Distributed sensing of a slowly time-varying sparse spectrum using matrix completion

Abstract

In this paper, we consider the problem of sensing a frequency spectrum in a distributed manner using as few measurements as possible while still guaranteeing a low detection error. To achieve this goal we use the newly developed technique of matrix completion which enables to recover a low rank matrix from a small subset of its entries. We model the sensed bandwidth at different cognitive radios as a spectrum matrix. It has been shown that in many cases the spectrum used by a primary user is underutilized. Therefore the spectrum matrix often has a low rank structure. By taking few measurements at several cognitive radios and reconstructing the matrix at a fusion center, we can dramatically reduce the required number of samples to reconstruct the utilization of the bandwidth. This is a key enabler for efficient and reliable spectrum reuse.