BS has limited storage space and connects to the central processor (CP) via a backhaul link. However, the resulting optimization problem is discrete and nonconvex and has a non-smooth objective function. To alleviate these problems, we construct two surrogates to approximate the objective function locally. These surrogates are strictly lower bounds and concave. Also, we build an upper-bound convex surrogate function to handle the backhaul cost constraint and derive a minorization-maximization (MM)-based iterative algorithm. Besides, we adopt a quadratic transform method to recast the achievable rate and binary BS selection problems to a more tractable form to reduce time cost. We transform the resulting problem into a two-tier alternating optimization problem; the outer-tier problem is handled with closed-form expressions while the inner-tier one is solved by a convex framework. We thus develop a quadratic transform-based alternating (QTA) algorithm. Extensive simulation results confirm the superiority of our proposed transmit strategy and algorithms.