Compressed Sensing Algorithms for Structured Massive MIMO -- Phase II: From Massive MIMO to Massive Wireless Networks

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Phase I of this project focused on exploiting the structure of multipathpropagation to solve the dimensionality bottleneck problem ofmassive MIMO. Our results in Phase I clearly indicate that thestructure to be exploited resides in the ``invariants’’ of the channel,i.e., in those quantities that remains constant over a large time intervaland a large frequency bandwidth. In particular, these invariants arecontained, implicitly or explicitly, in the channel second-orderstatistics. Remarkably, our intuition and findings during the first 3years of the project have become ``instant classics’’ and literallythousands of papers have followed in our footprints, such that todaythe approaches that we have advocated at the beginning of the firstfunding phase have become mainstream. In Phase II, we build on theexperience and on the successes of Phase I and we broaden ourhorizon from the single massive MIMO system to a whole wirelessnetwork, where the large dimensionality arising from large number ofusers and base station antennas is the salient feature. We identifythree new overarching objectives and lay out our workplan organizedin three corresponding work packages. The first focuses on theefficient representation of large dimensional channel vectors forgeneral array geometries, where the aim is to generalize Szego’stheorem on large Toeplitz matrices to families of non-ToeplitzCovariance matrices generated by given array manifolds. The secondconsider the distributed sampling and learning of the path gainfunction between any two points of a given coverage area, referred toas network ``soft’’ topology. Finally, the third consider a bilinearcompressed sensing problem arising from multichannel splicing, thatis, combining multiple narrowband observations in order to obtain awideband measurement of the channel impulse response and achievea sufficiently high timing resolution such that precise ranging forindoor position using conventional RF signals is possible. We outlinemathematically precise problem definitions and concretemethodologies to address the problems, corroborated by preliminaryresults and previous background results obtained by the PI in theirprevious work. As such, although the objective of this proposal arechallenging, we are confident that significant progress can be made intime span of the project.