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

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

https://www.cs.montana.edu/courses/csci566/Ref/CR-Survey.pdf

NeXt generation/dynamic spectrum access/cognitive radio wireless networks: a survey

The spectrum sensing problem has gained new aspects with cognitive radio and opportunistic spectrum access concepts. It is one of the most challenging issues in cognitive radio systems. In this paper, a survey of spectrum sensing methodologies for cognitive radio is presented. Various aspects of spectrum sensing problem are studied from a cognitive radio perspective and multi-dimensional spectrum sensing concept is introduced. Challenges associated with spectrum sensing are given and enabling spectrum sensing methods are reviewed. The paper explains the cooperative sensing concept and its various forms. External sensing algorithms and other alternative sensing methods are discussed. Furthermore, statistical modeling of network traffic and utilization of these models for prediction of primary user behavior is studied. Finally, sensing features of some current wireless standards are given.

A survey of spectrum sensing algorithms for cognitive radio applications

Compounding the confusion is the use of the broad term cognitive radio as a synonym for dynamic spectrum access. As an initial attempt at unifying the terminology, the taxonomy of dynamic spectrum access is provided. In this article, an overview of challenges and recent developments in both technological and regulatory aspects of opportunistic spectrum access (OSA). The three basic components of OSA are discussed. Spectrum opportunity identification is crucial to OSA in order to achieve nonintrusive communication. The basic functions of the opportunity identification module are identified

A Survey of Dynamic Spectrum Access

We propose decentralized cognitive MAC protocols that allow secondary users to independently search for spectrum opportunities without a central coordinator or a dedicated communication channel. Recognizing hardware and energy constraints, we assume that a secondary user may not be able to perform full-spectrum sensing or may not be willing to monitor the spectrum when it has no data to transmit. We develop an analytical framework for opportunistic spectrum access based on the theory of partially observable Markov decision process (POMDP). This decision-theoretic approach integrates the design of spectrum access protocols at the MAC layer with spectrum sensing at the physical layer and traffic statistics determined by the application layer of the primary network. It also allows easy incorporation of spectrum sensing error and constraint on the probability of colliding with the primary users. Under this POMDP framework, we propose cognitive MAC protocols that optimize the performance of secondary users while limiting the interference perceived by primary users. A suboptimal strategy with reduced complexity yet comparable performance is developed. Without additional control message exchange between the secondary transmitter and receiver, the proposed decentralized protocols ensure synchronous hopping in the spectrum between the transmitter and the receiver in the presence of collisions and spectrum sensing errors

/pdf/decentralized-cognitive-mac-for-opportunistic-spectrum-18vduzyhe6.pdf

Decentralized cognitive MAC for opportunistic spectrum access in ad hoc networks: A POMDP framework

We derive a general formula for the lifetime-of wireless sensor networks which holds independently of the underlying network model including network architecture and protocol, data collection initiation, lifetime definition, channel fading characteristics, and energy consumption model. This formula identifies two key parameters at the physical layer that affect the network lifetime: the channel state and the residual energy of sensors. As a result, it provides not only a gauge for performance evaluation of sensor networks but also a guideline for the design of network protocols. Based on this formula, we propose a medium access control protocol that exploits both the channel state information and the residual energy information of individual sensors. Referred to as the max-min approach, this protocol maximizes the minimum residual energy across the network in each data collection.

On the lifetime of wireless sensor networks

We formulate and study a decentralized multi-armed bandit (MAB) problem. There are M distributed players competing for N independent arms. Each arm, when played, offers i.i.d. reward according to a distribution with an unknown parameter. At each time, each player chooses one arm to play without exchanging observations or any information with other players. Players choosing the same arm collide, and, depending on the collision model, either no one receives reward or the colliding players share the reward in an arbitrary way. We show that the minimum system regret of the decentralized MAB grows with time at the same logarithmic order as in the centralized counterpart where players act collectively as a single entity by exchanging observations and making decisions jointly. A decentralized policy is constructed to achieve this optimal order while ensuring fairness among players and without assuming any pre-agreement or information exchange among players. Based on a time-division fair sharing (TDFS) of the M best arms, the proposed policy is constructed and its order optimality is proven under a general reward model. Furthermore, the basic structure of the TDFS policy can be used with any order-optimal single-player policy to achieve order optimality in the decentralized setting. We also establish a lower bound on the system regret for a general class of decentralized polices, to which the proposed policy belongs. This problem finds potential applications in cognitive radio networks, multi-channel communication systems, multi-agent systems, web search and advertising, and social networks.

Distributed Learning in Multi-Armed Bandit With Multiple Players

Opportunistic spectrum access (OSA) that allows secondary users to independently search for and exploit instantaneous spectrum availability is considered. The design objective is to maximize the throughput of a secondary user while limiting the probability of colliding with primary users. Integrated in the joint design are three basic components: a spectrum sensor that identifies spectrum opportunities, a sensing strategy that determines which channels in the spectrum to sense, and an access strategy that decides whether to access based on potentially erroneous sensing outcomes. This joint design is formulated as a constrained partially observable Markov decision process (POMDP), and a separation principle is established. The separation principle reveals the optimality of myopic policies for the design of the spectrum sensor and the access strategy, leading to closed-form optimal solutions. Furthermore, it decouples the design of the sensing strategy from that of the spectrum sensor and the access strategy, and reduces the constrained POMDP to an unconstrained one. Numerical examples are provided to study the tradeoff between sensing time and transmission time, the interaction between the physical layer spectrum sensor and the MAC layer sensing and access strategies, and the robustness of the ensuing design to model mismatch.

Qing Zhao

Papers

A Survey of Dynamic Spectrum Access

Decentralized cognitive MAC for opportunistic spectrum access in ad hoc networks: A POMDP framework

On the lifetime of wireless sensor networks

Distributed Learning in Multi-Armed Bandit With Multiple Players

Joint Design and Separation Principle for Opportunistic Spectrum Access in the Presence of Sensing Errors