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

该项目的第一阶段重点是利用多径传播的结构来解决大规模MIMO的维度瓶颈问题。我们在第一阶段的结果清楚地表明，要利用的结构存在于通道的"不变量“中，即，在大的时间间隔和大的频率带宽上保持恒定。特别地，这些不变量被隐含地或明确地包含在信道二阶统计量中。值得注意的是，我们在项目前30年的直觉和发现已经成为“即时经典”，成千上万的论文跟随我们的足迹，以至于今天我们在第一个资助阶段开始时倡导的方法已经成为主流。在第二阶段中，我们建立在第一阶段的经验和成功的基础上，我们将视野从单个大规模MIMO系统扩展到整个无线网络，其中大量用户和基站天线产生的大维度是显着特征。我们确定了三个新的总体目标，并制定了我们的工作计划，分为三个相应的工作包。第一部分研究了一般阵列几何条件下的高维信道向量的有效表示，目的是将Szego关于大Toeplitz矩阵的定理推广到由给定阵列流形生成的非Toeplitz协方差矩阵族。第二种考虑在给定的覆盖区域内任意两点之间的路径增益函数的分布式采样和学习，称为网络“软”拓扑。最后，第三个考虑双线性压缩感知问题所产生的多通道拼接，即，结合多个窄带观测，以获得宽带测量的信道冲激响应和足够高的定时分辨率，使得精确的测距forindoor位置使用传统的RF信号是可能的。我们概述了数学上精确的问题定义和具体的方法来解决问题，证实了先前的结果和PI在他们以前的工作中获得的背景结果。因此，虽然这项建议的目标具有挑战性，但我们有信心在项目的时间跨度内取得重大进展。

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.