稀疏貝氏學習於多天線及張量系統之應用

在本論文中，我們將稀疏式貝葉斯學習（SBL）方法擴展到可以使用多個非恆定維的線性量測可得的情況下，推導相關演算法的實現細節。我們假設要從線性測量中恢復的稀疏訊號向量具有共同的非零位置。因此，我們將這些訊號向量建模為在SBL 框架內具有複數高斯先驗分佈的隨機向量。然後，我們將所得的SBL 算法應用於估計三個MIMO 系統相關的訊號通道響應。對於第一個系統，提出了一種簡單的角域點對點MIMO 訊號通道估測算法。對於第二個系統，提出了可調式智慧表面（RIS）輔助網路下的訊號通道算法。對於第三系統，我們解決低秩矩陣的矩陣填充問題，並應用在可切換式的天線陣列系統之下。然後，第一個系統的特殊結構促使我們將稀疏向量訊號還原延伸到稀疏張量訊號還原。此延伸降低了具有特殊結構的線性逆問題的計算複雜性。然後，我們發現，當天線陣列在空間中規則排列時，可以將空間頻率域中的通道估計公式化為具有特殊結構的線性逆問題。對於第二個系統，完成通道估計後，基於估計的結果，以控制RIS 上的移相器。這樣，RIS 可以控制發射機和接收機之間的通道品質。由於一般的通訊系統並無控制通道品質，因此該概念的出現打破原先傳統通訊系統的框架。

關鍵字

稀疏貝氏學習；通道估計；張量

並列摘要

We extend the method of sparse Bayesian learning (SBL) to solve the linear inversion problem with multiple linear measurements of nonconstant dimensions. We derive the detailed relations needed for SBL-based algorithmic implementations. We assume that the sparse signal vectors to be recovered from linear measurements have a common support set and thus model these signal vectors as random vectors with the same zero mean complex Gaussian prior distribution within the SBL framework. We then apply the resulting SBL algorithms to estimate channel responses associated with three MIMO systems. The first system we consider is a point-to-point MIMO system for which an angle domain channel estimate is developed. The second system is a reconfigure intelligent surface (RIS) aided MIMO system which consists of a source-to-RIS link and a RIS-to-destination (receiver) link. Separate estimation on the component links are not feasible due to the unresolvable complex amplitude ambiguity. Instead, we decouple the effect of the RIS from the component channels and are able to estimate the composite channel. The third system of interest is a switch based MIMO system. The difficult in estimating the corresponding channel comes from the fact that the corresponding channel matrix may be rank deficient unless one has accumulated sufficient measurements which is time-consuming. We present a channel estimator that can do with only few measurements by solving the associated matrix completion problem. When both sides of a MIMO links employ planar arrays the conventional linear array based approaches becomes computational demanding. We mitigate the dimensional issue by formulating the problem at hand as a tensor signal recovery or a dictionary learning problem. As the resulting tensor system has the special sparsity structure that any given row of every unfolding matrices of the tensor involved is simultaneously zero or non-zero, the hyperparameters in the corresponding SBL fomulation render a Kronecker-like prior distributions. Channel estimation in the spatial-frequency domain then become a linear inversion problem with such a special structure when the antenna configuration has a regular arrangement. The RIS controls the end-to-end link quality in that its phase shifting vector (PSV) relays and guides the incoming electromagnetic energy toward the destination antenna (arrays). Conceivably, the optimal PSV should have the CSI of both component links, i.e., where are the incoming angles of arrivals and to which direction(s) it should relay or reflect. Therefore, a fundamental issue concerning the design of a RIS-aided system is finding the optimal phase shifting vector (PSV) of the RIS that maximizes the system capacity. We consider both single user and multiuser cases using the projected gradient descent and semi-definite relaxation methods for the former and fractional programming and sequential objective function approximation methods to solve the latter case.