在xDSL應用中DMT系統時序誤差校正之最佳插補濾波器設計

Abstract

DMT調變是一種在有限通道長度下，可傳輸高速度資料的調變技術。當這種調變技術應用到xDSL系統中，因為傳輸資料多且密度大， 所以時序誤差會對系統性能造成影響。本篇論文主要目的是在全數位時序恢復系統架構下，設計插補濾波器來補償接收端與傳輸端取樣相位。在DMT系統下，我們定義各載波之符號元誤差均方值的總和為成本函數，然後設計內差插補濾波器係數以及頻域等化器以獲得最小成本函數值。其中成本函數為插補濾波器係數以及頻譜等化器兩變數的非線性多項式， 利用替代類別最小誤差法使得係數收斂到最小值成本函數值。當應用到ADSL系統時，載波數目為256，濾波器階數為4，係數多項式階數為3時，模擬結果顯示最高頻率載波的符號元失真比率皆在50dB以上，此現象可以應用到更多載波數目的非常快速數位用戶端迴路系統(VDSL)上，且成本函數值比[6]小10倍。若將濾波器階數提升為5，係數多項式階數為4時，則最高頻率載波的符號元失真比率皆在70dB以上，成本函數值比[6]小780倍。

Discrete multitone(DMT) modulation is a multicarrier technique that allows the transmission of high speed data over band limited channels. This type of system is very sensitive to synchronization errors when used in Digital Subscribe Loop application(xDSL), due to the high number of carrier and high-density constellations involved. The main purpose of the thesis is to design the interpolation filter coefficients compensating for sampling phase of transmitter and receiver in all-digital timing recovery system. We define that the cost-funciton is the sum of mean square error of every carrier, and design the interpolation filter coefficients and frequency equalizer(FEQ) to minimize the cost function value. Employing Least-Mean-Square(LMS) and Alternating-Coordinate Minimization(ACM) to the nonlienar cost function obtains the optimal interpolation filter coefficients. When it applys to Asymmetric Digital Subscirber Loop(ADSL) system with 256 carriers, the fourth order of filter and the third order of polynomials(M=4,P=3), the simulaiton results indicate that the SDR of the highest frequency carrier is above 50 dB, and this phenomenon can be applied to VDSL system with more carriers. The cost function value of optimal coefficients is almost 10 smaller than [6]. If we increase the order of filter to 5, the order of polynomials to 4, the SDR of the highest frequency carrier is over 70dB and the cost function value is 780 times of that of [6].