In this chapter we deal with the following nonlinear fractional programming problem: 

$$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$

where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Nonlinear Fractional Programming

Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas $M$ than scheduled users $K$ because the users’ channels are likely to be near-orthogonal when $M/K > 10$ . However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users $K^\star$ depends on $M$ and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of $K^\star$ in the large- $M$ regime is derived in closed form, while simulations are used to show what happens at finite $M$ , in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal $M/K$ is less than 10 in many cases of practical relevance. Interestingly, $K^\star$ depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same $K$ .

Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?

Deploying small cell base stations (SBS) under the coverage area of a macro base station (MBS), and caching popular contents at the SBSs in advance, are effective means to provide high-speed and low-latency services in next generation mobile communication networks. In this paper, we investigate the problem of content caching (CC) and user association (UA) for edge computing. A joint CC and UA optimization problem is formulated to minimize the content download latency. We prove that the joint CC and UA optimization problem is NP-hard. Then, we propose a CC and UA algorithm (JCC-UA) to reduce the content download latency. JCC-UA includes a smart content caching policy (SCCP) and dynamic user association (DUA). SCCP utilizes the exponential smoothing method to predict content popularity and cache contents according to prediction results. DUA includes a rapid association (RA) method and a delayed association (DA) method. Simulation results demonstrate that the proposed JCC-UA algorithm can effectively reduce the latency of user content downloading and improve the hit rates of contents cached at the BSs as compared to several baseline schemes.

Optimized Content Caching and User Association for Edge Computing in Densely Deployed Heterogeneous Networks

We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we depart from classical purely model-based approaches and propose a hybrid method that retains key modeling elements in conjunction with data-driven components. More precisely, we put forth a neural network architecture inspired by the algorithmic unfolding of the iterative weighted minimum mean squared error (WMMSE) method, that we denote by unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE are parameterized using graph neural networks (GNNs), where the time-varying underlying graphs are given by the fading interference coefficients in the wireless network. These GNNs are trained through a gradient descent approach based on multiple instances of the power allocation problem. We show that the proposed architecture is permutation equivariant, thus facilitating generalizability across network topologies. Comprehensive numerical experiments illustrate the performance attained by UWMMSE along with its robustness to hyper-parameter selection and generalizability to unseen scenarios such as different network densities and network sizes.

Unfolding WMMSE Using Graph Neural Networks for Efficient Power Allocation

Deploying small cell base stations (SBS) under the coverage area of a macro base station (MBS), and caching popular contents at the SBSs in advance, are effective means to provide high-speed and low-latency services in next generation mobile communication networks. In this paper, we investigate the problem of content caching (CC) and user association (UA) for edge computing. A joint CC and UA optimization problem is formulated to minimize the content download latency. We prove that the joint CC and UA optimization problem is NP-hard. Then, we propose a CC and UA algorithm (JCC-UA) to reduce the content download latency. JCC-UA includes a smart content caching policy (SCCP) and dynamic user association (DUA). SCCP utilizes the exponential smoothing method to predict content popularity and cache contents according to prediction results. DUA includes a rapid association (RA) method and a delayed association (DA) method. Simulation results demonstrate that the proposed JCC-UA algorithm can effectively reduce the latency of user content downloading and improve the hit rates of contents cached at the BSs as compared to several baseline schemes. 

End-to-end congestion control has been extensively studied for over 30 years as one of the most important mechanisms to ensure efficient and fair sharing of network resources among users. As future networks are becoming more and more complex, conventional rule-based congestion control approaches tend to become inefficient and even ineffective. Inspired by the great success that machine learning (ML) has achieved in addressing large-scale and complex problems, researchers have begun to shift their attention from the rule-based method to an ML-based approach. This article presents a selected review of the recent applications of ML to the field of end-to-end congestion control. In this survey, we start with a brief review of the relationship between congestion control and ML. We then review the recent works that apply ML to congestion control. These works either help the agent to make an intelligent congestion control decision or achieve enhanced performance. Finally, we highlight a series of realistic challenges and shed light on potential future research directions.

Machine Learning for End-to-End Congestion Control

The energy-efficient power control of interfering links in a large wireless network is a challenging task. In this paper, we propose a deep learning based power control scheme, termed PowerNet, that uses the devices’ geographical location information (GLI). We show that it is possible to bypass the complex channel estimation process and directly perform power control with GLI when the channel state information (CSI) can be viewed as a function of distance dependent path-loss. The time consuming and complex channel estimation process can thus be avoided. Moreover, with a proper training, PowerNet transforms the on-line complexity to off-line training, and is amenable for real-time services. Different from conventional deep neural network (DNN) that adopts fully connected structure, the proposed PowerNet leverages convolutional layers to better capture the interference pattern across different links in large wireless networks and utilizes deep residual learning to further enhance its robustness. Simulation results demonstrate that PowerNet can achieve a near-optimal performance at a remarkably high speed without explicit channel estimation. PowerNet also exhibits a great generalization ability in terms of problem sizes and channel fading types.

Energy-Efficient Power Control in Wireless Networks With Spatial Deep Neural Networks

Radio access network (RAN) in 5G is expected to satisfy the stringent delay requirements of a variety of applications. The packet scheduler plays an important role by allocating spectrum resources to user equipments (UEs) at each transmit time interval (TTI). In this paper, we show that optimal scheduling is a challenging combinatorial optimization problem, which is hard to solve within the channel coherence time with conventional optimization methods. Rule-based scheduling methods, on the other hand, are hard to adapt to the time-varying wireless channel conditions and various data request patterns of UEs. Recently, integrating artificial intelligence (AI) into wireless networks has drawn great interest from both academia and industry. In this paper, we incorporate deep reinforcement learning (DRL) into the design of cellular packet scheduling. A delay-aware cell traffic scheduling algorithm is developed to map the observed system state to scheduling decision. Due to the huge state space, a recurrent neural network (RNN) is utilized to approximate the optimal action-policy function. Different from conventional rule-based scheduling methods, the proposed scheme can learn from the interactions with the environment and adaptively choosing the best scheduling decision at each TTI. Simulation results show that the DRL-based packet scheduling can achieve the lowest average delay compared with several conventional approaches. Meanwhile, the UEs’ average queue lengths can also be significantly reduced. The developed method also exhibits great potential in real-time scheduling in delay-sensitive scenarios.

Delay-aware Cellular Traffic Scheduling with Deep Reinforcement Learning

Today's popular video coding standards, such as H.264/AVC, are widely used to encode video into bit streams for storage and transmission. With the explosive growth of various video applications, H.264/AVC may not fully satisfy their requirements anymore. There is an increasing demand for high compression efficiency and low complexity video coding standards. In this article, we provide an overview of existing and emerging video coding standards. We review the timeline of the development of the popular H.26X family video coding standards, and introduce several emerging video coding standards such as AV1, VP9 and VVC. As for future video coding, considering the success of machine learning in various fields and hardware acceleration, we conclude this article with a discussion of several future trends in video coding.

An Overview of Emerging Video Coding Standards

Existing wireless multi-view video (MVV) transmission schemes use digital compression to achieve a better coding efficiency. However, the digital schemes suffer from the cliff effect, which refers to the phenomenon that the video quality is a step function of wireless channel quality. In this paper, we first consider a soft MVV transmission scheme where the correlations between the inter-view data and texture-depth data are exploited by a 5-dimensional discrete cosine transform (5D-DCT). The linearly transformed 5D-DCT signals are modulated in an analog manner so that the video quality gracefully improves when the channel quality becomes better. The cumbersome bit and rate controls in digital solutions are replaced by simple power controls. Second, as with the increase of the number of cameras and data depths, the data size of MVV increases linearly. To reduce the heavy data traffic in soft MVV transmission, we proposed efficient resource (bandwidth and power) allocation algorithms. Simulations results demonstrate that the proposed distortion-resource (DR) optimization algorithm can ensure a best viewing quality under a resource constraint and the proposed resource-distortion (RD) optimization algorithm can minimize the resource usage for a target video quality requirement. Third, the impact of power control across texture and depth frame and the impact of view positions on synthesized virtual view quality are investigated. The efficacy of the proposed algorithm on both the reference viewpoint as well as the virtual viewpoint is verified via simulations.

/pdf/joint-power-and-channel-resource-optimization-in-soft-multi-2ik4g4xx00.pdf

Ticao Zhang

Papers

Machine Learning for End-to-End Congestion Control

Energy-Efficient Power Control in Wireless Networks With Spatial Deep Neural Networks

Delay-aware Cellular Traffic Scheduling with Deep Reinforcement Learning

An Overview of Emerging Video Coding Standards

Joint Power and Channel Resource Optimization in Soft Multi-View Video Delivery