We study an Age-of-Information (AoI) scheduling problem where users can tolerate occasional violations of AoI for each source at the base station. Each user’s AoI is associated with a violation tolerance constraint. We are interested in determining whether a set of users, each with a given AoI deadline, a violation tolerance constraint, and a packet loss rate (due to channel condition) is schedulable, and if so, find a feasible scheduler. For this problem, we study two cases: 1) the stable tolerant case where the tolerance rate is higher than the packet loss rate for each source and 2) the unstable tolerant case where the tolerance rate is lower than the packet loss rate for at least one source. For the stable tolerant case, we design an algorithm called stable tolerant scheduler (STS), which can find a feasible scheduler for any network when the system load is no greater than$\ln 2$(roughly 70%). When the system load is between$\ln 2$and 1, we offer a necessary and sufficient condition for STS to find a feasible scheduler by solving an optimization problem. Likewise, for the unstable tolerance case, we develop a scheduler called unstable tolerant scheduler (UTS) and its corresponding schedulability conditions. Through extensive simulations, we show that STS and UTS match our theoretical results.

Open radio access network (O-RAN) enables cooperative signal processing among multiple cells at a centralized O-RAN distributed unit (O-DU). It is a key technology for cellular networks to increase spectrum efficiency. To achieve cooperative signal processing across multiple cells, a new scheduler is needed. Specifically, the scheduler must jointly determine RB allocation, MCS assignment, and beamforming matrices for all users from all the cells that are involved in multi-cell processing. In addition, the scheduler must obtain its scheduling solution within each TTI (i.e., at most 1 ms) to be useful for the frame structure defined by 5G NR. In this paper, we present O-$\mathbf M^{3}$—a real-time scheduler formulti-cellMIMO networks under the O-RAN architecture. O-$\mathbf M^{3}$can meet the stringent timing requirement with joint optimization of beamforming matrices, RB allocation, and MCS assignment among multiple cells. O-$\mathbf M^{3}$is developed through a novel multi-pipeline design that exploits parallelism. Under this design, one pipeline performs a sequence of operations for cell-edge users to explore joint transmission, and in parallel, the other pipeline is performed for cell-center users to explore MU-MIMO transmission. We implement O-$\mathbf M^{3}$on a commercial off-the-shelf (COTS) GPU. Experimental results show that O-$\mathbf M^{3}$is capable of offering a scheduling solution within 500$\mu \text{s}$for an O-RAN system with 7 O-RAN radio units (O-RUs), 100 users, 100 RBs, and$2\times 8$MIMO. O-$\mathbf M^{3}$can also meet the 1 ms requirement for$2\times 12$MIMO systems. Meanwhile, O-$\mathbf M^{3}$can provide ~40% throughput gain on average through joint transmission across multiple cells.

Channel State Information (CSI) is a critical piece of information for MU-MIMO beamforming. However, CSI estimation errors are inevitable in practice. The random and uncertain nature of CSI estimation errors poses significant challenges to MU-MIMO beamforming. State-of-the-art works addressing such a CSI uncertainty can be categorized into model-based and data-driven works, both of which have limitations when providing a performance guarantee to the users. In contrast, this paper presents Limited Sample-based Beamforming (LSBF)—a novel approach to MU-MIMO beamforming that only uses a limited number of CSI data samples (without assuming any knowledge of channel distributions). Thanks to the use of CSI data samples, LSBF enjoys flexibility similar to data-driven approaches and can provide a theoretical guarantee to the users—a major strength of model-based approaches. To achieve both, LSBF employs chance-constrained programming (CCP) and utilizes the$\infty $-Wasserstein ambiguity set to bridge the unknown CSI distribution with limited CSI samples. Through problem decomposition and a novel bilevel formulation for each subproblem based on limited CSI data samples, LSBF solves each subproblem with a binary search and convex approximation. We show that LSBF significantly improves the network performance while providing a probabilistic data rate guarantee to the users.

Hybrid beamforming (HB) architecture has been widely considered for 5G mmWave systems. It reduces hardware complexity by allowing the number of RF chains to be far fewer than the number of antennas. A major practical challenge for HB is to obtain a beamforming solution in real-time. In 5G NR, new frame structures with short TTIs are employed to support mmWave communications. Under such frame structures, it is necessary to obtain a beamforming solution with a time resolution varying from 1 ms to 125$\mu$s – an extremely stringent time requirement considering the complexity involved in HB. In this paper, we present the design and implementation ofTurbo-HB– a novel beamforming design under the HB architecture that is capable of offering the beamforming matrices in less than 500$\mu$s. The key ideas of Turbo-HB include: (i) reducing the complexity of computation-intensive SVD operations by exploiting channel sparsity at mmWave frequencies, and (ii) achieving large-scale parallel computation with minimal memory access. We implement Turbo-HB on an off-the-shelf Nvidia GPU and conduct extensive experiments. Our experimental results demonstrate that Turbo-HB can obtain a beamforming solution in 500$\mu$s for up to 100 RBs and 10 MU-MIMO users on each RB while offering competitive throughput performance compared to state-of-the-art (non-real-time) algorithms.

Degree-of-freedom (DoF)-based models have been proven to be highly successful in modeling and analysis of MIMO systems. Among existing DoF-based models, the number of DoFs used for interference cancellation (IC) is solely based on the number of interfering data streams. However, from both experimental and simulation results, we find that signal strengths of an interference link vary significantly in different directions in the eigenspace. In this paper, we exploit the difference in interference signal strengths in the eigenspace and perform IC with DoFs only on those directions with strong signals. To differentiate interference signal strengths on an interference link, we introduce a novel concept called “effective rank threshold.” Based on this threshold, DoFs are consumed only to cancel strong interferences in the eigenspace while weak interferences are treated as noise in throughput calculation. To better understand the benefits of this approach, we study a fundamental trade-off between network throughput and effective rank threshold for an MU-MIMO network. Our simulation results show that network throughput under optimal rank threshold is significantly higher than that under existing DoF IC models. To ensure the new DoF IC model is feasible at PHY layer, we propose an algorithm to set the weights for all nodes that can offer our desired DoF allocation.

Multi-User (MU)-MIMO technology plays a vital role in 5G NR. Under MU-MIMO transmission, multiple users can share the same time-frequency resources simultaneously. For 5G MU-MIMO systems, it is challenging to design a scheduler. The scheduler needs to determine resource block (RB) allocation, the number of data streams and modulation and coding scheme (MCS) for each user in each transmission time interval (TTI). In particular, multiple users can be co-scheduled on the same RB for MU-MIMO transmission. In addition, it is necessary for the scheduler to find a scheduling solution within each TTI to be useful. In this paper, we present mCore$+$, a novel design and implementation that can achieve$\sim$500$\mu$s timing performance for 5G MU-MIMO systems. mCore$+$is meticulously designed with a multi-phase optimization and heavily leverages large-scale parallel computation. In each phase, mCore$+$either decomposes the optimization problem into a number of independent sub-problems, or reduces the search space into a smaller but most promising subspace, or both. mCore$+$is validated on a commercial-off-the-shelf GPU platform. Experimental results show that mCore$+$can offer a scheduling solution in$\sim$500$\mu$s for up to 100 RBs, 100 users, 29 MCS levels and$4 \times 12$MIMO systems. Also, mCore$+$can achieve better or comparable throughput performance compared to other state-of-the-art algorithms.

Cloud Radio Access Network (C-RAN) is a novel centralized architecture for cellular networks. C-RAN can significantly improve spectrum efficiency by performing cooperative signal processing for multiple cells at a centralized baseband unit (BBU) pool. However, a new resource scheduler is needed before we can take advantage of C-RAN's multi-cell processing capability. Under C-RAN architecture, the scheduler must jointly determine RB allocation, MCS assignment, and beamforming matrices for all users under all covering cells. In addition, it is necessary to obtain a scheduling solution within each TTI (at most 1 ms) to be useful for the frame structure defined by 5G NR. In this paper, we present M3—a sub-ms scheduler for multi-cell MIMO networks under C-RAN architecture. M3addresses the stringent timing requirement through a novel multi-pipeline design that exploits parallelism. Under this design, one pipeline performs a sequence of operations for cell-edge users to explore joint transmission, and in parallel, the other pipeline is for cell-center users to explore MU-MIMO transmission. Experimental results show that M3is capable of offering a scheduling solution within 1 ms for 7 remote radio heads (RRHs), 100 users, 100 RBs, and 2×12 MIMO. Meanwhile, M3provides ~40%. throughput gain on average by employing joint transmission.

Accurate estimation of Channel State Information (CSI) is essential to design MU-MIMO beamforming. However, errors in CSI estimation are inevitable in practice. State-of-the-art works model CSI as random variables and assume certain specific distributions or worst-case boundaries, both of which suffer performance issues when providing performance guarantees to the users. In contrast, this paper proposes a Data-Driven Beamforming (D2BF) that directly handles the available CSI data samples (without assuming any particular distributions). Specifically, we employ chance-constrained programming (CCP) to provide probabilistic data rate guarantees to the users and introduce ∞-Wasserstein ambiguity set to bridge the unknown CSI distribution with the available (limited) data samples. Through problem decomposition and a novel bilevel formulation for each subproblem, we show that each subproblem can be solved by binary search and convex approximation. We also validate that D2BF offers better performance than the state-of-the-art approach while meeting probabilistic data rate guarantees to the users.

Age of Information (AoI) is an application layer performance metric that quantifies the freshness of information. This paper investigates scheduling problems at network edge when there is an AoI requirement for each source node, which we call Maximum AoI Threshold (MAT). Specifically, we want to determine whether or not a vector of MATs corresponding to the source nodes is schedulable, and if so, find a feasible scheduler for it. For a small network, we present an optimal procedure calledCyclic Scheduler Detection(CSD) that can determine the schedulability with absolute certainty. For a large network where CSD is not applicable, we present a novel low-complexity procedure, calledFictitious Polynomial Mapping(FPM), and prove that FPM can find a feasible scheduler for any MAT vector when the load is under$\ln 2$. We use extensive numerical results to validate our theoretical results and show that the performance of FPM is significantly better than a state-of-the-art scheduling algorithm.

MU-MIMO technology enables a base station (BS) to transmit signals to multiple users simultaneously on the same frequency band. It is a key technology for 5G NR to increase the data rate. In 5G specifications, an MU-MIMO scheduler needs to determine RBs allocation and MCS assignment to each user for each TTI. Under MU-MIMO, multiple users may be coscheduled on the same RB and each user may have multiple data streams simultaneously. In addition, the scheduler must meet the stringent real-time requirement (~1 ms) during decision making to be useful. This paper presents mCore, a novel 5G scheduler that can achieve ~1 ms scheduling with joint optimization of RB allocation and MCS assignment to MU-MIMO users. The key idea of mCore is to perform a multi-phase optimization, leveraging large-scale parallel computation. In each phase, mCore either decomposes the optimization problem into a number of independent sub-problems, or reduces the search space into a smaller but most promising subspace, or both. We implement mCore on a commercial-off-the-shelf GPU. Experimental results show that mCore can offer the best scheduling performance for up to 100 RBs, 100 users, 29 MCS levels and 4 × 12 antennas when compared to other state-of-the-art algorithms. It is also the only algorithm that can find its scheduling solution in ~1 ms.

We study an Age of Information (AoI) scheduling problem where AoI for each source at the base station (BS) can tolerate occasional violations, which we define as a violation tolerance constraint. The problem is to determine whether a set of users with given AoI deadlines, tolerance rates, and packet loss rates (due to each source's channel condition) is schedulable, and if so find a feasible scheduler. We study two cases: (i) the stable tolerant case where the tolerance rate is higher than the packet loss rate for all sources; (ii) the unstable tolerant case where the tolerance rate is lower than the packet loss rate for at least one source. For stable tolerant case, we design an algorithm called stable tolerant scheduler (STS), which can find a feasible scheduler for any network when system load is no greater than ln 2. For unstable tolerance case, we develop unstable tolerant scheduler (UTS) and identify a schedulability condition for it. Through extensive simulations, we show that STS and UTS match our theoretical results.

The Age of Information (AoI) is a key metric to measure the freshness of information for IoT applications. Most of the existing analytical models for AoI are overly idealistic and do not capture state-of-the-art transmission technologies such as 5G as well as channel dynamics in both frequency and time domains. In this article, we present Kronos, a real-time 5G-compliant scheduler that minimizes AoI for IoT data collection. Kronos is designed to cope with highly dynamic channel conditions. Its main function is to perform RB allocation and to select the modulation and coding scheme for each source node based on channel conditions, with the objective of minimizing long-term AoI. To meet the stringent real-time requirement for 5G, we develop a GPU-based implementation of Kronos on commercial off-the-shelf Nvidia GPUs. Through extensive experimentation, we show that Kronos can find near-optimal solutions under submillisecond time scale. To the best of our knowledge, this is the first real-time AoI scheduler that is 5G compliant.

Hybrid beamforming (HB) architecture has been widely recognized as the most promising solution to mmWave MIMO systems. A major practical challenge for HB is to obtain a solution in ~1 ms, which is an extremely stringent but necessary time requirement for its deployment in the field. In this paper, we present the design and implementation of Turbo-HB, codename for a novel beamforming design under the HB architecture that can obtain the beamforming matrices in about 1 ms. The key ideas in Turbo-HB include (i) reducing the complexity of SVD techniques by exploiting the limited number of channel paths at mmWave frequencies, and (ii) designing and implementing a parallelizable algorithm for a large number of matrix transformations. We validate Turbo-HB by implementing it on an off-the-shelf Nvidia GPU. Through extensive experiments, we show that Turbo-HB can meet ~1 ms timing requirement while delivering competitive throughput performance compared to state-of-the-art algorithms.

Age of Information (AoI) is an application layer performance metric that quantifies the freshness of information. This paper investigates scheduling problems at network edge when each source node has an AoI requirement (which we call Maximum AoI Threshold (MAT)). Specifically, we want to determine whether or not a vector of MATs for the source nodes is schedulable, and if so, find a feasible scheduler for it. For a small network, we present an optimal procedure called Cyclic Scheduler Detection (CSD) that can determine the schedulability with absolute certainty. For a large network where CSD is not applicable, we present a novel low-complexity procedure, called Fictitious Polynomial Mapping (FPM), and prove that FPM can find a feasible scheduler for any MAT vector when the load is under ln 2. We use extensive numerical results to validate our theoretical results and show that the performance of FPM is significantly better than a state-of-the-art scheduling algorithm.

Degree-of-freedom (DoF) based models have become prevalent in studying MIMO-based wireless networks. However, most existing DoF-based models assume the channel matrix is of full-rank. Such a simplifying assumption has gradually become problematic, particularly when the number of antennas increases and the propagation environment is not close to ideal. In this paper, we address this problem by developing a general theory for the DoF-based model under general channel rank conditions. We start with a fundamental understanding on how MIMO's DoFs are consumed at each node for spatial multiplexing (SM) and interference cancellation (IC) in the presence of rank-deficient channels. Based on this understanding, we develop a DoF model that can be used for identifying the DoF region of a multi-link MIMO network and for studying DoF scheduling in MIMO networks under general channel rank conditions. Specifically, we find that for IC, shared DoF consumption at both transmit and receive nodes is critical for efficient DoF allocation. Further, we show that DoF consumption under the existing full-rank assumption is a special case of our generalized DoF model. Based on case studies, we show that the general IC model can achieve larger feasible DoF regions or improved objective values than existing unilateral IC models. The findings of this paper pave the way for future research of many-antenna networks under general channel rank conditions.

Age of information (AoI) is a powerful new metric to quantify the freshness of information and has gained increasing popularity in IoT applications. Existing models on AoI remain primitive and do not consider state-of-the-art transmission technologies such as 5G. They also fail to consider the impact of dynamic channel conditions. In this paper, we present Kronos, a 5G-compliant AoI scheduling algorithm that can cope with highly dynamic channel conditions. Kronos is capable of performing RB allocation and selecting MCS for each source node based on channel conditions, with the objective of minimizing long-term AoI. To meet the stringent real-time requirement for 5G, we propose a GPU-based implementation of Kronos on low-cost offthe-shelf GPUs. Through simulations and experiments, we show that Kronos can find near-optimal AoI scheduling solutions in sub-millisecond time scale. To the best of our knowledge, this is the first 5G-compliant real-time AoI scheduler that can cope with dynamic channel conditions.

Degree-of-Freedom (DoF) based models have been widely used to study MIMO networks. To cancel interference, the number of DoFs used in the state-of-the-art DoF models is solely based on the number of interfering data streams. However, by decomposing an interference into the eigenspace, we find that signal strengths varies significantly in different directions for the same interference link. In this paper, we exploited the difference in interference signal strength in the eigenspace and differentiate strong and weak interference signals via their singular values. By introducing a concept of effective rank threshold, we propose to use DoFs only to cancel strong interference in the eigenspace based on this threshold while treating weak interference signals as noise in throughput calculation. We explore a fundamental tradeoff between network throughput and effective rank threshold. Using simulation results on MU-MIMO networks, we show that network throughput under optimal rank threshold setting is significantly higher than that under existing DoF IC models. To ensure feasibility at the PHY layer, we present an algorithm that can find Tx and Rx weights at each node that can offer our desired DoF allocation.

In recent years, degree-of-freedom (DoF) based models were proven to be very successful in studying MIMO-based wireless networks. However, most of these studies assume channel matrix is of full-rank. Such assumption, although attractive, quickly becomes problematic as the number of antennas increases and propagation environment is not close to ideal. In this paper, we address this problem by developing a general theory for DoF-based model under rank-deficient conditions. We start with a fundamental understanding on how MIMO's DoFs are consumed for spatial multiplexing (SM) and interference cancellation (IC) in the presence of rank deficiency. Based on this understanding, we develop a general DoF model that can be used for identifying DoF region of a multi-link MIMO network and for studying DoF scheduling in MIMO networks. Specifically, we found that shared DoF consumption at transmit and receive nodes is critical for optimal allocation of DoF for IC. The results of this paper serve as an important tool for future research of many-antenna based MIMO networks.

This paper proposes a new energy efficiency (EE) model with circuit power consumption in downlink massive multiple-input multiple-output (MIMO) systems, and analyzes how the number of transmit antennas and the transmit power affect the EE. A concise model of the distribution of the mutual information and a new realistic power consumption model are used to draw a closed-form expression for the EE model. Mathematical analysis proves that the EE is a concave function of the number of transmit antennas and the transmit power, and the EE increases first and then decreases as the transmit power increases, indicating the existence of the optimal number of transmit antennas and the transmit power. An iterative algorithm is given to compute jointly the optimal number of transmit antennas and the transmit power. Simulation results show that when the circuit power consumption is comparable to the transmit power, there exists an optimal number of transmit antennas to maximize the EE.

Future small cells are expected to be energy-efficient and utilize green technologies. To this end, a promising solution is to employ automatic energy harvesting techniques, such as power splitting (PS) which harvests energy from ambient radio frequency (RF) signals in modern communication systems. In this paper, optimization on PS ratio design is investigated to maximize the average harvested energy in the context of general largescale K-tier heterogeneous cellular networks (HCNs). Specifically, coverage probabilities and average energy harvesting expressions are derived with the stochastic geometry treatment to elucidate the performance of future green networks. Then optimal fixed PS ratios for each tier are obtained under coverage performance constraints. Moreover, with receivers' position information effortlessly provided in future networks, a dynamic location-based PS ratio design (DLPS) is proposed to further enhance the energy harvesting performance. Simulation results are given to demonstrate that the average harvested energy is effectively increased by more than 30% when coverage probability requirement is greater than 0.7 by our proposed DLPS compared with the optimal fixed PS ratio while maintaining the coverage performance. Furthermore, rather than drawing the conclusions about the merits of our PS strategy, this work is to provide a tractable analytical framework for addressing the energy harvesting issues in such HCNs.

As cells are getting smaller, more random and chaotic in future heterogeneous cellular networks (HCNs), mitigating interference to enhance coverage performance has become one of the key challenges. To elucidate the coverage and throughput performance of downlink HCNs, a tractable framework with frequency division (FD) scenario is provided. Coverage probability and average cell throughput expressions are carried out to further understand how FD effects system performance with the stochastic geometry treatment. Furthermore, with some plausible assumptions, we derive the specific closed-form expressions in some special cases. Simulation results show that the coverage performance is effectively improved by using FD comparing with conventional frequency sharing (FS) scenario, which are firmly consistent with our theoretical derivation. The analytical results of the present work also demonstrate that although some throughput will be lost compared to FS, it is still acceptable since UEs could choose any tier which offers greatest performance under FD scenario, hence this work further provides mobile operators a guideline for resource allocation schemes in future chaotic multi-tier networks.