Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\star}$ is composed of zero-mean independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise, for example, when we have two independent samples for each entry of $\mathbf{M}^{\star}$ and arrange them into an {\em asymmetric} data matrix $\mathbf{M}$. The aim is to estimate the leading eigenvalue and eigenvector of $\mathbf{M}^{\star}$. We demonstrate that the leading eigenvalue of the data matrix $\mathbf{M}$ can be $O(\sqrt{n})$ times more accurate --- up to some log factor --- than its (unadjusted) leading singular value in eigenvalue estimation. Further, the perturbation of any linear form of the leading eigenvector of $\mathbf{M}$ --- say, entrywise eigenvector perturbation --- is provably well-controlled. This eigen-decomposition approach is fully adaptive to heteroscedasticity of noise without the need of careful bias correction or any prior knowledge about the noise variance. We also provide partial theory for the more general rank-$r$ case. The takeaway message is this: arranging the data samples in an asymmetric manner and performing eigen-decomposition could sometimes be beneficial.Comment: accepted to Annals of Statistics, 2020. 37 page

Network Coding Tree Algorithm for Multiple Access System

Network coding is famous for significantly improving the throughput of networks. The successful decoding of the network coded data relies on some side information of the original data. In that framework, independent data flows are usually first decoded and then network coded by relay nodes. If appropriate signal design is adopted, physical layer network coding is a natural way in wireless networks. In this work, a network coding tree algorithm which enhances the efficiency of the multiple access system (MAS) is presented. For MAS, existing works tried to avoid the collisions while collisions happen frequently under heavy load. By introducing network coding to MAS, our proposed algorithm achieves a better performance of throughput and delay. When multiple users transmit signal in a time slot, the mexed signals are saved and used to jointly decode the collided frames after some component frames of the network coded frame are received. Splitting tree structure is extended to the new algorithm for collision solving. The throughput of the system and average delay of frames are presented in a recursive way. Besides, extensive simulations show that network coding tree algorithm enhances the system throughput and decreases the average frame delay compared with other algorithms. Hence, it improves the system performance

Low-complexity Location-aware Multi-user Massive MIMO Beamforming for High Speed Train Communications

Massive Multiple-input Multiple-output (MIMO) adaption is one of the primary evolving objectives for the next generation high speed train (HST) communication system. In this paper, we consider how to design an efficient low-complexity location-aware beamforming for the multi-user (MU) massive MIMO system in HST scenario. We first put forward a low-complexity beamforming based on location information, where multiple users are considered. Then, without considering inter-beam interference, a closed-form solution to maximize the total service competence of base station (BS) is proposed in this MU HST scenario. Finally, we present a location-aid searching-based suboptimal solution to eliminate the inter-beam interference and maximize the BS service competence. Various simulations are given to exhibit the advantages of our proposed massive MIMO beamforming method.Comment: This paper has been accepted for future publication by VTC2017-Sprin