Underlay cognitive radios (UCRs) allow a secondary user to enter a primary
user's spectrum through intelligent utilization of multiuser channel quality
information (CQI) and sharing of codebook. The aim of this work is to study
two-user Gaussian UCR systems by assuming the full or partial knowledge of
multiuser CQI. Key contribution of this work is motivated by the fact that the
full knowledge of multiuser CQI is not always available.

In this paper, we study the problem of recovering a low-rank matrix (the
principal components) from a high-dimensional data matrix despite both small
entry-wise noise and gross sparse errors. Recently, it has been shown that a
convex program, named Principal Component Pursuit (PCP), can recover the
low-rank matrix when the data matrix is corrupted by gross sparse errors. We
further prove that the solution to a related convex program (a relaxed PCP)
gives an estimate of the low-rank matrix that is simultaneously stable to small
entrywise noise and robust to gross sparse errors.

This paper is about a curious phenomenon. Suppose we have a data matrix,
which is the superposition of a low-rank component and a sparse component. Can
we recover each component individually? We prove that under some suitable
assumptions, it is possible to recover both the low-rank and the sparse
components exactly by solving a very convenient convex program called Principal
Component Pursuit; among all feasible decompositions, simply minimize a
weighted combination of the nuclear norm and of the L1 norm.