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

Abstract

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.

Structured random measurements in signal processing

“…For low-rank matrix recovery, one also considers linear measurements, but the structural signal model is that the signal is approximated by a low-rank matrix. This problem closely relates to applications in recommender systems and signal processing [4,3,26,41], but also has connections to quantum physics [63,60].…”

“…Another important task arising in so-called cognitive radio is to decide whether certain frequency bands are occupied or not so that free bands may be potentially used for wireless transmission by a user. In [41] an approach to this problem via low rank matrix recovery was introduced.…”

Robust matrix completion with complex noise

“…In a diverse array of real-world applications such as collaborative filtering (Rao et al, 2015), quantum-state tomography (Gross, 2011), spectrum sensing (Corroy et al, 2011) and recommender system (Ramlatchan et al, 2018), we are interested in recovering a large-scale low-rank data matrix from noisy and highly incomplete observations. This problem, usually termed as matrix completion, has attracted a lot of attention over a decade (Candes and Plan, 2010;Keshavan et al, 2010;Candes and Plan, 2011;Ma et al, 2017;Chi et al, 2019;Chen et al, 2020a,b).…”