Spectrum scarcity is one of the major issues faced in Wireless communication technology. Efficient spectrum utilization is of utmost importance to alleviate the problem of interference and reduced data rates. Cognitive Radios adapt themselves according to the available spectrum and thereby enhance transmission and reception of data, without affecting adjacent band users. The pre-requisite for such an objective is the precise calculation of spectrum boundaries. Many methods have been suggested and revised from time to time. The Wavelet Edge Detection is one of the most widely used Spectrum Sensing techniques. This technique observes the spatial distribution of spectral data at multiple resolutions. The aim of this paper is to familiarize the reader with the mathematics behind the application of wavelets for edge detection, which is made use of for spectrum sensing applications. The several variants of this scheme which was originally formulated by Mallat et al are discussed and the inherent flaws or complexities are pointed out. The importance of choosing a suitable wavelet system is explained. We then proceed further and present an adaptive algorithm which chooses a suitable wavelet system by analyzing the nature of the spectrum. The slope of the Power Spectral Density is used as an index to distinguish between sharp and blunt peaks. Sparse spectra with conspicuous peaks utilize Haar wavelet system whereas dense spectra with subtle peaks use Gaussian Wavelet System. Multi-scale sums are used since they produce more accurate results than multi-scale products. The simulations are carried out in the FM frequency band (88-108 MHz) using MATLAB.
Keywords
Cognitive Radio, Spectrum Sensing, Edge Detection, Continuous Wavelet Transform, Multi-Scale Product, Multi-Scale Sum.
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