通信接收機之數位訊號處理演算法： 同步，等化和通道估計

Abstract

數位通訊接收機設計，可分為訊號處理單元與資料處理單元。其中訊號處理單元用以解決訊號同步、通道等化與通道估計等問題。本論文以接收機之數位處理演算法設計為主題，探討各種通訊系統之同步、等化與通道估計議題。本論文根據應用之系統，分為三個部份。第一部份為有線單載波之接收機設計；第二部份為無線多載波系統之接收機設計；第三部份為寬頻多進多出系統之傳送與接收設計。

第一部份，單載波接收機設計議題，我們探討載波頻率回復與盲目決策回復等化器等議題。就載波回復機制問題，我們探討兩種技術：頻率估計與載波回復迴路。針對頻率估計議題，我們研究延滯交互相關之頻率估計技術。從中探討費氏(Fitz’s)演算法之效能，進而推演出一套低複雜度高精準度之多解析演算法並將此演算法運用於QAM 系統。針對載波回復迴路設計，我們根據星圖降階(reduced constellation)的概念提出一系列之盲目相位偵測器以增加頻率搜尋 範圍。此外考量收斂速度與穩定追蹤，我們進而推演出一套結合星圖降階與決策導向（decision-directed）的混合相位偵測器與迴路濾波器頻寬動態控制機制。就盲目決策回復等化器設計議題，我們探討盲目適應性演算法之加速，並且提出一套運用於盲目等化器之可變步階係數(Variable stepsize)演算法；此外，我們提出適應性演算法之軟式切換概念，並且提出一套結合盲目與決策導向之混合式適應性演算法以加速適應性訊號處理演算法之模式切換。最後，我們探討幾種結合載波回復與決策回復等化器設計之運作策略。

第二部份，多載波接收機設計議題，我們探討通道估計與WiMAX 系統中的細胞偵測既整數載波漂移估計等議題。首先，針對同步議題之細胞偵測既整數載波漂移估計，我們根據理論推導出最佳偵測演算法。針對最佳演算法化簡，推得頻域濾波概念，並且根據該概念推出幾種簡化之演算法。就通道估計議題，我們提出兩種類型的通道估計演算法。首先，我們探討多項式內插通道估計演算法的估計誤差之最佳化，提出濾波器窗口漂移(window shift)概念，在給定內插階數的情況下，推得最佳漂移量的理論值與其值估計方法。另一方面，我們採取近似最小誤差估計作為通道估計演算法。在這議題中，為得到在頻域的近似通道交互相關函數，我們推得通道的“延滯方均值”與 “延滯均值”簡易估計演算法。最後，我們將其估計法應用於梳型（comb-type） OFDM 與WiMAX 等系統之通道估計。

第三部份，寬頻多進多出(Wide-band MIMO)傳送接收機設計議題，我們討論最佳傳送器設計以及其接收機等化與通道估計演算法。針對錯誤更正碼保護之MIMO-OFDM 傳輸，加入一空間-頻率轉換(Space-frequency transform)，用以最佳化其分集增益(diversity gain)與編碼增益(coding gain)。該空頻轉換式採取兩階段運算程序：正交轉換(orthogonal transform)、空頻錯置(space-time interleaving)。在接收端，針對通道等化與解調設計，採取渦輪決策回復等化器作為遞迴解碼程序。在演算法實現，使用頻域等化器降低接收機複雜度，並且提出可分離之空頻錯置設計，如此可將空頻錯置與渦輪決策迴路分離。我們也提出結合遞迴通道估計與資料偵測演算法以降低嚮導符碼的使用。

The communication receiver can be divided into the signal processing unit and the data processing unit. The signal processing unit is mainly used to solve problems of the signal synchronization, the channel equalization and the channel estimation. The topic of this thesis is design of the signal processing algorithms and discusses various issues in synchronization, equalization and channel estimations. According to the application of the systems, this work is divided into three parts. Part I is the receiver design in wired single carrier (SC) system; Part II is the receiver design of multi-carrier orthogonal frequency-division multiplexing (OFDM) systems over a wireless channel; Part III is the transceiver design of the wide-band MIMO systems.

In Part I, the topics of the receiver design in SC systems, we address the carrier recovery and the blind decision-feedback equalization (DFE). In carrier recovery issue, we discuss two techniques: the carrier frequency estimation and the carrier recovery loop. For the carrier frequency estimation, we study the frequency estimator using the delay correlation, derive the performance of the Fitz’s algorithm, propose a low-complexity and high-accuracy multi-resolution algorithm, and then apply the proposed algorithm for the frequency estimation in QAM system. For the carrier recovery loop, we propose a series of the blind phase detections (PDs) according to the reduced-constellation concept, which can enhance the acquisition range of the carrier frequency offset. In addition, when considering the acquisition speed and the tracking stability, we furthermore derive a hybrid PD, which combines the decision-directed PD and the reduced-constellation PD, and the mechanism of the dynamic control of the loop bandwidth. In the design topic of blind DFE, we focus on the improvement of the convergence speed of the blind adaptive algorithm and propose a variable stepsize (VSS) algorithm, which is applicable to blind algorithms. In addition, we suggest the soft-switching concept of the adaptive mode and present a hybrid adaptive algorithm, which combines the blind algorithm and the DD-LMS algorithm, to speed up the operation mode switch of the adaptive algorithm. At final of this part, we discuss several operation strategies of the joint carrier recovery and the DFE.

In Part II, the topics of the receiver design in multi-carrier systems, we discuss the issues of the channel estimation and the joint estimation of the Cell-ID and integral CFO in WiMAX system. First, for the synchronization issue in joint estimation of the cell-ID and integral CFO, we derive an optimal detection algorithm according to theoretical derivation. Moreover, from the simplification of the optimal detection algorithm, we suggest the concept of the frequency domain filtering and propose several simple detection algorithms according to the concept. In the topic of the channel estimation, we propose two kinds of the channel estimation algorithms. First, we study the optimization of the estimate mean-square error of the polynomial interpolation. We introduce a window shift concept, derive the optimal window shift, and propose the estimation method of the value under a given interpolation order. Besides, we apply the approximate minimal mean-square error (MMSE) estimator to the channel estimation. In this topic, in order to derive the approximate cross-correlation function in frequency domain, we propose the simple estimation of the root-mean-square delay spread and the mean delay of the channel. We apply the estimators in the channel estimation of the comb-type OFDM and WiMAX systems.

In part III, the topic of the transceiver design in wide-band MIMO systems, we address the design of the optimal transmitter and the corresponding receiver. For the coded MIMO OFDM transmission, we insert a space-frequency transform (SFT) to maximize the diversity gain and the coding gain. The transform is realized in a two-step process: the orthogonal transform and then the space-frequency interleaving (SFI). At the receiver, for the design of the channel equalization and demodulation, we adopt the turbo-DFE as the iterative decoding process. In the algorithm realization, we use the frequency domain equalization to reduce the receiver implementation cost and propose the separable SFI design. By this way, the SFI can be moved outside the turbo-DFE loop. In addition, we propose the algorithm of joint channel estimation and the data detection to reduce the utilization of the pilot symbols.