應用在雙選擇性衰減通道中之正交分頻多工系統的同步技術

Abstract

在數位通訊系統中，接收訊號之同步技術是基頻接收機必要的功能。在探討同步技術之前，本論文首先推導在多個同步錯誤共存下的數學模型。這些同步錯誤包括有符元時間偏移(symbol time offset)、載波頻率偏移(carrier frequency offset)及取樣頻率偏移(sampling clock frequency offset)。這樣的分析是必需的，因為在實際的環境中，這些同步錯誤是不可避免且同時存在的。因此，理論之訊號對干擾雜訊比(signal-to-interference-and-noise ratio, SINR)可由此數學模型進一步求得，並界定出因同步誤差所造成之效能損失。 為了改善在正交分頻多工(orthogonal frequency-division multiplexing, OFDM)系統中的同步錯誤，尤其針對雙選擇性衰減通道(doubly-selective fading channels)的環境下，本論文提出四個基於不同準則之同步演算法。 第一個提出之同步演算法是基於最大或然性(maximum-likelihood) 準則。藉由接收到的頻域訊號之數學模型，此方法求得兩個連續符元的對數或然(log-likelihood)函數。基於此函數，本論文提出針對符元時間偏移及載波頻率偏移之最大或然估測。並且，為了降低整體運算複雜度，吾人進一步由原提出之最大或然估測，提出一簡化的估測。 第二個提出之符元時間偏移同步演算法是基於最小化干擾準則。這個方法利用引導(pilot)子载波的特性，置符元邊界於最小干擾之取樣點。再者，為了降低運算複雜度，吾人利用Parseval定理及取樣理論，轉換此頻域之規準(metric)，成為一低複雜度之時域規準。 第三個提出之同步演算法是基於最大化訊號對干擾雜訊比準則。除了干擾隨著同步錯誤會快速增加外，有用的訊號也會隨之衰減。藉由這項觀察，吾人利用頻域資料，以最大化訊號對干擾雜訊比準則，直覺地利用頻域資料估測出符元時間偏移及載波頻率偏移。再者，於此提出的最大化訊號對干擾雜訊比演算法，為無須訓練符元及引導子载波之非資料輔助(non-data-aided, NDA) 方法，如此可以提升傳輸效率。 第四個提出之同步演算法也是基於最大化訊號對干擾雜訊比準則。與第三個方法不同之處，此方法是利用時域的循環前置(cyclic prefix, CP)。在僅須較低的複雜度之下，此方法仍有令人滿意的效能。 此外，為了降低第三個方法所須運算量，本論文特別針對第三個方法，提出一追蹤（tracking）技術，也就是早晚閘(early-late-gate, ELG) 技術。這個技術可用在符元時間偏移及載波頻率偏移的追蹤上。 綜言之，除了效能外，本論文亦探討所提方法之複雜度及實用性。本論文提出之演算法各有不同之效能與複雜度，因此，它們可以適合於不同的應用及環境中。

For digital telecommunication systems, signal synchronizations are necessary for the baseband receivers. In this dissertation, before investigating the synchronization techniques, the mathematical model due to the combined effects of the symbol time offset (STO), carrier frequency offset (CFO), and sampling clock frequency offset (SCFO) is derived. The analysis of the combined impacts of these co-existing errors is desirable due to non-ideal synchronization process in a practical environment. With the derived model, the theoretical signal-to-interference-and-noise ratio (SINR) is formulated to characterize the incurred losses owing to the synchronization errors. To cope with the synchronization errors in orthogonal frequency-division multiplexing (OFDM) systems, four synchronization methods based on various optimization metrics are proposed, which can work effectively in the environments of doubly-selective fading channels. The first proposed method is based on the maximum-likelihood (ML) criterion. Based on the derived mathematical model of the received frequency-domain (FD) data, we formulate the log-likelihood function of two consecutive symbols. With this function, the ML estimation for the STO and CFO is proposed. In addition, to reduce the overall computational complexity, a simplified estimation is also proposed based on the originally derived ML estimation. The second proposed STO technique is based on the criterion of minimizing the interference. This method locates the symbol boundary at the sampling point with the minimum interference (MinITF) utilizing the pilot subcarriers. Moreover, to reduce the computational complexity, the proposed FD minimum-interference metric is converted into a low-complexity time-domain (TD) metric by utilizing the Parseval’s theorem and the sampling theory. The third proposed technique is based on the criterion of maximizing the SINR. In addition to drastic increase of the interference at wrong synchronization points, the desired signal power also decreases accordingly. Based on this observation, both the STO and CFO are intuitively estimated by maximizing the SINR metric of FD data. Moreover, the proposed maximum-SINR (MaxSINR) method is non-data-aided (NDA) without needing training symbols and pilot subcarriers so that the transmission efficiency can be improved. The fourth proposed technique is also based on the criterion of maximizing the SINR. In contrast to the FD-MaxSINR, the fourth proposed method is developed in time-domain and utilizes the CP. With its low-complexity, the proposed time-domain Maximum-SINR (TD-MaxSINR) still has satisfactory performance. To reduce overall computational complexity of the FD-MaxSINR technique, we specifically investigate a tracking technique for the proposed FD-MaxSINR metric, i.e., the low-complexity early-late-gate (ELG) technique. The ELG technique can be employed for both the STO and CFO estimations. In summary, besides the performance, we also focus on the complexities of the proposed techniques to investigate their practicalities. The proposed techniques exhibit different performances and complexities; therefore, they can be suited for different applications and environments.