均勻線性陣列下正交分頻多工系統中到達角與路徑數量估計之新方法

Abstract

正交分頻多工是一種被廣泛使用的多載波傳輸技術，能夠減少符號間干擾並有效降低等化器設計的複雜度。然而在雙選擇性通道中，都普勒擴展會破壞子載波間的正交性，導致子載波間干擾並顯著降低系統性能。因此，研究都普勒效應在正交分頻多工系統中的影響是一項重要議題。過去研究證實，基於分接延遲線的雙選擇性通道模型能有效描述雙選擇性通道。在基於分接延遲線的雙選擇性通道模型中，每一條通道路徑都對應一個不同的都普勒頻率偏移。為了估測多路徑通道下的都普勒頻率偏移與脈衝響應，本論文考慮了在接收端配置均勻線性陣列的正交分頻多工系統。 本論文提出一種新穎的基於子空間的到達角估測方法。我們所提出之方法相較於旋轉不變性技術在低訊噪比下表現更佳。透過所估得的到達角，便可有效分離來自不同路徑的接收訊號，我們接著進行後續的參數估測，其中包括離開角、都普勒頻率偏移以及通道響應。模擬結果顯示，透過我們所提出的到達角估測方法對於其他參數估計結果的提升優於旋轉不變性技術。 實務上由於路徑數或是訊號源數目通常是未知的，所以在通訊系統中估計路徑數對於後續的參數估計至關重要。然而，傳統方法如最小描述長度在低訊噪比條件下往往低估真實的訊號源數量，從而降低多徑分集增益並使系統性能下降。為了解決此問題，我們提出了一種基於改善傳統最小描述長度的方法，並介紹另一種基於訓練序列或導頻訊號的路徑數估測方法。這兩種所提方法在低訊噪比下明顯優於傳統最小描述長度方法。在數值模擬分析中，我們不僅驗證了所提方法在路徑數估測上的準確性，也展示了路徑數估測誤差對其他參數估計的最小均方誤差以及系統位元錯誤率的影響。

Orthogonal frequency division multiplexing (OFDM) is a widely used multicarrier transmission technique that mitigates inter-symbol interference (ISI) and enables low-complexity equalization. However, in doubly selective channels, Doppler spread disrupts subcarrier orthogonality, leading to inter-carrier interference (ICI) and significant performance degradation. The study of Doppler effect is an important issue in OFDM systems. In the past, the tapped delay line (TDL) model has been shown to be an efficient model for capturing the behavior of doubly selective channels. In the TDL model, each path is associated with a distinct Doppler frequency offset (DFO). In order to estimate the DFOs and impulse responses of multipath channels, we consider OFDM systems equipped with an uniform linear array (ULA) at the receiver. In this thesis, we propose a novel subspace-based AoA estimation method. The proposed method has a better performance than estimation of signal parameters via rotational invariance techniques (ESPRIT), especially when the signal-to-noise ratio (SNR) is low. Using the estimated AoAs, the received signals from different paths can be effectively separated, subsequent parametric estimations are performed, including angle-of-departure (AoD), DFO, and the channel response. Numerical simulations are conducted to show the accuracy improvement achieved by the proposed AoA estimation method compared to ESPRIT. In practical scenarios, the number of paths or signal sources are typically unknown. Although determining the path number is crucial for accurate parameter estimation, traditional approaches such as the minimum description length (MDL), often underestimate the true number of paths at low SNR, reducing multipath diversity gain and degrading system performance. To address this issue, we propose a refined MDL-based method and a new training sequence or pilot-based method for the estimation of path number. The two proposed methods outperform the MDL method, especially at low SNR region. Numerical simulations are provided to show the accuracy of the two proposed methods for path estimation and also highlight the impact of path number estimation accuracy on the mean squared error (MSE) of other parameters and the bit error rate (BER) of the systems.