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

In this paper, we exploit the capability of multi-agent deep reinforcement learning (MA-DRL) technique to generate a transmit power pool (PP) for Internet of things (IoT) networks with semi-grant-free non-orthogonal multiple access (SGF-NOMA). The PP is mapped with each resource block (RB) to achieve distributed transmit power control (DPC). We first formulate the resource (sub-channel and transmit power) selection problem as stochastic Markov game, and then solve it using two competitive MA-DRL algorithms, namely double deep Q network (DDQN) and Dueling DDQN. Each GF user as an agent tries to find out the optimal transmit power level and RB to form the desired PP. With the aid of dueling processes, the learning process can be enhanced by evaluating the valuable state without considering the effect of each action at each state. Therefore, DDQN is designed for communication scenarios with a small-size action-state space, while Dueling DDQN is for a large-size case. Our results show that the proposed MA-Dueling DDQN based SGF-NOMA with DPC outperforms the SGF-NOMA system with the fixed-power-control mechanism and networks with pure GF protocols with 17.5% and 22.2% gain in terms of the system throughput, respectively. Moreover, to decrease the training time, we eliminate invalid actions (high transmit power levels) to reduce the action space. We show that our proposed algorithm is computationally scalable to massive IoT networks. Finally, to control the interference and guarantee the quality-of-service requirements of grant-based users, we find the optimal number of GF users for each sub-channel.

Competitive MA-DRL for Transmit Power Pool Design in Semi-Grant-Free NOMA Systems.

In this paper, the non-regenerative relay assisted non-orthogonal multiple access (NOMA) system is proposed to enlarge the cellular coverage area and to enhance the system performance. To investigate the proposed system's performance, the closed-form expressions in terms of the system capacity are derived. In an effort to evaluate the performance of the proposed system model, the comparison between NOMA and conventional orthogonal multiple access (OMA) approach is provided. Simulation results are presented to verify the accuracy of the derived analytical results. Additionally, it is demonstrated that the system capacity performance is enhanced by NOMA compared to the OMA encoding scheme in the non-regenerative relay assisted system.

Performance analysis of non-regenerative relay assisted NOMA system

—A near-ﬁeld secure transmission framework is proposed. Employing the hybrid beamforming architecture, a base station (BS) transmits the conﬁdential information to a legitimate user (U) against an eavesdropper (E) in the near ﬁeld. A two- stage algorithm is proposed to maximize the near-ﬁeld secrecy capacity. Based on the fully-digital beamformers obtained in the ﬁrst stage, the optimal analog beamformers and baseband digital beamformers can be alternatingly derived in the closed-form expressions in the second stage. Numerical results demonstrate that in contrast to the far-ﬁeld secure communication relying on the angular disparity , the near-ﬁled secure communication in the near-ﬁeld communication mainly relies on the distance disparity between U and E.

Physical Layer Security in Near-Field Communications: What Will Be Changed?

Intelligent reflecting surface (IRS) enhanced multi-unmanned aerial vehicle (UAV) non-orthogonal multiple access (NOMA) networks are investigated. A new transmission framework is proposed, where multiple UAV-mounted base stations employ NOMA to serve multiple groups of ground users with the aid of an IRS. The three-dimensional (3D) placement and transmit power of UAVs, the reflection matrix of the IRS, and the NOMA decoding orders among users are jointly optimized for maximization of the sum rate of considered networks. To tackle the formulated mixed-integer non-convex optimization problem with coupled variables, a block coordinate descent (BCD)-based iterative algorithm is developed. Specifically, the original problem is decomposed into three subproblems, which are alternatingly solved by exploiting the penalty method and the successive convex approximation technique. The proposed BCD-based algorithm is demonstrated to be able to obtain a stationary point of the original problem with polynomial time complexity. Numerical results show that: 1) the proposed NOMA-IRS scheme for multi-UAV networks achieves a higher sum rate compared to the benchmark schemes, i.e., orthogonal multiple access (OMA)-IRS and NOMA without IRS; 2) the use of IRS is capable of providing performance gain for multi-UAV networks by both enhancing channel qualities of UAVs to their served users and mitigating the inter-UAV interference; and 3) optimizing the UAV placement can make the sum rate gain brought by NOMA more distinct due to the flexible decoding order design.

Intelligent Reflecting Surface Enhanced Multi-UAV NOMA Networks

A generalized downlink multi-antenna non-orthogonal multiple access (NOMA) transmission framework is proposed with the novel concept of cluster-free successive interference cancellation (SIC). In contrast to conventional NOMA approaches, where SIC is successively carried out within the same cluster, the key idea is that the SIC can be flexibly implemented between any arbitrary users to achieve efficient interference elimination. Based on the proposed framework, a sum rate maximization problem is formulated for jointly optimizing the transmit beamforming and the SIC operations between users, subject to the SIC decoding conditions and users’ minimal data rate requirements. To tackle this highly-coupled mixed-integer nonlinear programming problem, an alternating direction method of multipliers-successive convex approximation (ADMM-SCA) algorithm is developed. The original problem is first reformulated into a tractable biconvex augmented Lagrangian (AL) problem by handling the non-convex terms via SCA. Then, this AL problem is decomposed into two subproblems that are iteratively solved by the ADMM to obtain the stationary solution. Furthermore, to reduce the computational complexity and alleviate the parameter initialization sensitivity of ADMM-SCA, a Matching-SCA algorithm is proposed. The intractable binary SIC operations are solved through an extended many-to-many matching, which is jointly combined with an SCA process to optimize the transmit beamforming. The proposed Matching-SCA can converge to an enhanced exchange-stable matching that guarantees the local optimality. Numerical results demonstrate that: i) the proposed Matching-SCA algorithm achieves comparable performance and a faster convergence compared to ADMM-SCA; ii) the proposed generalized framework realizes scenario-adaptive communications and outperforms traditional multi-antenna NOMA approaches in various communication regimes.

Yuanwei Liu

Papers

Competitive MA-DRL for Transmit Power Pool Design in Semi-Grant-Free NOMA Systems.

Performance analysis of non-regenerative relay assisted NOMA system

Physical Layer Security in Near-Field Communications: What Will Be Changed?

Intelligent Reflecting Surface Enhanced Multi-UAV NOMA Networks

Cluster-Free NOMA Communications Toward Next Generation Multiple Access