This paper considers the problem of detecting the support (sparsity pattern)
of a sparse vector from random noisy measurements. Conditional power of a
component of the sparse vector is defined as the energy conditioned on the
component being nonzero. Analysis of a simplified version of orthogonal
matching pursuit (OMP) called sequential OMP (SequOMP) demonstrates the
importance of knowledge of the rankings of conditional powers.

We consider a broad class of interference coordination and resource
allocation problems for wireless links where the goal is to maximize the sum of
functions of individual link rates. Such problems arise in the context of, for
example, fractional frequency reuse (FFR) for macro-cellular networks and
dynamic interference management in femtocells. The resulting optimization
problems are typically hard to solve optimally even using centralized
algorithms but are an essential computational step in implementing rate-fair
and queue stabilizing scheduling policies in wireless networks.

We consider the general problem of estimating a random vector from
measurements generated by a linear transform followed by a componentwise
probabilistic measurement channel. We call this the linear mixing estimation
problem, since the linear transform couples the components of the input and
output vectors. The main contribution of this paper is a general algorithm
called linearized belief propagation (LBP) that iteratively "decouples" the
vector minimum mean-squared error (MMSE) estimation problem into a sequence of
componentwise scalar problems.