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Stochastic Optimization Based Dynamic User Scheduling and Hybrid Precoding for Broadband MmWave MIMO
... However, these fully digital beamforming methods aiming at instantaneous performance are impractical in the scope of mmWave networks. For mmWave communications, the joint problem has also been investigated in a single cell [43]- [46]. The authors in [43] formulate the joint problem as a non-convex and combinatorial optimization, where the objective is to maximize the instantaneous sum rate. ...
... The above two schemes solve the joint problem in a time-slot fashion, where the historical experience is ignored. For long-term performance metrics, the Lyapunov drift optimization framework is adopted to maximize the weighted long-term sum rate [45], [46], which cannot work properly in a multi-cell network due to extra inter-cell interferences. To the best of our knowledge, existing studies do not take into account the content demands of users, which are nevertheless of paramount importance in the future content-centric communication systems. ...
Millimeter-wave (mmWave) cloud-edge collaboration has emerged as an effective solution for low-latency transmission by harnessing the potentials of cloud and edge nodes (eNodes) as well as abundant bandwidth. In a mmWave dense network, centralized processing and coordinated multi-points processing require large amounts of signaling exchange overhead, which in turn increase the latency. As such, distributed mechanism is demanded. In this paper, we investigate joint user scheduling and beam selection strategies for eNodes and formulate the problem as a constrained Markov decision process. The objective and constraints are long-term average network delay cost minimization and instantaneous quality of service (QoS) guarantee for each user equipment. To update the distributed strategies, we apply the multi-agent reinforcement learning technique and propose a hybrid learning framework by extending the actor-critic model, where centralized training and decentralized execution are implemented. We utilize the Lagrange technique to design the reward functions. Additionally, a novel actor network architecture and an exploration scheme are proposed. Simulation results validate the effectiveness of the proposed intelligent distributed algorithm with a high degree of scalability, and show superior performance in terms of long-term average network delay cost and QoS satisfaction rates compared with other methods.
... The joint user scheduling and beamforming problem has also been investigated in the context of mmWave communications [5]- [8]. The problem is formulated as a non-convex and combinatorial optimization problem in [5]. ...
... Both works consider a single-cell scenario with the objective of instantaneous sum rate maximization. For long-term performance metrics, works [7], [8] adopte the Lyapunov drift optimization framework to maximize the weighted long-term sum rate in a single cell network. However, the above mentioned works do not take into account content demands of users, which should be fundamentally important to future communication systems. ...
In this paper, we consider a multi-cell downlink mmWave communication network, where the base stations (BS) are assumed to be incapable of synchronously accommodating service requests from all users. The objective is to develop the joint user scheduling and beam selection strategy that minimizes the long-term average delay cost while satisfying the instantaneous quality of service constraint of each user. To achieve the long-term performance, we propose a distributed algorithm to develop the joint strategy based on multi-agent reinforcement learning. Simulation results show that the proposed intelligent distributed algorithm can learn from the dynamic environment and enhance the long-term network performance.
... Although these previous studies [8]- [17] do not take JUSBA into consideration, they are still instructive to the interests of this paper. To the best of our knowledge, only a few studies have jointly considered the allocation of beams and the selection of users [19]- [21]. In [19], the joint optimization problem was formulated as a non-convex combinatorial optimization problem, and a DC-based (difference of two convex functions) method and a greedybased method were proposed. ...
... [20] exploited the problem in the Lyapunov-drift optimization framework for lens antenna array beam-based downlinks, and a BCU-based (block coordinated update) algorithm and a greedy-based algorithm were presented. With the help of Lyapunov-drift optimization tool, [21] proposed an algorithm that conducted user scheduling, resource allocation and analog precoder design for broadband mmWave mimo system under hybrid architecture. The above three methods provide an analytical way to solve combinatorial optimization problems that belong to NP-hard problems which have no mature approach to acquire an analytical solution. ...
Both millimeter wave (mmWave) communication and massive multiple-input multiple-output (MIMO) are important technologies in the 5G era. To reduce the cost of a mmWave massive MIMO system in practice, hybrid beamforming usually adopted, which however inevitability complicates both user selection and analog beam allocation. To this end, in this paper we jointly optimize user selection and beam allocation under a wideband frequency selective mmWave channel. To be practical, both beam collision and inter-user interference have been taken into account. To tackle the non-convexity of the formulated problem, we propose a ping-pong-like optimization method by using hybrid particle swarm optimization and simulated annealing (HPS). Concretely, the joint optimization problem is divided into two sub-problems and the near-optimal solution is approached via ping-pong iteration optimization. The Metropolis acceptance criterion of simulated annealing algorithm is introduced to overcome the drawback of traditional particle swarm optimization, improving global search capability of HPS algorithm. The simulation results verify the effectiveness and flexibility of the proposed method compared with existing methods.
Millimeter wave (mmWave) communication is expected to play a central role in next generation mobile systems (5G) and beyond, by providing multi-Gbps data rates. However, the severe pathloss and sensitivity to blockages at mmWave frequencies significantly challenge practical implementations. One effective way to mitigate these effects and to increase the communication range is beamforming in combination with relaying. In this paper, we study the beam scheduling problem for mmWave half-duplex (HD) relay networks, where the relay topology can be arbitrary. Based on theoretically optimal scheduling results, we first implement a network simplification procedure to reduce the network topology complexity, and then propose two practically relevant beam scheduling schemes: the deterministic edge coloring (EC) scheduler and the adaptive backpressure (BP) scheduler. The former consists of a very simple one-time computation of the sequence of scheduling states, which is then repeated periodically. The one-time computation depends on the underlying network topology, and therefore it must be repeated when such topology changes. As such, this approach is more suited to quasi-static scenarios. The latter is an “online” approach which updates scheduling weights and solves at each time slots a weighted sum rate maximization. Hence, it’s computational complexity may be significantly higher than that of EC, but it is better suited to dynamic time-varying scenarios. With the aid of computer simulations, we show that both the proposed schedulers guarantee network stability within the network capacity. Particularly, in comparison with two baseline schemes, the proposed schedulers achieve much smaller queuing backlogs, much smaller backlog fluctuations, and much lower packet end-to-end delays.
In beam-based massive multiple-input multiple-output systems, signals are processed spatially in the radio-frequency (RF) front-end and thereby the number of RF chains can be reduced to save hardware cost, power consumptions and pilot overhead. Most existing work focuses on how to select, or design analog beams to achieve performance close to full digital systems. However, since beams are strongly correlated (directed) to certain users, the selection of beams and scheduling of users should be jointly considered. In this paper, we formulate the joint user scheduling and beam selection problem based on the Lyapunov-drift optimization framework and obtain the optimal scheduling policy in a closed-form. For reduced overhead and computational cost, the proposed scheduling schemes are based only upon statistical channel state information. Towards this end, asymptotic expressions of the downlink broadcast channel capacity are derived. To address the weighted sum rate maximization problem in the Lyapunov optimization, an algorithm based on block coordinated update is proposed and proved to converge to the optimum of the relaxed problem. To further reduce the complexity, an incremental greedy scheduling algorithm is also proposed, whose performance is proved to be bounded within a constant multiplicative factor. Simulation results based on widely-used spatial channel models are given. It is shown that the proposed schemes are close to optimal, and outperform several state-of-the-art schemes.
Millimeter wave (mmW) frequencies between 30 and 300 GHz are a new frontier
for cellular communication that offers the promise of orders of magnitude
greater bandwidths combined with further gains via beamforming and spatial
multiplexing from multi-element antenna arrays. This paper surveys measurements
and capacity studies to assess this technology with a focus on small cell
deployments in urban environments. The conclusions are extremely encouraging;
measurements in New York City at 28 and 73 GHz demonstrate that, even in an
urban canyon environment, significant non-line-of-sight (NLOS) outdoor,
street-level coverage is possible up to approximately 200 m from a potential
low power micro- or picocell base station. In addition, based on statistical
channel models from these measurements, it is shown that mmW systems can offer
more than an order of magnitude increase in capacity over current
state-of-the-art 4G cellular networks at current cell densities. Cellular
systems, however, will need to be significantly redesigned to fully achieve
these gains. Specifically, the requirement of highly directional and adaptive
transmissions, directional isolation between links and significant
possibilities of outage have strong implications on multiple access, channel
structure, synchronization and receiver design. To address these challenges,
the paper discusses how various technologies including adaptive beamforming,
multihop relaying, heterogeneous network architectures and carrier aggregation
can be leveraged in the mmW context.
Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss
than the microwave signals currently used in most wireless applications. MmWave
systems must therefore leverage large antenna arrays, made possible by the
decrease in wavelength, to combat pathloss with beamforming gain. Beamforming
with multiple data streams, known as precoding, can be used to further improve
mmWave spectral efficiency. Both beamforming and precoding are done digitally
at baseband in traditional multi-antenna systems. The high cost and power
consumption of mixed-signal devices in mmWave systems, however, make analog
processing in the RF domain more attractive. This hardware limitation restricts
the feasible set of precoders and combiners that can be applied by practical
mmWave transceivers. In this paper, we consider transmit precoding and receiver
combining in mmWave systems with large antenna arrays. We exploit the spatial
structure of mmWave channels to formulate the precoding/combining problem as a
sparse reconstruction problem. Using the principle of basis pursuit, we develop
algorithms that accurately approximate optimal unconstrained precoders and
combiners such that they can be implemented in low-cost RF hardware. We present
numerical results on the performance of the proposed algorithms and show that
they allow mmWave systems to approach their unconstrained performance limits,
even when transceiver hardware constraints are considered.
This paper proposes efficient rate and power allocation algorithms for OFDMA downlink systems where each tone is taken by at most one user. Weighted sum rate maximization (WSRmax) and weighted sum power minimization (WSPmin) problems are considered. Since these resource allocation problems are non-convex, complexity of finding the optimal solutions is prohibitively high. This paper employs the Lagrange dual decomposition method to efficiently solve both optimization problems. Because of their non-convex nature, there is no guarantee for the solution obtained by the dual decomposition method to be optimal. However, it is shown that with practical number of tones, the duality gap is virtually zero and the optimal solutions can be efficiently obtained
Hybrid analog and digital beamforming is a promising candidate for large-scale mmWave MIMO systems because of its ability to significantly reduce the hardware complexity of the conventional fully-digital beamforming schemes while being capable of approaching the performance of fully-digital schemes. Most of the prior work on hybrid beamforming considers narrowband channels. However, broadband systems such as mmWave systems are frequency-selective. In broadband systems, it is desirable to design common analog beamformer for the entire band while employing different digital beamformers in different frequency sub-bands. This paper considers hybrid beamforming design for systems with OFDM modulation. First, for a SU-MIMO system where the hybrid beamforming architecture is employed at both transmitter and receiver, we show that hybrid beamforming with a small number of RF chains can asymptotically approach the performance of fully-digital beamforming for a sufficiently large number of transceiver antennas due to the sparse nature of the mmWave channels. For systems with a practical number of antennas, we then propose a unified heuristic design for two different hybrid beamforming structures, the fully-connected and the partially-connected structures, to maximize the overall spectral efficiency of a mmWave MIMO system. Numerical results are provided to show that the proposed algorithm outperforms the existing hybrid beamforming methods and for the fully-connected architecture the proposed algorithm can achieve spectral efficiency very close to that of the optimal fully-digital beamforming but with much fewer RF chains. Second, for the MU-MISO case, we propose a heuristic hybrid percoding design to maximize the weighted sum rate in the downlink and show numerically that the proposed algorithm with practical number of RF chains can already approach the performance of fully-digital beamforming.
Hybrid analog/digital precoding architectures can address the trade-off between achievable spectral efficiency and power consumption in large-scale MIMO systems. This makes it a promising candidate for millimeter wave systems, which require deploying large antenna arrays at both the transmitter and receiver to guarantee sufficient received signal power. Most prior work on hybrid precoding focused on narrowband channels and assumed fully-connected hybrid architectures. MmWave systems, though, are expected to be wideband with frequency selectivity. In this paper, a closed-form solution for fully-connected OFDM-based hybrid analog/digital precoding is developed for frequency selective mmWave systems. This solution is then extended to partially-connected but fixed architectures in which each RF chain is connected to a specific subset of the antennas. The derived solutions give insights into how the hybrid subarray structures should be designed. Based on them, a novel technique that dynamically constructs the hybrid subarrays based on the long-term channel characteristics is developed. Simulation results show that the proposed hybrid precoding solutions achieve spectral efficiencies close to that obtained with fully-digital architectures in wideband mmWave channels. Further, the results indicate that the developed dynamic subarray solution outperforms the fixed hybrid subarray structures in various system and channel conditions.
This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: • Queue stability theory • Backpressure, max-weight, and virtual queue methods • Primal-dual methods for non-convex stochastic utility maximization • Universal scheduling theory for arbitrary sample paths • Approximate and randomized scheduling theory • Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts.
Yu and Liu's strong duality theorem under the time-sharing property requires the Slater condition to hold for the considered general nonconvex problem, what is satised for the specic application. We further extend the scope of the theorem under Ky Fan
We are concerned with the allocation of the base station transmitter time in time-varying mobile communications with many users who are transmitting data. Time is divided into small scheduling intervals, and the channel rates for the various users are available at the start of the intervals. Since the rates vary randomly, in selecting the current user there is a conflict between full use (by selecting the user with the highest current rate) and fairness (which entails consideration for users with poor throughput to date). The proportional fair scheduler of the Qualcomm High Data Rate system and related algorithms are designed to deal with such conflicts. The aim here is to put such algorithms on a sure mathematical footing and analyze their behavior. The available analysis, while obtaining interesting information, does not address the actual convergence for arbitrarily many users under general conditions. Such algorithms are of the stochastic approximation type and results of stochastic approximation are used to analyze the long-term properties. It is shown that the limiting behavior of the sample paths of the throughputs converges to the solution of an intuitively reasonable ordinary differential equation, which is akin to a mean flow. We show that the ordinary differential equation (ODE) has a unique equilibrium and that it is characterized as optimizing a concave utility function, which shows that PFS is not ad-hoc, but actually corresponds to a reasonable maximization problem. These results may be used to analyze the performance of PFS. The results depend on the fact that the mean ODE has a special form that arises in problems with certain types of competitive behavior. There is a large set of such algorithms, each one corresponding to a concave utility function. This set allows a choice of tradeoffs between the current rate and throughout. Extensions to multiple antenna and frequency systems are given. Finally, the infinite backlog assumption is dropped and the data is allowed to arrive at random. This complicates the analysis, but the same results hold.
We provide an overview of the extensive results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends on the available channel information at either the receiver or transmitter, the channel signal-to-noise ratio, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for the broadcast channel. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize results for the MIMO broadcast and MAC for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We show that the capacity region of the MIMO multiple access and the largest known achievable rate region (called the dirty-paper region) for the MIMO broadcast channel are intimately related via a duality transformation. This transformation facilitates finding the transmission strategies that achieve a point on the boundary of the MIMO MAC capacity region in terms of the transmission strategies of the MIMO broadcast dirty-paper region and vice-versa. Finally, we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array and transmission strategies that exploit this structure exhibit signifi-
cant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper.
The design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints. The optimization problem is numerically difficult to solve when the problem does not have a convexity structure. This paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time-sharing condition, the duality gap of the optimization problem is always zero, regardless of the convexity of the objective function. Further, we show that the time-sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity. This result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain. We show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm. This new interpretation gives rise to more efficient dual update methods. It also suggests ways in which the dual objective may be evaluated approximately, further improving the numerical efficiency of the algorithm. We propose a low-complexity iterative spectrum balancing algorithm based on these ideas, and show that the new algorithm achieves near-optimal performance in many practical situations
We develop a dynamic control strategy for minimizing energy expenditure in a time-varying wireless network with adaptive transmission rates. The algorithm operates without knowledge of traffic rates or channel statistics, and yields average power that is arbitrarily close to the minimum possible value achieved by an algorithm optimized with complete knowledge of future events. Proximity to this optimal solution is shown to be inversely proportional to network delay. We then present a similar algorithm that solves the related problem of maximizing network throughput subject to peak and average power constraints. The techniques used in this paper are novel and establish a foundation for stochastic network optimization