  Analog beamforming is the predominant approach for millimeter wave (mmWave)
communication given its favorable characteristics for limited-resource devices.
In this work, we aim at reducing the spectral efficiency gap between analog and
digital beamforming methods. We propose a method for refined beam selection
based on the estimated raw channel. The channel estimation, an underdetermined
problem, is solved using compressed sensing (CS) methods leveraging angular
domain sparsity of the channel. To reduce the complexity of CS methods, we
propose dictionary learning iterative soft-thresholding algorithm, which
jointly learns the sparsifying dictionary and signal reconstruction. We
evaluate the proposed method on a realistic mmWave setup and show considerable
performance improvement with respect to code-book based analog beamforming
approaches.
