Adaptive Decision Feedback Equalization: Applications and Performance Analysis
|關鍵字:||適應性決策回授等化;最小均方;誤碼曲線;重複訓練;雙向等化;限制;最大可能序列估測;計算複雜度;DFE;LMS;error probability;multiple training;bi-directional equalization;constrained;MLSE;computational complexity|
另一種常用的等化技術為最大可能序列估測法(MLSE).最大可能序列估測的效能雖較決策回授等化好;但計算複雜度卻很高.最大可能序列估測法通常是以維特比演算法(VA)實現之;而維特比演算法的計算複雜度卻會隨通道長度呈指數形式成長.若以些微的效能損失為代價,一般可利用決策回授等化器來縮短通道響應,藉以降低維特比演算法的計算複雜度.但有時此種組合的運算量仍嫌太高.在本論文的第三部份中,我們為此提出了以限制性決策回授等化器來縮短通道效應,藉以更進一步降低運算複雜度.基本想法是將縮短後的通道係數限制於某些離散值上.此舉可將維特比演算法中所需用於計算分支量度(branch metrics)的乘法運算轉換成位元轉移(bit shift)運算.所減低的運算量,有利於最大可能序列估測法的實際運用.模擬結果顯示,所提之限制性決策回授等化器與最大可能序列估測法的組合不但計算量低,更保有傳統組合絕大部分的效能.最後我們也將上述方法用於延遲決策回授序列估測法(DDFSE),用以偵測訊號間干擾環境下的格狀編碼調變(TCM)訊號.亦是利用限制所縮短通道的係數值來達到延遲決策回授序列估測法中的維特比演算法的實作複雜度.|
In digital communication systems, intersymbol interference (ISI) is one of the main causes degrading system performance. The decision feedback equalizer (DFE) has been considered a simple yet effective remedy for this problem. This thesis consists of three parts. In the first part, we consider the performance analysis of adaptive DFE. Analysis of the DFE error probability is known to be a difficult problem. This is primarily due to the nonlinear operation involved in the decision process. The problem is further complicated if the DFE is operated in a time-varying channel. In this case, an adaptive algorithm must be used to track the channel variation. Then, a decision error not only propagates through the feedback filter affecting the future outputs, but also through the adaptive algorithm updating the tap weights toward a wrong direction. We specifically take this effect into account and analyze the error probability of the DFE under the slowly fading channels. We consider the most widely used adaptive algorithm, namely, the least mean square (LMS) algorithm. Closed-form expressions are derived for the training mode as well as the decision-directed mode. The validity of the theoretical results are verified through computer simulations. Although the LMS algorithm is simple, its convergence is slow. As a result, it is not suitable for DFE adaptation in fast varying channels. In the second part of the thesis, we then propose an extended multiple-training LMS algorithm accelerating the convergence process. The convergence properties of the multiple-training LMS algorithm are also analyzed. We prove that the multiple-training LMS algorithm can converge regardless its initial value and derive closed-form expressions for the weight error vector power. We then apply this algorithm to the IS-136 system. Taking advantage of the IS-136 downlink slot format, we divide a slot into two subslots. Bi-directional processing is then applied to each individual subslot. The proposed LMS-based DFE has a low computational complexity and is suitable for real-world implementation. Simulations with a 900MHz carrier show that our algorithm can meet the 3% bit error rate (BER) requirement for mobile speeds up to 100 km/hr. Another commonly used equalization method is called the maximum likelihood sequence estimator (MLSE). The MLSE can outperform the DFE, however, its computational complexity is higher. The MLSE is usually implemented by the Viterbi algorithm (VA). The computational complexity of the VA grows exponentially with the length of the channel response. With some performance reduction, a decision-feedback equalizer (DFE) can be used to shorten the channel response reducing the computational requirement for the VA. However, for many real-world applications, the complexity of the DFE/MLSE approach may be still too high. In the third part of the thesis, we propose a constrained DFE further reducing the computational complexity of the VA. The basic idea is to pose some constraints on the DFE such that the postcursors of the shortened channel response have only discrete values. As a result, the multiplication operations can be replaced by shift operations making the VA almost multiplication free. This will greatly facilitate the real world applications of the MLSE algorithm. Simulation results show that while the proposed algorithm remains almost the original MLSE performance, the VA is much more efficient than the conventional approach. Finally, we consider the delayed decision-feedback sequence estimation (DDFSE) for detection of the trellis coded modulation (TCM) signal in presence of the intersyombol interference (ISI). We use the constrained DFE to shape the channel response such that the post cursors have discrete values. This greatly reduces the implementation complexity of the VA involved in the DDFSE.
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