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 article investigates a non-orthogonal multiple access (NOMA) enhanced Internet of Things (IoT) network. In order to provide connectivity, a novel cluster strategy is proposed, where multiple devices can be served simultaneously. Two potential scenarios are investigated: 1) NOMA enhanced terrestrial IoT networks and 2) NOMA enhanced aerial IoT networks. We utilize stochastic geometry tools to model the spatial randomness of both terrestrial and aerial devices. New channel statistics are derived for both terrestrial and aerial devices. The exact and the asymptotic expressions in terms of coverage probability are derived. In order to obtain further engineering insights, short-packet communication scenarios are investigated. From our analysis, we show that the performance of NOMA enhanced IoT networks is capable of outperforming OMA enhanced IoT networks. Moreover, based on simulation results, there exists an optimal value of the transmit power that maximizes the coverage probability.

NOMA Enhanced Terrestrial and Aerial IoT Networks with Partial CSI.

Non-orthogonal multiple access (NOMA) is capable of serving different numbers of users in the same time-frequency resource element, and this feature can be leveraged to carry additional information. In the orthogonal frequency division multiplexing (OFDM) system, we propose a novel enhanced NOMA scheme, called NOMA with informative envelope (NOMA-IE), to explore the ﬂexibility of the envelope of NOMA signals. In this scheme, data bits are conveyed by the quantiﬁed signal envelope in addition to classic signal constellations. The subcarrier activation patterns of different users are jointly decided by the envelope former. At the receiver, successive interference cancellation (SIC) is employed, and we also introduce the envelope detection coefﬁcient to eliminate the error ﬂoor. Theoretical expressions of spectral efﬁciency and energy efﬁciency are provided for the NOMA-IE. Then, considering the binary phase shift keying modulation, we derive the asymptotic bit error rate for the two-subcarrier OFDM subblock. Afterwards, the expressions are extended to the four-subcarrier case. The analytical results reveal that the imperfect SIC and the index error are the main factors degrading the error performance. The numerical results demonstrate the superiority of the NOMA-IE over the OFDM and OFDM-NOMA, especially in the high signal-to-noise ratio (SNR) regime.

Is the Envelope Beneficial to Non-Orthogonal Multiple Access?

A simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided communication system is investigated, where an access point sends information to multiple users located on both sides of the STARRIS. Different from prior works which assume that the phase-shift coefficients for transmission and reflection signals can be independently adjusted, a coupled transmission and reflection phase-shift model is considered. Based on this model, a fast beam splitting (FBS) technique is proposed for STAR-RISs to split signals into a multiple beams. Exploiting the FBS technique, the number of split beams can be controlled by using STAR-RIS with one-bit phase shifters and by reconfiguring only a small portion of its elements.

Fast Beam Splitting Technique for STAR-RISs with Coupled T&R Phase Shifts

A novel simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) aided downlink non-orthogonal multiple access (NOMA) communication framework is proposed. Two STAR-RIS protocols are investigated, namely the energy splitting (ES) and the mode switching (MS). However, since the STAR-RIS has a massive number of reconfigurable elements, the passive beamforming problem has enormous action dimensions and extremely high complexity, resulting in an increased training time and performance degradation for the artificial intelligent agent. To resolve this predicament, a partitioning approach is proposed to divide the STAR-RIS into several tiles. A distributed learning approach is conceived for the partitioning and the corresponding tile-based passive beamforming of each STAR-RIS, as well as the power allocation for users to maximize the average throughput achieved by multiple base stations. In particular, the deep reinforcement learning (DRL) agent is employed at each BS, and an access-free federated learning (AFFL) model, which gathers the features of federated learning (FL) and transfer learning (TL) is proposed to accelerate or even exempt the training process for agents. Simulation results indicate that 1) the ES protocol is preferred for being employed in the NOMA networks compared with the MS protocol; 2) the tile-based passive beamforming approach outperforms benchmarks while the STAR-RIS has a large size; 3) the proposed AFFL framework effectively reduces or exempts the training overhead.

STAR-RISs Assisted NOMA Networks: A Distributed Learning Approach

The novel concept of non-orthogonal multiple access (NOMA) aided joint radar and multicast-unicast communication (Rad-MU-Com) is investigated. Employing the same spectrum resource, a multi-input-multi-output (MIMO) dual-functional radar-communication (DFRC) base station detects the radar-centric user (R-user), while transmitting mixed multicast-unicast messages both to the R-user and to the communication-centric user (C-user). In particular, the multicast information is intended for both the R- and C-users, whereas the unicast information is only intended for the C-user. More explicitly, NOMA is employed to facilitate this double spectrum sharing, where the multicast and unicast signals are superimposed in the power domain and the superimposed communication signals are also exploited as radar probing waveforms. A beamformer-based NOMA-aided joint Rad-MU-Com framework is proposed for the system having a single R-user and a single C-user. Based on this framework, the unicast rate maximization problem is formulated by optimizing the beamformers employed, while satisfying the rate requirement of multicast and the predefined accuracy of the radar beam pattern. The resultant non-convex optimization problem is solved by a penalty-based iterative algorithm to find a high-quality near-optimal solution. Finally, our numerical results reveal that significant performance gains can be achieved by the proposed scheme over the benchmark schemes.

Yuanwei Liu

Papers

NOMA Enhanced Terrestrial and Aerial IoT Networks with Partial CSI.

Is the Envelope Beneficial to Non-Orthogonal Multiple Access?

Fast Beam Splitting Technique for STAR-RISs with Coupled T&R Phase Shifts

STAR-RISs Assisted NOMA Networks: A Distributed Learning Approach

Joint Radar and Multicast-Unicast Communication: A NOMA Aided Framework