適應性決策回授等化:應用與效能分析

Abstract

在高速數位傳輸系統中,訊號間干擾(ISI)為降低系統效能的主要因素之一.決策回授等化(DFE)為此問題之一簡單且有效的補救方法.本論文分成三部份.第一部份旨在探討適應性決策回授等化器的效能分析.由於決策回授等化涉有非線性運算,使得決策回授等化器的誤碼效能分析極為棘手.當決策回授等化器利用適應性演算法來追蹤通道變化時,此分析工作更形複雜,這是因為決策錯誤訊號不但會被遞回至回授濾波器而影響以後的輸出; 亦會影響演算法,使得等化器係數被調錯.後者在一般文獻上很少被討論.而在我們對於適應性決策回授等化器所做的分析工作中,我們特別著眼於一般常用的最小均方(LMS)決策回授等化器在慢速衰變通道環境下的誤碼表現,而且我們也把誤碼遞延對於適應性等化器係數的效應考慮進去.我們導出了完整的數式來估測最小均方決策回授等化器在訓練模式與決策導引模式之下的誤碼曲線,並由實驗結果來驗證其正確性. 雖然最小均方演算法十分簡單,但其缺點是收斂速度慢.在快速變化通道環境下並不實用.在本論文第二部份中,我們利用重複訓練之最小均方演算法 來加快收斂速度,並分析其收斂特性.我們不但證明了重複訓練最小均方演算法的可收斂性,並能估計係數誤差向量的二階統計特性.我們也加入了雙向等化技術,並利用北美無線標準IS-136系統的下傳資料碼框結構,將其分塊,來對此系統做等化.所提出的等化方法不但計算量低,適合實作,由模擬結果顯示,當載波頻率為900MHz時,所提的等化方式在移動速率高至每小時100公里的環境下,仍可達到系統要所求的3\%誤碼率(BER)以下. 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.