Deep Learning for Geometrically-Consistent Angular Power Spread Function Estimation in Massive MIMO

In 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 array. The angular power spread function (APSF) of the corresponding M-dim channel vector describes the angular density of the received signal power at the array. In many applications, such as channel sounding and Uplink-Downlink covariance transformation in FDD systems, estimating the APSF is required either implicitly or explicitly. However, the existing literature on the subject has mainly focused on channel covariance estimation from a set of noisy pilot observations. It is also assumed that the APSF consists only of discrete components corresponding to Line-of-Sight (LoS) paths and specular scattering. It turns out that while covariance estimation is a well-posed problem, APSF estimation is a much harder task and is in general ill-posed. The reason is that the propagation environment can also include diffuse scattering elements, resulting in continuous APSF components. Therefore, the APSF is a function belonging to the infinite-dimensional space of non-negative measures over the angle domain. In this paper, we show that under a geometrically-consistent, group-sparse structure on the APSF, which is prevalent in massive MIMO channels, one is able to estimate the APSF properly. We propose an algorithm based on deep neural networks (DNNs) that learns this structure and yields precise APSF estimates, even when the number of available pilot observations is relatively small. We empirically show that our proposed method outperforms the state-of-the-art method in various performance metrics.