[论文解读] MIMO Over-the-Air Computation for High-Mobility Multi-Modal Sensing

Guangxu Zhu, Kaibin Huang|arXiv (Cornell University)|Mar 29, 2018

Indoor and Outdoor Localization Technologies参考文献 38被引用 5

一句话总结

本文提出了一种用于高速移动多模态传感的MIMO空中计算（MIMO-AirComp）方案，通过基于Grassmann流形的均衡器实现多种功能（如温度、污染、湿度的平均值）的空间复用，该均衡器最小化总均方误差。该解为信道子空间的加权质心，并建立了AirComp多播的对偶性，从而实现无需正交反馈信道的高效信道反馈。

ABSTRACT

In future Internet-of-Things networks, sensors or even access points can be mounted on ground/aerial vehicles for smart-city surveillance or environment monitoring. To support the high-mobility sensing with low network latency, a technique called over-the-air-computation (AirComp) was recently developed which enables an access-point to receive a desired function of sensing-data from concurrent-transmissions by exploiting the superposition property of a multi-access-channel. This work aims at further developing AirComp for next-generation multi-antenna multi-modal sensor networks. Specifically, we design beamforming and channel-feedback techniques for multi-function AirComp. Given the objective of minimizing sum-mean-squared-error of computed functions, the optimization of receive-beamforming for multi-function AirComp is a NP-hard problem. The approximate problem based on tightening transmission-power constraints, however, is shown to be solvable using differential-geometry. The solution is proved to be the weighted-centroid of points on a Grassmann-manifold, where each point represents the subspace spanned by the channel matrix of a sensor. As a by-product, the beamforming problem is found to have the same form as the classic problem of multicast-beamforming, establishing the AirComp-multicasting-duality. Its significance lies in making the said Grassmannian-centroid solution transferable to the latter problem which otherwise is solved using the computation-intensive semidefinite-relaxation-technique. Last, building on the AirComp-beamforming solution, an efficient channel-feedback technique is designed for an access-point to receive the beamformer from distributed sensor transmissions of designed signals that are functions of local channel-state-information.

研究动机与目标

• 为解决高速移动物联网传感器网络中传统正交接入方案导致的过度延迟问题，实现超高速数据聚合。
• 通过MIMO-AirComp实现在多天线传感器网络中对多种传感功能（如几何平均、平均值）的空间复用。
• 通过在Grassmann流形上采用闭式均衡器，利用空间分集最小化AirComp中的总均方误差。
• 设计一种高效的信道反馈方案，使多个传感器能够通过基于本地信道状态信息（CSI）的功能编码信号同时反馈，而无需正交反馈信道。

提出的方法

• 通过将问题表述为在Grassmann流形上寻找子空间加权质心，推导出接近最优的MIMO-AirComp均衡器，其中每个子空间对应一个传感器的信道系数矩阵。
• 利用微分几何求解优化问题，证明该均衡器在空间分集条件下可最小化总均方误差。
• 通过证明MIMO-AirComp均衡问题与多播波束成形问题具有相同的数学形式，建立了AirComp-多播对偶性。
• 设计一种反馈技术，传感器传输基于其本地CSI功能生成的信号，实现在无正交反馈信道情况下的同时反馈。
• 依赖无约束问题的解来推导最优均衡器，该解天然满足正交性约束。
• 证明全局最小值对应于由信道统计特性导出的正定矩阵G的主特征向量。

实验结果

研究问题

• RQ1 如何设计MIMO-AirComp以在高速移动多模态传感器网络中支持多种传感功能的空间复用？
• RQ2 在空间分集条件下，MIMO-AirComp中最小化总均方误差的最优均衡器结构是什么？
• RQ3 MIMO-AirComp均衡问题能否与波束成形中的现有问题相关联？若能，这种关联如何促成新解法？
• RQ4 当传感器密度高导致正交反馈信道不切实际时，如何在MIMO-AirComp中实现高效反馈？
• RQ5 最优均衡器的数学结构是什么？如何以闭式表达计算？

主要发现

• 最优MIMO-AirComp均衡器被推导为Grassmann流形上子空间的加权质心，对应于正定矩阵G的主特征向量。
• 该解在相同空间分集约束下，总均方误差低于任何其他均衡器。
• 正式建立了AirComp-多播对偶性，表明MIMO-AirComp均衡问题在数学上等价于多播波束成形问题。
• Grassmann质心解可迁移至多播波束成形问题，为计算更复杂的半定松弛方法提供一种闭式替代方案。
• 所提出的反馈方案通过基于本地CSI的功能编码信号，实现多个传感器的同时反馈，消除了对正交反馈信道的需求。
• 无约束问题的解产生一个非平凡的驻点，满足正交性约束，从而证实最优均衡器也适用于约束问题。