الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
Compressive Sensing is a new technique that enables the reconstruction of signals sampled at a rate lower than the Nyquist rate; which is known to be the minimum sampling rate required for lossless reconstruction of a signal. This technique relies on the sparsity of the signal, whether the signal itself is sparse, or it has a sparse representation in a certain domain. Our research focuses on the application of compressive sensing in Cognitive Radio, particularly in the process of spectrum sensing. In wideband systems, where cognitive radio is employed, unlicensed users are allowed to access the spectrum opportunistically by sensing the spectrum to determine the channels that are unoccupied by licensed users in order to avoid interference with them. One of the main problems of spectrum sensing is that sampling the wideband spectrum at Nyquist rates or higher and processing the information acquired is an expensive, time-consuming process that involves a huge amount of data. For this reason, compressive sensing is considered for wideband spectrum sensing, since it enables secondary users (cognitive radio users) to rapidly and efficiently scan the spectrum for vacant bands. A study of wavelets and wavelet transforms is an integral part of this thesis, since the wavelet transform is an efficient tool for edge detection. It also provides a sparse representation of the spectrum signal; hence the wavelet transform is important in our study of compressive sensing. This thesis adopts a wavelet transform approach to compressive sensing and the role of both techniques in spectrum sensing, as well as finding new methods and proposing modifications aimed to improve the performance of spectrum sensing, including multiscale wavelet transform in compressive sensing, parallel processing, genetic algorithm for signal reconstruction and the stationary wavelet transform.