Hybrid Atomic Norm Sparse/Diffuse Channel Estimation

Abstract: In this paper, the hybrid sparse/diffuse (HSD) channel model in frequency domain is proposed. Based on the structural analysis on the resolvable paths and diffuse scattering statistics in the channel, the Hybrid Atomic-Least-Squares (HALS) algorithm is designed to estimate sparse/diffuse components with a combined atomic and l2 regularization. A theoretical analysis is conducted on the Lagrangian dual problem and the conditions needed to be satisfied by primal and dual solutions are provided. This analysis, in turn, suggests an algorithm for optimal frequency support estimation. Debiased methods for improved channel estimation are provided. Given differing amounts of side information, performance bounds are derived in terms of a genie-aided estimator and constrained Cramer-Rao lower bounds (CRLB). Numerical results via simulations on synthetic data as well as real experimental data validate the efficacy of the proposed method. There are clear tradeoffs with respect to the properties of the channel with respect to performance: sparsity of specular paths and relative energy of diffuse components.