Sparse Blind Demixing

This chapter extends the models presented in Chaps. 2 and 3 to the scenario involving device activity detection. The new setting induces a sparse blind demixing model for developing methods for joint device activity detection, data decoding, and channel estimation in IoT networks. The signal model is first presented, in the scenario with either a single-antenna or multi-antenna BS. A convex relaxation approach is first introduced as a basic method to solve the nonconvex estimation problem. We further present a difference-of-convex-functions (DC) approach which turns out to be a powerful tool to solve the resulting sparse and low-rank optimization problem with matrix lifting. Furthermore, a smooth Riemannian optimization algorithm operating on the product manifold is introduced for solving the sparse blind demixing problem directly.