壓縮感測技術應用在循環字首之單載波通訊的稀疏通道估測

Abstract

在近年來，單載波頻域等化系統在無線通訊研究上被廣泛的探討，使其可作為正交分頻多工系統的替代系統，而對於單載波頻域等化系統的符元判斷效能，則取決於通道估測，傳統上，單載波頻域等化系統其通道估測技術是根據最小平方法的原理，然而，當通道具有稀疏特性存在時，使用此方法將無法根據通道稀疏特性來有效估測通道，在本論文中，我們提出將壓縮感測技術應用於單載波頻域等化系統的通道估測上，在此部分內容關於通道估測的系統矩陣，其為循環矩陣，首先，我們推導出了隨機循環矩陣其滿足限制等距性質的機率，此結果將比目前存在的其它結果更為準確，最後，我們使用壓縮感測技術中的Dantizg selector方法來估測稀疏通道，並利用互次不相關性質對系統矩陣做分析，提出了一組關於最佳訓練序列的形式，使壓縮感測技術在復原稀疏資料上更有效率，並以模擬驗證之。

In recent years, single carrier frequency domain equalization (SC-FDE) has been widely considered in the research of wireless communications as an alternative to the orthogonal frequency division multiplexing. The symbol decision performance of SC-FDE relies on accurate channel estimation. Traditional channel estimation techniques for SC-FDE are based on the least-squares (LS) principle, which however does not take account of the sparse nature of wireless channels. In this thesis, we study compressive-sensing (CS) based sparse channel estimation for SC-FDE, in which the training system is described by a circulant matrix. We first characterize the probability that a random circulant matrix can satisfy the restricted isometry property (RIP). The result is seen to be tighter than existing solutions. By using the Dantizg selector for signal recovery, we propose a new optimal training pattern via minimization of the mutual incoherence (MI). Simulation results are used to illustrate the performance of the proposed scheme.