Phase I of this project focused on exploiting the structure of multipath propagation to solve the dimensionality bottleneck problem of massive MIMO. Our results in Phase I clearly indicate that the structure to be exploited resides in the "invariants" of the channel, i.e., in those quantities that remains constant over a large time interval and a large frequency bandwidth. In particular, these invariants are contained, implicitly or explicitly, in the channel second-order statistics. Remarkably, our intuition and findings during the first 3 years of the project have become "instant classics" and literally thousands of papers have followed in our footprints, such that today the approaches that we have advocated at the beginning of the first funding phase have become mainstream.

In Phase II, we build on the experience and on the successes of Phase I and we broaden our horizon from the single massive MIMO system to a whole wireless network, where the large dimensionality arising from large number of users and base station antennas is the salient feature. We identify three new overarching objectives and lay out our workplan organized in three corresponding work packages. The first focuses on the efficient representation of large dimensional channel vectors for general array geometries, where the aim is to generalize Szego’s theorem on large Toeplitz matrices to families of non-Toeplitz Covariance matrices generated by given array manifolds. The second consider the distributed sampling and learning of the path gain function between any two points of a given coverage area, referred to as network "soft" topology. Finally, the third consider a bilinear compressed sensing problem arising from multichannel splicing, that is, combining multiple narrowband observations in order to obtain a wideband measurement of the channel impulse response and achieve a sufficiently high timing resolution such that precise ranging for indoor position using conventional RF signals is possible. We outline mathematically precise problem definitions and concrete methodologies to address the problems, corroborated by preliminary results and previous background results obtained by the PI in their previous work. As such, although the objective of this proposal are challenging, we are confident that significant progress can be made in time span of the project.