基於最大似然原則之正交分頻多工及廣義分頻多工系統的初始同步

Abstract

初始同步對於接收器（receiver）的設計來說至關重要。同步器的目的在於將符元時間（symbol timing）和載波頻率（carrier frequency）校準，並進一步取得訊號框（frame）的同步。在一個接收器內部，綜合考量以上這些任務，我們論證說明了適當的同步器結構應包含兩步驟的首次取得同步，加上後續的回授追蹤迴路。對應首次取得同步的這兩個步驟，吾人分別提出了一個盲式（blind），基於循環前綴（cyclic prefix）而得之最大似然估計器（maximum-likelihood estimator，MLE），以及一個資料輔助式（data-aided），類最大似然估計器（quasi-MLE）。以上所提出的演算法，原則上，也適用於追蹤迴路。和既有研究不同的是，吾人所提出應用在時變多路徑通道（time-varying multipath channels）之真正最佳最大似然估計器（即前者），是利用更為完整的信號相關模型（signal correlation model）推導而得，並且過程中沒有任何近似或妥協。此法所得之關於載波頻率偏移（offset）的最佳估計值，過程中涉及了一個一元四次方程式的解，而非過去文獻所以為的，單純只是一個複數的角度值。衍生自此較為複雜的最大似然估計器，我們也提出了一個低複雜度估計器作為替代方案。雖然後者表現出和前者幾無差別的效能，然而其計算複雜度甚且只有一個既有競爭對手複雜度之約莫一半左右。再者，我們也確認了此低複雜度估計器可推廣適用於廣義分頻多工（generalized frequency-division multiplexing，GFDM）系統，一個第五代無線通訊網路的重要競爭者。完整包羅的模擬結果驗證了吾人所提方法相較於過去研究成果的優越性以及穩健性。此奠基於最大似然估計之理論框架所作的推導演繹，加上深入的理論分析，對未來可能的相關研究提供了深思熟慮的內在觀點。

Initial synchronization is of vital importance to receiver design. The objectives of a synchronizer consist of the alignment of symbol timing and carrier frequency, as well as frame synchronization. Considering the above tasks inside a receiver, we justify the synchronizer structure composed of two acquisition steps and feedback tracking loops. For the two acquisition steps, a blind cyclic prefix (CP)-based maximum-likelihood (ML) estimator (MLE) and a data-aided quasi-MLE are proposed, respectively. The same algorithms, in principle, are also applicable to the tracking loops. Different from existing studies, the truly optimal MLE for time-varying multipath channels is obtained by exploiting a more complete signal correlation model, without any approximation or compromise. The optimal estimate of carrier frequency offset is involved in the solution of a quartic equation, rather than simply the phase angle of a complex number. Deduced from the MLE, a reduced-complexity alternative (dubbed RCE) yields indistinguishable performance, at a roughly half lower complexity than an existing rival. We also confirm the RCE's applicability to generalized frequency-division multiplexing (GFDM), which is an important contender for fifth-generation wireless communication networks. Comprehensive simulation results verify the superiority and robustness of the proposed schemes over previous methods. The derivations based on the ML estimation framework, along with the in-depth theoretical analysis, offer thoughtful insights for future related studies.