High-Dimensional Data Analysis with Low-Dimensional Models Principles, Computation, and Applications

In this chapter, we present an application of compressive sensing to a crucial problem in modern wireless (radio) communication: How can cognitive radios efficiently identify available spectrum? We will see that this problem can be cast as one of recovering the support of a sparse signal, in the presence of noise. We will see how the methods and algorithms described in this book will allow us to break theoretical limits of conventional approaches, and, once properly implemented in hardware, they can significantly advance the state of the art, by enabling better tradeoffs between energy consumption and scan time. Besides its practical importance, this application is very interesting as it is kind of dual to the situation in the magnetic resonance imaging that we studied in the preceding chapter. In MRI, the measurements are the Fourier transform of the image of interest and the sparse patterns are in the image domain; whereas for spectrum sensing, the sparse patterns are in the Fourier domain which we do not measure directly.