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

The organization of behavior: A neuropsychological theory

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Spectrum sensing is the very task upon which the entire operation of cognitive radio rests. For cognitive radio to fulfill the potential it offers to solve the spectrum underutilization problem and do so in a reliable and computationally feasible manner, we require a spectrum sensor that detects spectrum holes (i.e., underutilized subbands of the radio spectrum), provides high spectral-resolution capability, estimates the average power in each subband of the spectrum, and identifies the unknown directions of interfering signals. Cyclostationarity is another desirable property that could be used for signal detection and classification. The multitaper method (MTM) for nonparametric spectral estimation accomplishes these tasks accurately, effectively, robustly, and in a computationally feasible manner. The objectives of this paper are to present: 1) tutorial exposition of the MTM, which is expandable to perform space-time processing and time-frequency analysis; 2) cyclostationarity, viewed from the Loeve and Fourier perspectives; and 3) experimental results, using Advanced Television Systems Committee digital television and generic land mobile radio signals, followed by a discussion of the effects of Rayleigh fading.

/pdf/spectrum-sensing-for-cognitive-radio-1nggwiu43v.pdf

Spectrum Sensing for Cognitive Radio

In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.

https://iopscience.iop.org/article/10.1088/0264-9381/27/24/249002/pdf

Quantum Measurement and Control

A cognitive radio network is a multiuser system, in which different users compete for limited resources in an opportunistic manner, interacting with each other for access to the available resources. The fact that both users and spectrum holes (i.e., unused spectrum subbands) can come and go makes a cognitive radio network a highly dynamic and challenging wireless environment. Therefore, finding robust resource-allocation algorithms, which are capable of achieving reasonably good solutions fast enough in order to guarantee an acceptable level of performance under worst case interference conditions, is crucial in such environment. The focus of this paper is the transmit-power control in cognitive radio networks, considering a noncooperative framework. Moreover, tools from control theory are used to study both the equilibrium and transient behaviors of the network under dynamically varying conditions.

Robust Transmit Power Control for Cognitive Radio

In this paper, we describe a cognitive radar (CR) that mimics the visual brain. Although the visual brain and radar are different in that the visual brain does not transmit a probing signal to the environment while the active radar greatly relies on the probing signal it transmits to the environment, both of them are observers of the surrounding environment. As such, there is much that we can learn from the visual brain in building a new generation of CRs that outperform traditional radars. In this paper, we confine the discussion, in both analytic and experimental terms, to CR aimed at target tracking. From a theoretical perspective, using the posterior Cramer-Rao lower bound (PCRLB), it is shown that a cognitive tracking radar has the potential to improve tracking performance significantly. In particular, computer experiments are presented, which demonstrate that CR can indeed go beyond the theoretical limits of traditional active radars (TARs) as well as fore-active radars (FARs); the latter are radars equipped with feedback from the receiver to the transmitter. Moreover, computer experiments are presented to demonstrate another practical benefit resulting from the combined use of memory and executive attention in CR for a target-tracking application. Specifically, it is shown that with the provision of these two cognitive processes, the transition in switching from one transmit waveform to another goes forward in a smooth manner. Such a capability is beyond that of TAR or FAR.

Cognitive Radar: Step Toward Bridging the Gap Between Neuroscience and Engineering

This article proposes to integrate two entities, the Internet of Things and a cognitive dynamic system (CDS), and studies a smart home scenario as the application of interest. As a people-centric IoT, the smart home aims to enhance the intelligence level of the living environment and improve the quality of human life. Cognition, the distinct principles of which are perception?action cycle, memory, attention, intelligence, and language, can play a key role to pave the way for building truly smart homes. With cognition as its foundation, the engineering paradigm of CDS provides step-by-step guidelines for systematic development of smart homes. Hence, CDS can significantly contribute to the interactive IoT ecosystem.

Smart Home: Cognitive Interactive People-Centric Internet of Things

This paper is inspired by how cognitive control manifests itself in the human brain and does so in a remarkable way. It addresses the many facets involved in the control of directed information flow in a dynamic system, culminating in the notion of information gap, defined as the difference between relevant information (useful part of what is extracted from the incoming measurements) and sufficient information representing the information needed for achieving minimal risk. The notion of information gap leads naturally to how cognitive control can itself be defined. Then, another important idea is described, namely the two-state model, in which one is the system's state and the other is the entropic state that provides an essential metric for quantifying the information gap. The entropic state is computed in the perceptual part (i.e., perceptor) of the dynamic system and sent to the controller directly as feedback information. This feedback information provides the cognitive controller the information needed about the environment and the system to bring reinforcement leaning into play; reinforcement learning (RL), incorporating planning as an integral part, is at the very heart of cognitive control. The stage is now set for a computational experiment, involving cognitive radar wherein the cognitive controller is enabled to control the receiver via the environment. The experiment demonstrates how RL provides the mechanism for improved utilization of computational resources, and yet is able to deliver good performance through the use of planning. The paper finishes with concluding remarks.

Cognitive Control

Cognitive radio provides a basis for addressing the practical issue of spectrum scarcity. This issue has been raised due to the continuing advances in wireless technology, which has led to ever-increasing demand for larger bandwidth. The issue of spectrum scarcity has been exacerbated due to inefficient use of the electromagnetic spectrum. Adopting the novel idea of cognitive radio for secondary usage of underutilized spectrum results in the existence of two worlds of wireless communications going on side by side: the legacy wireless world and the cognitive wireless world. Spectrum holes (i.e., the unused spectrum subbands) are the medium, through which these two worlds dynamically interact. Releasing subbands by primary users allows the cognitive radio users to sustain communication and perform their normal tasks. Combination of the two wireless worlds can be viewed as a spectrum-supply chain network, in which the legacy owners and their customers (primary users) play the role of the suppliers and cognitive radios (secondary users) play the role of consumers. This paper discusses two classes of spectrum-supply chain networks based on two regimes, one allows open-access to the spectrum, and the other is a market-driven regime. Each one of them has its own merits and suitability for a different environment; therefore, they have complementary roles. Analytic models are developed for these two classes of networks, which allow for analysis of both equilibrium and transient behaviors.

Peyman Setoodeh

Papers

Robust Transmit Power Control for Cognitive Radio

Cognitive Radar: Step Toward Bridging the Gap Between Neuroscience and Engineering

Smart Home: Cognitive Interactive People-Centric Internet of Things

Cognitive Control

Cognitive Radio Networks: The Spectrum Supply Chain Paradigm