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

Simultaneous transmitting and reflecting intelligent omini-surfaces
(STAR-IOSs) are able to achieve full coverage "smart radio environments". By
splitting the energy or altering the active number of STAR-IOS elements,
STAR-IOSs provide high flexibility of successive interference cancellation
(SIC) orders for non-orthogonal multiple access (NOMA) systems. Based on the
aforementioned advantages, this paper investigates a STAR-IOS-aided downlink
NOMA network with randomly deployed users. We first propose three tractable
channel models for different application scenarios, namely the central limit
model, the curve fitting model, and the M-fold convolution model. More
specifically, the central limit model fits the scenarios with large-size
STAR-IOSs while the curve fitting model is extended to evaluate multi-cell
networks. However, these two models cannot obtain accurate diversity orders.
Hence, we figure out the M-fold convolution model to derive accurate diversity
orders. We consider three protocols for STAR-IOSs, namely, the energy splitting
(ES) protocol, the time switching (TS) protocol, and the mode switching (MS)
protocol. Based on the ES protocol, we derive analytical outage probability
expressions for the paired NOMA users by the central limit model and the curve
fitting model. Based on three STAR-IOS protocols, we derive the diversity gains
of NOMA users by the M-fold convolution model. The analytical results reveal
that the diversity gain of NOMA users is equal to the active number of STAR-IOS
elements. Numerical results indicate that 1) in high signal-to-noise ratio
regions, the central limit model performs as an upper bound, while a lower
bound is obtained by the curve fitting model; 2) the TS protocol has the best
performance but requesting more time blocks than other protocols; 3) the ES
protocol outperforms the MS protocol as the ES protocol has higher diversity
gains.

STAR-IOS Aided NOMA Networks: Channel Model Approximation and Performance Analysis

We introduce clustered millimeter-wave (mmWave) networks with invoking non-orthogonal multiple access (NOMA) techniques, where the NOMA users are modeled as Poisson cluster processes and each cluster contains a base station (BS) located at the center. To provide realistic directional beamforming, an actual antenna array pattern is deployed at all BSs. We propose three distance-dependent user selection strategies to appraise the path loss impact on the performance of our considered networks. With the aid of such strategies, we derive tractable analytical expressions for the coverage probability and system throughput. Specifically, closed-form expressions are deduced under a sparse network assumption to improve the calculation efficiency. It theoretically demonstrates that the large antenna scale benefits the near user, while such influence for the far user is fluctuant due to the randomness of the beamforming. Moreover, the numerical results illustrate that: 1) the proposed system outperforms traditional orthogonal multiple access techniques and the commonly considered NOMA-mmWave scenarios with the random beamforming; 2) the coverage probability has a negative correlation with the variance of intra-cluster receivers; 3) 73 GHz is the best carrier frequency for the near user, and 28 GHz is the best choice for the far user; and 4) an optimal number of the antenna elements exists for maximizing the system throughput.

Clustered Millimeter-Wave Networks With Non-Orthogonal Multiple Access

This article investigates autonomous resource allocation of multiple UAVs enabled communication networks with the goal of maximizing long-term rewards. To model the uncertainty of environments, we formulate the long-term resource allocation problem as a stochastic game, where each UAV becomes a learning agent and each resource allocation solution corresponds to an action taken by the UAVs. Furthermore, we propose 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 the proposed MARL algorithm provides acceptable performance compared to the case with complete information exchanges among UAVs.

The Application of Multi-Agent Reinforcement Learning in UAV Networks

In this letter, we study efficient uplink channel estimation design for a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted two-user communication systems. We first consider the time switching (TS) protocol for STAR-RIS and propose an efficient scheme to separately estimate the channels of the two users with optimized training (transmission/reflection) pattern. Next, we consider the energy splitting (ES) protocol for STAR-RIS under the practical coupled phase-shift model and devise a customized scheme to simultaneously estimate the channels of both users. Although the problem of minimizing the resultant channel estimation error for the ES protocol is difficult to solve, we propose an efficient algorithm to obtain a high-quality solution by jointly designing the pilot sequences, power-splitting ratio, and training patterns. Numerical results show the effectiveness of the proposed channel estimation designs and reveal that the STAR-RIS under the TS protocol achieves a smaller channel estimation error than the ES case.

Channel Estimation for STAR-RIS-aided Wireless Communication

A novel framework for Quality of experience (QoE)-driven deployment and movement of multiple unmanned aerial vehicles (UAVs) is proposed. The problem of joint non-concave 3D deployment and dynamic movement for maximizing the sum mean opinion score (MOS) of users is formulated, which is proved to be NP-hard. In an effort to solve this problem, we proposed a three-step approach to obtain 3D deployment and dynamic movement of multiple UAVs. More specifically, in the first step, GAK-means algorithm is invoked to obtain the cell partitioning of ground users. Secondly, Q-learning based deployment algorithm is proposed, in which each UAV is considered as an agent, making its own decision to obtain 3D position. In contrast to conventional genetic algorithm based learning algorithms, the proposed algorithm is capable of training the policy of making decision offline. Thirdly, Q-learning algorithm is invoked when the ground users roam. Unlike the other trajectory obtaining algorithms, the proposed approach enables each UAV learn its movement gradually through trials and errors, and updates the direction selection strategy until it reaches convergence. Numerical results reveal that the proposed 3D deployment scheme outperforms K-means algorithm and IGK algorithm with low complexity. Additionally, with the aid of proposed approach, 3D real-time dynamic movement of UAVs is obtained.

Yuanwei Liu

Papers

STAR-IOS Aided NOMA Networks: Channel Model Approximation and Performance Analysis

Clustered Millimeter-Wave Networks With Non-Orthogonal Multiple Access

The Application of Multi-Agent Reinforcement Learning in UAV Networks

Channel Estimation for STAR-RIS-aided Wireless Communication

Deployment and Movement for Multiple Aerial Base Stations by Reinforcement Learning