  In the spatial channel models used in multi-antenna wireless communications,
the propagation from a single-antenna transmitter (e.g., a user) to an
M-antenna receiver (e.g., a Base Station) occurs through scattering clusters
located in the far field of the receiving antenna array. The Angular Spread
Function (ASF) of the corresponding M-dim channel vector describes the angular
density of the received signal power at the array. The modern literature on
massive MIMO has recognized that the knowledge of covariance matrix of user
channel vectors is very useful for various applications such as hybrid digital
analog beamforming, pilot decontamination, etc. Therefore, most literature has
focused on the estimation of such channel covariance matrices. However, in some
applications such as uplink-downlink covariance transformation (for FDD massive
MIMO precoding) and channel sounding some form of ASF estimation is required
either implicitly or explicitly. It turns out that while covariance estimation
is well-known and well-conditioned, the ASF estimation is a much harder problem
and is in general ill-posed. In this paper, we show that under additional
geometrically-consistent group-sparsity structure on the ASF, which is
prevalent in almost all wireless propagation scenarios, one is able to estimate
ASF properly. We propose sparse dictionary-based algorithms that promote this
group-sparsity structure via suitable regularizations. Since generally it is
difficult to capture the notion of group-sparsity through proper
regularization, we propose another algorithm based on Deep Neural Networks
(DNNs) that learns this structure. We provide numerical simulations to assess
the performance of our proposed algorithms. We also compare the results with
that of other methods in the literature, where we re-frame those methods in the
context of ASF estimation in massive MIMO.
