最佳量化量測振幅之壓縮式感測與無線感測網路的應用

Abstract

本論文是一個將壓縮式感測(Compressive Sensing, CS)應用於無線感測網路(Wireless Sensor Network, WSN)的研究，將壓縮過後的量測值拿去做量化，利用這個資訊來幫助我們來估計出原始的稀疏訊號。 在目前，壓縮式感測經常被應用於無線感測網路，為了節省資源現在最常見的是單一位元式的壓縮式感測，也就是只保留量化後的正負值來重建回原稀疏訊號[4-7]；甚至近來有人將量化後的振福保留下來，利用此資訊來幫助重建訊號[8]，本篇論文就以[8]為基礎，針對在有量測雜訊和有通道雜訊的影響之下，結合量化後的振幅資訊，去進一步做二位元的壓縮式感測的推廣及研究。 在模擬中我們可觀察到，我們提出的方法其理論值和模擬值都相當的吻合，並且比均勻量化拿去做重建後的效果有更好的準確度。

關鍵字: 壓縮式感測、量化、無線感測網路

Integration of compressive sensing (CS) into the design of wireless sensor networks (WSNs) has received considerable attention. One-bit CS is particularly attractive in this scenario due to its capability of reducing the communication and computation costs of local sensors. Considering the practical communication links are error-prone, the issue of robust signal recovery for one-bit CS is concerned by more people. In the previous work, an MSE-optimal 1-bit quantizer is proposed to enhance signal reconstruction performance. In this paper, we try to extend and consider the specific 2-bit case first, by which the representation points of local binary quantizers are designed to minimize the loss of data fidelity caused by local sensing noise, quantization, and channel flipping, and conventional sparse signal reconstruction is performed at fusion center (FC) using the decoded and de-mapped binary data. The representation points of binary quantizer are designed by minimizing the mean square error (MSE) of data mismatch, taking into account the distributions of the nonzero signal entries, local sensing noise, and channel flipping; an analytic MSE formula is then obtained. Using numerical search to find the optimal quantizer. Finally, we extend to multiple bits case which considered one specific assignment of representation points. Numerical simulations are used to confirm the advantage of the proposed scheme and we get improved reconstruction performance as compared to simple uniform quanitzer.

Keywords: compressive sensing, quantization, wireless sensor networks