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 finitealphabet 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 semidefinite relaxation (SDR) for efficient Boolean programming. A few toy simulations show how our method can outperform existing works.

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: Zhi Tian, Geert Leus, Vincenzo Lottici
• Keywords: Efficient Boolean Programming, ICASSP 2009, Signal Processing, Sparse Finite-alphabet Signal, Sparsity Property