A Sparse Approach for Identification of Signal Constellations Over Additive Noise Channels

Identification of unknown linear modulations over arbitrary additive noise channels is addressed within the framework of sparse linear regression. A regularized least squares problem with a sparsity inducing penalty is formulated to estimate the distribution of the transmitted symbols, which complete characterizes the underlying signal constellation. Separable and iterative algorithms that deliver reduced computational complexity are obtained based on the majorization-minimization framework. The proposed method can be employed to construct a modulation dictionary tailored to the target communications system before performing hypothesis testing-based classification.