在正交分頻多工系統中精準的通道估測是一個重要的議題，利用領航訊號（Pilots）來進行估測是最常見的方法，其中包含最小平方誤差法(LS)、最大相似機率法(ML)、最小均方誤差法(MMSE)最常應用於多路徑環境通道估測。在許多文獻中證明出為了滿足尼奎斯比率（Nyquist Rate），均勻分布的領航訊號是最好的估測方法來達到最小均方誤差。在下一世代的無線通訊環境中，傳送速率越來越高和傳輸的涵蓋範圍較大產生較長時間的延遲或較高的延遲概觀(Delay Profile)，使多路徑傳輸通道中很少存在明顯的傳輸路徑。因此，為了精準的通道估測必須在載波上擺放更多的領航訊號，導致犧牲了頻寬的使用效率。除此之外，可以從傳統的通道估測方法在估測多路徑稀疏通道中看出其效率不佳。在本篇論文中，我們將利用壓縮感測方法來估測與追蹤無線傳輸環境中的稀疏多路徑通道。我們利用公式化的貝式第一階準則(ℓ1-norm)最佳化問題來對大化通道還境中的事前機率參數。根據第一階準則最佳化問題的特性故及了通道的稀疏性和變異性便可由凸型(convex)最佳化解出。除此之外，我們還提出了有效率的子梯度(subgradient)疊代演算法來取得最佳解和調式性步階(adaptive step size)來減少疊代的次數。在最後的模擬結果中可看出我們提出的通道估測方法比傳統的離散傅立葉通道估測方法更能在稀疏多路通道增進估測的準確率。Channel estimation is an important issue for successfully implementing an orthogonal frequency division multiplexing (OFDM) system. Pilot-aided channel estimation is the most common approach, and the least square (LS), maximum likelihood (ML), or minimum mean square error (MMSE) criteria are often applied to estimate the multipath channel gains. It has been evident from the literature that the uniformly distributed pilot tones which satisfy the Nyquist criterion is the best way to attain the minimum square error for channel estimation. For the next-generation wireless communication, the wireless channels could behave like a sparse multipath channel in which merely contains a few significant paths with a long delay spread owing to high data rate transmission and large cell coverage. Therefore, it is required to embed a great amount of pilot tones over subcarriers to get an accurate channel estimate at the sacrifice of spectral efficiency. Otherwise, a significant performance degradation can be observed for the conventional channel estimation methods in sparse multipath channels. In this thesis, we apply the compressive sensing (CS) technique to estimate and track the sparse multipath channels in wireless mobile environments. We first formulate a Bayesian ℓ1-norm optimization problem by maximizing the posteriori probability of the channel parameters. The associated ℓ1-norm optimization problem, which involves the features of the channel sparsity and channel variation, is solved by the convex optimization technique. Besides, an efficient iterative subgradient algorithm is derived to attain the optimal solution, and an adaptive step size is proposed to effectively reduce the iteration number. Compared with the conventional discrete Fourier transform (DFT)-based channel estimation, simulation results show that the proposed channel estimation scheme can greatly improve the channel estimation accuracy in sparse multipath channels.
