Multi-group Multicast Beamforming Research Articles

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

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.

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.

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.

Wireless Index Coded Transmission by Spatial Multiplexing With Multiple Antennas

Index coding, a.k.a. coded multicasting, is one of the promising transmission schemes that can reduce the number of transmissions by leveraging the stored data in the users' memory. With multiple antennas, index coding gain can be further multiplied by spatially multiplexing but joint design of index code and beamforming has not been addressed well in literature. This paper figures out the gain of spatially multiplexed index code by jointly designing the multicast beamformer and index code. Since the optimal joint design problem itself is NP-hard, we take a two-step approach. At the first step, for an arbitrary index code, conjugate gradient-based multi-group multicast beamforming is designed. At the second step, the index code minimizing the total transmission time is selected. Our simulation results exhibit a substantial gain of spatially multiplexed index code by the proposed scheme.

Multi-Group Multicast Beamforming by Superiorized Projections Onto Convex Sets

In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a semidefinite program in a real Hilbert space, which allows us to approximate a point in the feasible set by iteratively applying a bounded perturbation resilient fixed-point mapping. Inspired by the superiorization methodology, we use this mapping as a basic algorithm, and we add in each iteration a small perturbation with the intent to reduce the objective value and the distance to nonconvex rank-constraint sets. We prove that the sequence of perturbations is bounded, so the algorithm is guaranteed to converge to a feasible point of the relaxed semidefinite program. Simulations show that the proposed approach outperforms existing algorithms in terms of both computation time and approximation gap in many cases.

Outage-Constrained Robust Multigroup Multicast Beamforming for Satellite-Based Internet of Things Coexisting With Terrestrial Networks

Satellite-based Internet of Things (IoT) is recognized as a cost-effective approach for global access. In this article, we aim at improving the spectrum efficiency of satellite systems to serve a huge number of IoT devices. To this end, we present a cognitive satellite-terrestrial framework, where a multibeam satellite system with full frequency reuse shares the spectrum with terrestrial networks based on the underlay paradigm. Considering DVB-S2X recommendations, geometric configurations, and channel characteristics, we investigate a robust multigroup multicast beamforming design for the satellite-based IoT coexisting with terrestrial networks in the presence of a phase error on channel state information, and characterize the achievable rate region under the outage probability constraint for the terminal and the power consumption constraint for the satellite. Based on the concept of rate profile, an associated optimization problem is formulated to design robust beamformers and determine the Pareto boundary of the region. To solve the intractable problem, we propose a two-level iterative algorithm on the basis of joint bisection search and penalty function enabled nonsmooth optimization. In particular, we develop a Bernstein-type inequality aided method and a large deviation inequality aided method to obtain a tractable and conservative approximation for the probabilistic constraint, respectively. Numerical results are provided to confirm the validity and superiority of our proposed scheme over the existing approaches and reveal the impact of key parameters on the achievable system performance.

Rate-Splitting Multiple Access for Multigroup Multicast and Multibeam Satellite Systems

This work focuses on the promising Rate-Splitting Multiple Access (RSMA) and its beamforming design problem to achieve max-min fairness (MMF) among multiple co-channel multicast groups with imperfect channel state information at the transmitter (CSIT). Contrary to the conventional linear precoding (NoRS) that relies on fully treating any residual interference as noise, we consider a novel multigroup multicast beamforming strategy based on RSMA. RSMA relies on linearly precoded Rate-Splitting (RS) at the transmitter and Successive Interference Cancellation (SIC) at the receivers, and has recently been shown to enable a flexible framework for non-orthogonal transmission and robust interference management in multi-antenna wireless networks. In this work, we characterize the MMF Degrees-of-Freedom (DoF) achieved by RS and NoRS in multigroup multicast with imperfect CSIT and demonstrate the benefits of RS strategies for both underloaded and overloaded scenarios. Motivated by the DoF analysis, we then formulate a generic transmit power constrained optimization problem to achieve MMF rate performance. The superiority of RS-based multigroup multicast beamforming compared with NoRS is demonstrated via simulations in both terrestrial and multibeam satellite systems. In particular, due to the characteristics and challenges of multibeam satellite communications, our proposed RS strategy is shown promising to manage its inter-beam interference.

Multi-Antenna Interference Management for Coded Caching

A multi-antenna broadcast channel scenario is considered where a base station delivers contents to cache-enabled user terminals. A joint design of coded caching (CC) and multigroup multicast beamforming is proposed to benefit from spatial multiplexing gain, improved interference management and the global CC gain, simultaneously. The developed general content delivery strategies utilize the multiantenna multicasting opportunities provided by the CC technique while optimally balancing the detrimental impact of both noise and inter-stream interference from coded messages transmitted in parallel. Flexible resource allocation schemes for CC are introduced where the multicast beamformer design and the receiver complexity are controlled by varying the size of the subset of users served during a given time interval, and the overlap among the multicast messages transmitted in parallel, indicated by parameters $\alpha$ and $\beta$, respectively. Degrees of freedom (DoF) analysis is provided showing that the DoF only depends on $\alpha$ while it is independent of $\beta$. The proposed schemes are shown to provide the same degrees-of-freedom at high signal-to-noise ratio (SNR) as the state-of-art methods and, in general, to perform significantly better, especially in the finite SNR regime, than several baseline schemes.

Multi-Group Multicast Beamforming: Optimal Structure and Efficient Algorithms

This paper considers the multi-group multicast beamforming optimization problem, for which the optimal solution has been unknown due to the non-convex and NP-hard nature of the problem. By utilizing the successive convex approximation numerical method and Lagrangian duality, we obtain the optimal multicast beamforming solution structure for both the quality-of-service (QoS) problem and the max-min fair (MMF) problem. The optimal structure brings valuable insights into multicast beamforming: We show that the notion of uplink-downlink duality can be generalized to the multicast beamforming problem. The optimal multicast beamformer is a weighted MMSE filter based on a group-channel direction: a generalized version of the optimal downlink multi-user unicast beamformer. We also show that there is an inherent low-dimensional structure in the optimal multicast beamforming solution independent of the number of transmit antennas, leading to efficient numerical algorithm design, especially for systems with large antenna arrays. We propose efficient algorithms to compute the multicast beamformer based on the optimal beamforming structure. Through asymptotic analysis, we characterize the asymptotic behavior of the multicast beamformers as the number of antennas grows, and in turn, provide simple closed-form approximate multicast beamformers for both the QoS and MMF problems. This approximation offers practical multicast beamforming solutions with a near-optimal performance at very low computational complexity for large-scale antenna systems.

Low Complexity Algorithms for Robust Multigroup Multicast Beamforming

Existing methods for robust multigroup multicast beamforming obtain feasible points using semidefinite relaxation (SDR) and Gaussian randomization, and have high computational complexity. In this letter, we consider the robust multigroup multicast beamforming design to minimize the sum power (SP) or per-antenna power (PAP) under the signal-to-interference-plus-noise ratio (SINR) constraints and to maximize the worst-case SINR under the SP constraint or PAP constraints, respectively. The resulting optimization problems are challenging non-convex problems with infinitely many constraints. For each problem, using the majorization-minimization (MM) approach, we propose an iterative algorithm to obtain a feasible solution which is shown to be a stationary point under certain conditions. We also show that the proposed algorithms have much lower computational complexity than existing SDR-based algorithms.

Improved ADMM-based algorithms for multi-group multicasting in large-scale antenna systems with extension to hybrid beamforming

In this paper, multi-group multicast beamforming is considered for the full digital and hybrid beamforming. The wireless system comprises of a multiple-antenna base station and single-antenna users. Quality-of-service (QoS)-aware design is investigated where the optimization objective is to minimize the total transmitted power subject to the signal-to-interference-plus-noise ratio (SINR) constraint at each user. In addition to the SINR constraints, per-antenna power constraint is included for each antenna of the base station. The original optimization problem for full digital beamforming is transformed into an equivalent form such that the alternating direction method of multipliers (ADMM) can be applied in an effective and computationally inexpensive manner for the large-scale antenna systems. In this new formulation, the beamformer weight vectors are decomposed into two subspaces in order to decrease the number of dual variables and multiplications. The optimum update equations are obtained for the proposed ADMM algorithm. This new reformulation is used for two different hybrid beamforming structures employing phase shifters and vector modulators. Optimum updates are derived for each system. The proposed algorithms decrease computational complexity of the existing ADMM algorithms due to the effective reformulation as well as the direct solution of the nonconvex problem. In the simulation results, it is shown that the proposed methods have better convergence behavior and less computational time than the benchmark algorithms. Furthermore, the proposed method for hybrid beamforming with vector modulators performs better than its counterpart in the literature in terms of transmitted power.

Outage Constrained Robust Multigroup Multicast Beamforming for Multi-Beam Satellite Communication Systems

We investigate outage constrained robust multigroup multicast beamforming for multi-beam satellite communication systems with full frequency reuse. Based on a satellite downlink beam domain channel model with channel phase uncertainty taken into account, we first investigate robust multigroup multicast beamforming with the aim to maximize the worst-case outage signal-to-interference-plus-noise ratio under the outage and the per-beam power constraints. We then cast the outage constrained robust beamforming design into the convex optimization framework with some approximation techniques. Simulation results show that the proposed robust multigroup multicast beamformer can provide significant performance gains in terms of multicast rate and outage probability over the conventional approach.

Rate-Splitting for Max-Min Fair Multigroup Multicast Beamforming in Overloaded Systems

In this paper, we consider the problem of achieving max-min fairness amongst multiple co-channel multicast groups through transmit beamforming. We explicitly focus on overloaded scenarios in which the number of transmitting antennas is insufficient to neutralize all inter-group interference. Such scenarios are becoming increasingly relevant in the light of growing low-latency content delivery demands, and also commonly appear in multibeam satellite systems. We derive performance limits of classical beamforming strategies using degrees of freedom (DoF) analysis unveiling their limitations; for example, rates saturate in overloaded scenarios due to inter-group interference. To tackle interference, we propose a strategy based on degraded beamforming and successive interference cancellation. While the degraded strategy resolves the rate-saturation issue, this comes at a price of sacrificing all spatial multiplexing gains. This motivates the development of a unifying strategy that combines the benefits of the two previous strategies. We propose a beamforming strategy based on rate-splitting (RS), which divides the messages intended to each group into a degraded part and a designated part, and transmits a superposition of both degraded and designated beamformed streams. The superiority of the proposed strategy is demonstrated through DoF analysis. Finally, we solve the RS beamforming design problem and demonstrate significant performance gains through simulations.

ADMM-Based Fast Algorithm for Multi-Group Multicast Beamforming in Large-Scale Wireless Systems

Multi-group multicast beamforming in wireless systems with large antenna arrays and massive audience is investigated in this paper. Multicast beamforming design is a well-known non-convex quadratically constrained quadratic programming (QCQP) problem. A conventional method to tackle this problem is to approximate it as a semi-definite programming problem via semi-definite relaxation, whose performance, however, deteriorates considerably as the number of per-group users goes large. A recent attempt is to apply convex-concave procedure (CCP) to find a stationary solution by treating it as a difference of convex programming problem, whose complexity, however, increases dramatically as the problem size increases. In this paper, we propose a low-complexity high-performance algorithm for multi-group multicast beamforming design in large-scale wireless systems by leveraging the alternating direction method of multipliers (ADMM) together with CCP. In specific, the original non-convex QCQP problem is first approximated as a sequence of convex subproblems via CCP. Each convex subproblem is then reformulated as a novel ADMM form. Our ADMM reformulation enables that each updating step is performed by solving multiple small-size subproblems with closed-form solutions in parallel. Numerical results show that our fast algorithm maintains the same favorable performance as state-of-the-art algorithms but reduces the complexity by orders of magnitude.

User grouping and admission control for multi-group multicast beamforming in MIMO systems

In this paper, we consider the multi-group multicasting problem in a MIMO wireless cellular system, whereby the base station can generate multiple beampatterns to serve multiple groups simultaneously. Each user is interested in multiple multicast groups, but is only allowed to be assigned to one of them eventually during each transmission interval. We formulate it as a joint optimization problem of multicast beamformer design as well as user grouping, and admission control is also considered to account for the quality of service demands of individual users. To deal with this NP-hard problem, we adopt the big-M formulation method and the semidefinite relaxation scheme to reformulate it to a mixed-integer semidefinite programming problem. Three algorithms are developed to solve the obtained approximate problem with different computational costs. Simulation results are presented to demonstrate the performance of the proposed algorithms in terms of the number of admitted users, power consumption and computation time.

Distributed Cooperative Multicast in Cognitive Multi-Relay Multi-Antenna Systems

In this letter, cooperative multicast in cognitive relay systems is investigated, where multiple multi-antenna relay nodes help forward the transmitted message from different sources to the corresponding destinations. Our objective is to maximize the global transmission rate scaling factor by cooperatively optimizing the forwarding matrix for each relay node. To solve the problem effectively, we first prove that the optimal forwarding matrix at each relay node is the combination of a multi-stream matched-filter receiver and a multi-stream adaptive beamformer, and then demonstrate that the beamformer design problem can be further transformed into the cognitive multi-group multicast beamforming problem. Finally, a bisection-based algorithm is proposed to find the optimal beamforming vector. Compared to the existing cooperative multicast schemes, the proposed scheme can achieve higher transmission rate and provide better protection for primary nodes.