最佳化功率分配於無線感測網路之線性一致離散估測

Abstract

本論文以一致性多路存取通道與線性最小均方差融合規則為基礎，探討無線感測網路的離散估測，我們討論三種不同感測網路的離散估測：(i) 以群聚單輸入單輸出感測網路為基礎的估測、(ii) 單輸入單輸出感測網路在未知通道下的估測、以及 (iii) 多輸入多輸出感測網路下的估測；於每一種感測網路下，我們皆討論系統總功率有限的情況下，利用最佳化功率分配來得到最小估測失真。首先，我們討論一純量訊號於群聚感測網路中的離散估測，我們證明最佳的放大矩陣為一個利用兩已知向量做外積所得到的秩一矩陣，由此最佳的放大矩陣，我們證明利用感測器合作能夠改善系統的效能。第二，我們探討一純量訊號在未知通道的無線網路中的離散估測，我們利用二階段法來估測訊號：先分配訓練功率於各感測器來估測通道，再用最佳功率分配策略或平均功率分配策略結合前一步驟所得到的估測通道來估測信號，我們證明不論是最佳功率分配策略或是平均功率分配策略，最佳的訓練功率是相同的；當感測器的數量增加時，在通道未知的情況下所造成的的效能損失也會增加。最後，我們討論一向量訊號於多輸入多輸出感測網路的離散估測，我們利用奇異值分解法將求編碼矩陣的問題表示為凸面最佳化問題，藉此，我們推導出最佳編碼矩陣的封閉解，我們利用數值模擬來證明於三種感測網路下的分析結果。

We study distributed estimation in wireless sensor networks with coherent multiple access channel model and LMMSE fusion rule. In this thesis, three different sensor network systems for distributed estimation are discussed: (i) estimation using single-input single-output (SISO) cluster-based sensor network, (ii) estimation using SISO sensor network over unknown channels, and (iii) estimation using multiple-input multiple-output (MIMO) sensor network. In each network system, we study the problem of minimizing estimation distortion by optimally allocating power under a total power constraint. We first discuss distributed estimation of a scalar signal with cluster-based sensor network. We show that the optimal amplification matrix for each cluster is a rank one matrix, which is a scaled outer product of two known vectors. With the optimal amplification matrices, we also show that collaboration can improve performance. Secondly, we consider distributed estimation of a scalar signal using sensor network with unknown channels. We adopt a two-phase approach, which first optimally allocates the training power for channel estimation, and then uses the equal power scheme or optimal power scheme for source signal estimation. We reveal that the optimal training powers for the optimal and equal power schemes are the same. Moreover, as the number of sensors increases, the penalty caused by channel estimation becomes worse. Finally, we discuss distributed estimation of a vector signal using MIMO sensor network. Based on singular value decomposition technique, the problem of choosing coding matrices can be formulated as a convex optimization problem, based on which we derive closed form expression of optimal coding matrices. We use simulations to verify the analytical results in the three network systems.