Spectrum Sensing for Cognitive Radio

Fundamentals and Applications

Kamal M. Captain, Manjunath V. Joshi

• Verlag: CRC Press
• Jahr: 2021
• ISBN:
  9781000472080
• Auflage: 1
• Thema: Technik & Maschinenbau
• Thema: Elektrotechnik & Telekommunikation

This comprehensive reference text discusses concepts of cognitive radio and the advances in the field of spectrum sensing.

This text discusses the concept of cognitive radio for next generation wireless communication and a very critical aspect of cognitive radio – that is, spectrum sensing – in detail. It covers important topics including narrowband spectrum sensing, wideband spectrum sensing, cooperative spectrum sensing, system and channel models, detection algorithms, approximation of decision statistics, and theoretical analysis of detection algorithms in detail. Separate chapters are dedicated to discussing the analysis and use of detection algorithms for narrowband spectrum sensing, wideband spectrum sensing, and cooperative wideband spectrum sensing.

Aimed at graduate students and academic researchers in the fields of electrical engineering and electronics and communication engineering, this text:

• Discusses concepts of cognitive radio and research in spectrum sensing.

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• Presents mathematical analysis of algorithms considering practical environment.

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• Explains novel wideband spectrum sensing algorithms with detailed analysis.

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• Provides mathematical derivations to help readers.

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• Discusses basic spectrum sensing algorithms, from narrowband spectrum sensing to the more advanced wideband spectrum sensing.

1Fundamentals of Probability Theory

DOI: 10.1201/​9781003088554-1

In this chapter, the fundamentals of probability, random variables, and random process are discussed briefly. This chapter is introduced to give a quick overview of these topics to the readers¹.

1.1 Introduction

A signal can be classified as being deterministic or random. For the deterministic signal, there is no uncertainty associated with its value at a particular time instant. A mathematical formula exactly defines the deterministic signals. Random signals are unpredictable; that is, the future values of the random signals cannot be predicted with certainty even if the entire history of the signal is known.

Consider the signal $y\left(t\right)=A\sin \left(2\pi ft+\theta \right)$. If we assume the values of A, f, and θ to be constant and known, we can determine the value of $y\left(t\right)$ for all values of t. The values of these parameters, if not known, can be obtained by observing the signal for a short period of time. Now, if we assume that the signal $y\left(t\right)$ be the output of a signal generator having inferior frequency stability and if this signal generator is set to produce the sinusoid of frequency f, the actual frequency output will be $f^{{}^{\prime }}\in \left(f+\Delta f\right)$. This generated signal may not remain same and could vary over time. It may not be of great use to observe the signal over a long period of time to predict future values. We can say that the output of signal generator varies randomly. Another example of a random signal is the received signal...