基於最大可能性序列估計等化器應用於GSM系統之研究

Abstract

GSM系統因為接收到的信號受有碼際干擾（Intersymbol Interference; ISI），所以在接收端需要等化器（Equalizer）來消除ISI。一般應用於GSM的等化器有基於維特比演算法（Viterbi Algorithm; VA）的等化器和決策迴授等化器（Decision Feedback Equalizer; DFE）。其中基於維特比演算法的等化器是最佳的，不過卻比較複雜有實現上的困難。而決策迴授等化器雖是次佳的但卻比較容易實現。 這篇論文提供了兩種適用於GSM系統的決策迴授等化器，一是基於威能-霍樸（Wiener-Hopf）方程式的決策迴授等化器，另一是基於正規化最小均方演算法（NLMS）的決策迴授等化器，並對這兩種等化器做模擬比較。在論文中導出了基於威能-霍樸（Wiener-Hopf）方程式的tap weight封閉式且提供了NLMS應用於GSM系統上有效的訓練方法。而從模擬結果可發現在低 時，基於威能-霍樸方程式的決策迴授等化器有較好的性能（performance）。但隨著 的增加基於威能-霍樸方程式的決策迴授等化器開始出現error floor，且基於NLMS決策迴授等化器的性能漸漸超越基於威能-霍樸方程式的決策迴授等化器。

Due to the intersymbol interference (ISI), the GSM receivers need to use equalizers to cancel the ISI of the received signals. In general, there are two approaches to design equalizers for GSM systems: an equalizer based on the Viterbi Algorithm (VA) and a decision feedback equalizer (DFE). The equalizer based on the Viterbi Algorithm is the optimum solution but is impractical for implementation. For the decision feedback equalizer, it has less complexity though it is sub-optimal. In this thesis, we simulate and compare two decision feedback equalizers used for GSM systems: one is based on the Wiener-Hopf equation, the other is based on the normalized least mean square error (NLMS) algorithm. We also derive the close form of the tap weights for the Wiener-Hopf equation and propose an effective training method for the NLMS algorithm. From our simulation results, for low Eb/N0, the decision feedback equalizers based on Wiener-Hopf equation have better performance. While Eb/N0 is increasing, there is an error floor in the equalizers based on the Wiener-Hopf equation and the performance of the equalizers based on the NLMS algorithm is better.