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

该项目第一阶段的重点是利用多径传播的结构来解决海量MIMO的维度瓶颈问题。我们在第一阶段的结果清楚地表明，待利用的结构驻留在信道的“不变量”中，即在大时间间隔和大频带上保持恒定的那些量。具体地说，这些不变量隐式或显式地包含在信道二阶统计量中。值得注意的是，我们在项目的前三年中的直觉和发现已经成为“即时经典”，从字面上来说，成千上万的论文跟踪了我们的足迹，因此今天我们在第一个资金阶段开始时倡导的方法已经成为主流。在第二阶段，我们在第一阶段的经验和成功的基础上，将我们的视野从单一的大规模MIMO系统扩展到整个无线网络，其中由大量用户和基站天线产生的大维度是显著特征。我们确定了三个新的总体目标，并将我们的工作计划安排在三个相应的工作包中。第一个重点是一般阵列几何的高维通道向量的有效表示，其目的是将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。第二种考虑了给定覆盖区域中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，第三章考虑了由多通道拼接引起的双线性压缩感知问题，即组合多个窄带观测以获得信道冲激响应的宽带测量，并获得足够高的时间分辨率，使得使用常规RF信号对室内位置进行精确测距成为可能。我们概述了数学上精确的问题定义和具体的方法来解决这些问题，并得到了PI在他们之前的工作中获得的初步结果和以前的背景结果的证实。因此，尽管这项提案的目标具有挑战性，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.