透過全世界數以萬計的電話線傳輸媒介，美國國家標準局及歐洲電信標準局，特於1993年將能克服通道嚴重失真具有顯著效果的離散多載波技術（DMT）定成標準，進而達到高速且可靠的傳輸需求。
在離散多載波ADSL接收機不使用分離器（splitter）的情況下，一旦通道增益突然發生改變，等化器的係數有可能需要重新估計。幸運的是，某些發生的狀況可以事先被決定，而且被當做參考原型（profile）儲存起來，以便日後拿來和快速重訓的結果相比對，做為下一次穩態參考使用。在本論文中，首先提出一個喚起機制來決定何時應該進入快速重訓程序（the fast retrain procedure），接下來會討論等化器的重訓方法。最後提出兩個原型更新（profile update）的方法，而在參考原型狀態是有限的前提下，方法二將被用來改善更新機制的效率，以期達到節省能源的目的。

在離散多載波系統中，分頻通道獨立等化技術（per tone equalization）－是一種在各別副頻道（subchannel）上擁有自己的多級頻域等化器（multi-taps FEQ），被用來代替一般傳統的接收機（時域等化器搭配單級頻域等化器），進而使訊雜比（SNR）達到最大值的另類架構。此外，這種架構對同步延遲（synchronization delay）具有較低的敏感度。然而在分頻通獨立等化技術的模型中，通道長度被侷限在N個最大的取樣點之中，其中N代表離散多載波系統裡逆向快速富立葉（IFFT）的輸入點數，並且使用非直接式等化方法（indirect method）來求得頻域等化器的係數及訊雜比值。然而當通道長度超過N時，被用來計算代價函數（cost function）的複合矩陣（compound matrix）大小將隨之上昇。再者，此方法需要準確的通道估計。在論文的後半段，將為多級頻域等化器介紹一簡單的訓練法，並且在各個副頻道上加上一些回授級，進而提昇系統的輸出訊雜比。

In order to satisfy the demand for reliable high-speed data transmission through billions of telephone lines around the world, the American National Standards Institute (ANSI) and the European Telecommunication Standards Institute (ETIC) have chosen the discrete multi-tone (DMT) modulation as the standard line code for ADSL to combat the severely distorted channel since 1993.
In a DMT-based splitter-less ADSL receiver, the coefficients of equalizers may be reinitialized whenever a gross channel changes abruptly. Fortunately, some of these situations may be determined from the predetermined states and can be stored as a profile used to compare with the results from fast retraining and was chosen as the next steady state. In this thesis, the invoking mechanism of fast retraining was first proposed to determine when we should enter the fast retraining stage. Subsequently, the retraining method of equalizers will be discussed during fast retraining. Finally, the profile-updated method will be proposed to improve the efficiency of updating profiles, i.e., the power-saving issue of updating profiles when the states of profiles are not infinite and some of them appear frequently.

Per Tone Equalization (PTE) for DMT-based systems, an alternative receiver structure with a complex multi-taps frequency-domain equalizer (FEQ) per tone, was proposed to maximize the signal-to-noise ratio (SNR) for each individual tone instead of the usual structure consisting of a real time-domain equalizer in combination with a complex 1-tap FEQ per tone. Moreover, PTE has a reduced sensitivity to the synchronization delay. However, the channel model length is truncated to N maximum samples where N is the IFFT size in the DMT-based system, and use the indirect method of equalization to calculate taps in FEQ and SNR per tone. Whenever the channel response is longer than N, then the size of the compound matrix for calculating modified cost function grows with the channel length. Moreover, this method needs the exact channel estimation. In this thesis, the simple training method (the direct method) will be introduced for multi-tap FEQ, and will add several feedback taps per tone to slightly raise the SNR during the fast retraining interval.

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