There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Table Of Integrals Series And Products

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

Mobile-edge computing (MEC) networks are facing limited coverage and harsh wireless transmission environments that severely hinder the computation capacity of the Internet-of-Things (IoT) devices. To overcome these issues, this article proposes a novel MEC framework empowered by an unmanned aerial vehicle (UAV) relay and a reconfigurable intelligence surface (RIS). To fully exploit the potentials in terms of computation enhancement brought by the joint UAV and RIS design, we formulate a max–min computation capacity problem via determining the uplink signal detection, active beamforming of UAV, passive beamforming of RIS, time slot partition, computation bits of UAV, and UAV’s trajectory. We develop a concave–convex procedure (CCCP)-based algorithm in an alternating optimization manner over three subproblems to solve the formulated problem. It finds that the CCCP-based algorithm is conducive to decouple the intractable expressions by converting them into new but tractable second-order cone (SOC) constrains. To evaluate the performance of the proposed CCCP-based algorithm, we later design a direct algorithm by exploiting the implicit convexity of the problem. Simulation results demonstrate that the proposed CCCP-based algorithm derives a comparable performance as the direct algorithm, and achieves about 2.57-Mb max-min computation capacity higher compared with the straight flight case, and 8.08-Mb max–min computation capacity higher compared with the case without RIS, which validate the superiority of the joint UAV and RIS design for computation enhancement.

Computation Capacity Enhancement by Joint UAV and RIS Design in IoT

Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted non-orthogonal multiple access (NOMA) communication systems are investigated in its vicinity, where a STAR-RIS is deployed within a predefined region for establishing communication links for users. Both beamformer-based NOMA and cluster-based NOMA schemes are employed at the multi-antenna base station (BS). For each scheme, the STAR-RIS deployment location, the passive transmitting and reflecting beamforming (BF) of the STAR-RIS, and the active BF at the BS are jointly optimized for maximizing the weighted sum-rate (WSR) of users. To solve the resultant non-convex problems, an alternating optimization (AO) algorithm is proposed, where successive convex approximation (SCA) and semi-definite programming (SDP) methods are invoked for iteratively addressing the non-convexity of each sub-problem. Numerical results reveal that 1) the WSR performance can be significantly enhanced by optimizing the specific deployment location of the STAR-RIS; 2) both beamformer-based and cluster-based NOMA prefer asymmetric STAR-RIS deployment.

Joint Location and Beamforming Design for STAR-RIS Assisted NOMA Systems

Grant-free non-orthogonal multiple access (GF-NOMA) is a potential multiple access framework for internet-of-things (IoT) networks to enhance connectivity. However, the resource allocation problem in GF-NOMA is challenging and the effectiveness of such a solution is limited due to the absence of closed-loop power control. In this paper, we design a prototype of layer-based transmit power pool by utilizing multi-agent reinforcement learning to provide open-loop power control and offload the computing tasks at the base station (BS) side. IoT users in each layer decide their own transmit power level from this layer-based power pool, instead of transmitting on the allocated sub-channel with allocated transmit power level. The proposed algorithm does not require any information exchange between IoT users and does not rely on any assistance from the BS. Numerical results confirm that the double deep Q network based GF-NOMA algorithm achieves high accuracy and finds out an accurate transmit power level for each layer. Moreover, the proposed GF-NOMA system outperforms the traditional GF with orthogonal multiple access techniques in terms of throughput.

Transmit Power Pool Design for Uplink IoT Networks with Grant-free NOMA

Unmanned aerial vehicles (UAVs) are capable of serving as aerial base stations (BSs) for providing both cost-effective and on-demand wireless communications. This article investigates dynamic resource allocation of multiple UAVs enabled communication networks with the goal of maximizing long-term rewards. More particularly, each UAV communicates with a ground user by automatically selecting its communicating users, power levels and subchannels without any information exchange among UAVs. To model the uncertainty of environments, we formulate the long-term resource allocation problem as a stochastic game for maximizing the expected rewards, where each UAV becomes a learning agent and each resource allocation solution corresponds to an action taken by the UAVs. Afterwards, we develop a multi-agent reinforcement learning (MARL) framework that each agent discovers its best strategy according to its local observations using learning. More specifically, we propose an agent-independent method, for which all agents conduct a decision algorithm independently but share a common structure based on Q-learning. Finally, simulation results reveal that: 1) appropriate parameters for exploitation and exploration are capable of enhancing the performance of the proposed MARL based resource allocation algorithm; 2) the proposed MARL algorithm provides acceptable performance compared to the case with complete information exchanges among UAVs. By doing so, it strikes a good tradeoff between performance gains and information exchange overheads.

Multi-Agent Reinforcement Learning Based Resource Allocation for UAV Networks

In millimeter Wave (mmWave) massive multi-input multi-output (MIMO) systems, the novel sub-connected architecture has been introduced which can further reduce power consumption compared with the fully-connected architecture. In this paper, we propose an energy-efficient hybrid precoding design with quality of service (QoS) constraints for sub-connected architecture. Firstly, the total energy efficiency optimization problem with nonconvex constraints is decomposed into two separate optimization sub-problems whose solution is a optimal single precoder respectively. Then, the first optimization sub-problem analog domain concerned is solved by a cross-entropy-based algorithm according to the machine learning theory. Finally, the second optimization sub-problem digital domain concerned is solved by an iterative optimization algorithm from fractional programming theory. Simulation results demonstrate that the performance of the proposed precoding algorithm. The performance of the proposed algorithm is capable of achieving near optimal solution. It is also demonstrated that the proposed algorithm can enhance the energy efficiency of networks while guaranteeing the QoS of users.

Yuanwei Liu

Papers

Computation Capacity Enhancement by Joint UAV and RIS Design in IoT

Joint Location and Beamforming Design for STAR-RIS Assisted NOMA Systems

Transmit Power Pool Design for Uplink IoT Networks with Grant-free NOMA

Multi-Agent Reinforcement Learning Based Resource Allocation for UAV Networks

Energy-Efficient Hybrid Precoding for mmWave Massive MIMO Systems