Distributed Wideband Spectrum Sensing

Abstract

Spectrum Sensing is a key technology for Cognitive Radio: the initial task of any cognitive device will be to accurately sense and classify spectral bands. The sampling rates required by many bands (for example TV Whitespaces) makes spectrum sensing costly with current technology. Currently many spectra are sparse and this sparsity can be exploited by using the modern paradigm of
Compressive Sampling. This thesis explores two methods to reduce the sampling rate per device.
The first method, which is described in Chapter 5 is to use a distributed network of sensors to reduce the sensing load. The second method is to avoid reconstruction of the spectrum itself, but to infer the occupied bands directly from the compressive measurements, this is described in Chapters 6 & 7. In other words we do not reconstruct the spectrum as an intermediate step for
classification.

In Chapter 5, we develop a distributed ADMM algorithm for the LASSO with exact, closed form, expressions for the minima per iteration, reducing the computational cost of the algorithm. This allows us to perform spectral reconstruction which is blind to statistics such as the signal sparsity, using only simple statistical operations such as least squares and shrinkage. Numerical experiments show that the algorithm performs to within $10^{-2}$ of an equivalent centralised algorithm. The algorithm displays the rapid convergence of ADMM, but with a substantially reduced computational burden.

Chapter 6 introduces a novel model of the spectral gradient, this is to combat the problem with current approaches to spectrum recovery - that should TVWS bands come into use, they will not remain sparse. Instead of seeking a sparse gradient we require sparsity in the gradient of the spectrum. In Chapter 6 we develop a model of the spectral gradient which allows reconstruction from Compressive measurements. This model is combined with the ADMM algorithm
from Chapter 5, to reconstruct actual TVWS data, which was provided by OFCOM.

In Chapter 6, we also develop a novel estimator based on this new model of spectral gradient. This estimator allows us to estimate the occupancy of the original signal, but without reconstructing the signal as an intermediate step. We develop novel algorithms to estimate the occupancy based on this estimator, and we run experiments on synthetic data to quantify the performance of these
algorithms. We find that we can achieve a 90% AUC even with only 2% of the equivalent Nyquist samples at an SNR of -10.5dB.

We develop the ideas of Chapter 6 in Chapter 7, where we extand the model into two dimensions. We show how a multi-stage problem can be reduced to a single stage problem, and we apply the methods of Chapter 6. Thus we are able to achieve similar performance on a multi-dimensional problem.

Finally in Chapter 8, we consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give conditions under which the algorithm performs essentially optimally in the sense of information-theoretic capacity. This has
applications to the allocation of spectrum to cognitive radios, in the case where a database gives prior information that a particular band will be occupied.

Date of Award	16 Jan 2018
Original language	English
Awarding Institution	University of Bristol
Supervisor	Oliver T Johnson (Supervisor) & Robert J Piechocki (Supervisor)