Super-Resolution mmWave Channel Estimation using Atomic Norm Minimization

Abstract: We propose super-resolution MIMO channel estimators for millimeter-wave (mmWave) systems that employ hybrid analog and digital beamforming and generalized spatial modulation, respectively. Exploiting the inherent sparsity of mmWave channels, the channel estimation problem is formulated as an atomic norm minimization that enhances sparsity in the continuous angles of departure and arrival. Both pilot-assisted and data-aided channel estimators are developed, with the former one formulated as a convex problem and the latter as a non-convex problem. To solve these formulated channel estimation problems, we develop a computationally efficient conjugate gradient descent method based on non-convex factorization which restricts the search space to low-rank matrices. Simulation results are presented to illustrate the superior channel estimation performance of the proposed algorithms for both types of mmWave systems compared to the existing compressed-sensing-based estimators with finely quantized angle grids.