Detection of sparse signals under finite-alphabet constraints

In this paper, we solve the problem of detecting the entries of a sparse finite-alphabet signal from a limited amount of data, for instance obtained by compressive sampling. While existing methods either rely on the sparsity property, the finite-alphabet property, or none of those properties to solve the under-determined system of linear equations, we capitalize on both the sparsity and the finite-alphabet features of the signal. The problem is first formulated in a Bayesian framework to incorporate the prior knowledge of sparsity, which is then shown to be solvable using sphere decoding (SD) or semi-definite relaxation (SDR) for efficient Boolean programming. A few toy simulations show how our method can outperform existing works.