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

This paper proposes a novel framework of resource allocation in intelligent reflecting surface (IRS) aided multi-cell non-orthogonal multiple access (NOMA) networks, where a sum-rate maximization problem is formulated. To address this challenging mixed-integer non-linear problem, we decompose it into an optimization problem (P1) with continuous variables and a matching problem (P2) with integer variables. For the nonconvex optimization problem (P1), iterative algorithms are proposed for allocating transmit power, designing reflection matrix, and determining decoding order by invoking relaxation methods such as convex upper bound substitution, successive convex approximation and semidefinite relaxation. For the combinational problem (P2), swap matching-based algorithms are proposed to achieve a two-sided exchange-stable state among users, BSs and sub-channels. Numerical results are provided for demonstrating that the sum-rate of the NOMA networks is capable of being enhanced with the aid of the IRS.

Intelligent Reflecting Surface Aided Multi-Cell NOMA Networks

A cooperative full duplex (FD) non-orthogonal multiple access (NOMA) scheme over Rician fading channels is considered. To be practical, imperfect successive interference cancellation (ipSIC) and residual hardware impairments (RHIs) at transceivers are taken into account. To evaluate the performance of the considered system, the analytical approximate expressions for the outage probability (OP) and the ergodic rate (ER) of the considered system are derived, and the asymptotic performance is also explored. Simulation results manifest that the FD cooperative NOMA can improve the ergodic sum rate (ESR) of the system compared to the half duplex (HD) mode.

Hardware Impairments Aware Full-Duplex NOMA Networks Over Rician Fading Channels.

A novel intelligent reflecting surface (IRS)-aided multi-robot network is proposed, where multiple mobile wheeled robots are served by an access point (AP) through non-orthogonal multiple access (NOMA). The goal is to maximize the sum-rate of all robots by jointly optimizing trajectories and NOMA decoding orders of robots, reflecting coefficients of the IRS, and the power allocation of the AP, subject to the quality of service (QoS) of each robot. To tackle this problem, a dueling double deep Q-network (D3QN) based algorithm is invoked for jointly determining the phase shift matrix and robots’ trajectories. Specifically, the trajectories for robots contain a set of local optimal positions, which reveals that robots make the optimal decision at each step. Numerical results demonstrated that the proposed D3QN algorithm outperforms the conventional algorithm, while the performance of IRS-NOMA network is better than the orthogonal multiple access (OMA) network.

Trajectory and Passive Beamforming Design for IRS-aided Multi-Robot NOMA Indoor Networks

In this paper, we investigate a robust beamforming design in a millimeter wave (mmWave) communication network with consideration of the random blockages. The network with multiple remote radio units (RRUs) is taken into account, where the joint transmission coordinated multi-point (JT-CoMP) scheme is adopted to improve the spectrum efficiency. To further enhance the communication performance and maintain the reliability of the network, an active intelligent reflecting surface (IRS) panel is deployed. We formulate the robust beamforming design of the mmWave communication network as an optimization problem aiming at minimizing the total transmit power at the RRUs subject to the average signal-to-interference-plus-noise ratio (SINR) constraints and power constraint over the active IRS. To deal with the challenge caused by the variables coupling, an algorithm based on the alternating optimization (AO) and semidefinite programming (SDP) is proposed. Numerical results illustrate that: i) the transmit power of the network can be reduced by deploying both the passive and active IRSs; ii) the integration of the active IRS and CoMP scheme can obtain a significant performance gain compared to that of the conventional passive IRS and CoMP.

Blockage-Aware Beamforming Design for Active IRS-Aided mmWave Communication Systems

Spectrum scarcity is one of the most important challenges in wireless communications networks due to the sky-rocketing growth of multimedia applications. As the latest member of the multiple access family, non-orthogonal multiple access (NOMA) has been recently proposed for 3GPP Long Term Evolution (LTE) and envisioned to be a key component of the 5th generation (5G) mobile networks for its potential ability on spectrum enhancement. The feature of NOMA is to serve multiple users at the same time/frequency/code, but with different power levels, which yields a significant spectral efficiency gain over conventional orthogonal multiple access (OMA). This thesis provides a systematic treatment of this newly emerging technology, from the basic principles of NOMA, to its combination with simultaneously information and wireless power transfer (SWIPT) technology, to apply in cognitive radio (CR) networks and Heterogeneous networks (HetNets), as well as enhancing the physical layer security and addressing the fairness issue. First, this thesis examines the application of SWIPT to NOMA networks with spatially randomly located users. A new cooperative SWIPT NOMA protocol is proposed, in which near NOMA users that are close to the source act as energy harvesting relays in the aid of far NOMA users. Three user selection schemes are proposed to investigate the effect of locations on the performance. Besides the closed-form expressions in terms of outage probability and throughput, the diversity gain of the considered networks is determined. Second, when considering NOMA in CR networks, stochastic geometry tools are used to evaluate the outage performance of the considered network. New closed-form expressions are derived for the outage probability. Diversity order of NOMA users has been analyzed based on the derived outage probability, which reveals important design insights

Yuanwei Liu

Papers

Intelligent Reflecting Surface Aided Multi-Cell NOMA Networks

Hardware Impairments Aware Full-Duplex NOMA Networks Over Rician Fading Channels.

Trajectory and Passive Beamforming Design for IRS-aided Multi-Robot NOMA Indoor Networks

Blockage-Aware Beamforming Design for Active IRS-Aided mmWave Communication Systems

Non-Orthogonal Multiple Access for 5G: Design and Performance Enhancement