BigBand: GHz-Wide Sensing and Decoding on Commodity Radios

The goal of this paper is to make sensing and decoding GHz of spectrum simple, cheap, and low power. Our thesis is simple: if we can build a technology that captures GHz of spectrum using commodity Wi-Fi radios, it will have the right cost and power budget to enable a variety of new applications such as GHz-widedynamic access and concurrent decoding of diverse technologies. This vision will change today s situation where only expensive power-hungry spectrum analyzers can capture GHz-wide spectrum. Towards this goal, the paper harnesses the sparse Fourier transform to compute the frequency representation of a sparse signal without sampling it at full bandwidth. The paper makes the following contributions. First, it presents BigBand, a receiver that can sense and decode a sparse spectrum wider than its own digital bandwidth. Second, it builds a prototype of its design using 3 USRPs that each samples the spectrum at 50 MHz, producing a device that captures 0.9 GHz -- i.e., 6x larger bandwidth than the three USRPs combined. Finally, it extends its algorithm to enable spectrum sensing in scenarios where the spectrum is not sparse

An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. To make this possible, CS relies on two principles: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality. Our intent in this article is to overview the basic CS theory that emerged in the works [1]–[3], present the key mathematical ideas underlying this theory, and survey a couple of important results in the field. Our goal is to explain CS as plainly as possible, and so our article is mainly of a tutorial nature. One of the charms of this theory is that it draws from various subdisciplines within the applied mathematical sciences, most notably probability theory. In this review, we have decided to highlight this aspect and especially the fact that randomness can — perhaps surprisingly — lead to very effective sensing mechanisms. We will also discuss significant implications, explain why CS is a concrete protocol for sensing and compressing data simultaneously (thus the name), and conclude our tour by reviewing important applications

FPS-SFT: A Multi-dimensional Sparse Fourier Transform Based on the Fourier Projection-slice Theorem

We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of M-D DFT of the M-D data onto those lines. The M-D sinusoids that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving practical problems