称号及び氏名

博士（工学）Hai Lin

学位授与の日付

平成 17 年 2 月 28 日

論「Studies on Bayesian Technique for Digital Communication

文名Channel Equalization」（Bayesian 技術を用いたデジタル通信システムにおけるチャネル等化に関する研究）
論文審査委員

主査 教授 山下 勝己
副査 教授

勝山 豊

副査 教授

大橋 正治

Summary
In the past decade, the requirement for speed and reliability of informationtransmission increases very quickly, and certainly it will keep growing in the comingfuture. High speed data transmission usually suffers from the disturbance in thecommunication channel. During the transmission, the channel brings additive noise
and its frequency selective nature, due to limited bandwidth or multipath fading,introduces InterSymbol interference (ISI). As a consequence, the transmitted signal
waveform may be severely disturbed, which will cause the loss of information at thereceiver end. Reliable transmission can not be achieved without the compensation forthese disturbances. The equalization in digital communication systems is acompensation process, which combats the ISI and additive noise to reconstruct thetransmitted signal, and the compensator in this process is called equalizer.
Traditionally, the equalization is treated as an inverse filtering problem, where thetransversal structure based linear equalizer (LE) tries to form an approximation to theinverse of the distorting channel. However, due to the noise enhancement, the accurateapproximation and good equalization performance can not be achieved by this low
computationally demanding equalizer. From the estimation theory, it is known that thebest performance is obtained by detecting the entire transmitted sequence using theMaximum Likelihood Sequence Estimation (MLSE). High complexity and deferring
decisions associated with the MLSE are however often unacceptable in many practicalcommunications systems. Recent researches focus on Neural Network (NN) based
equalizers, which consider the equalization as a geometric classification problem andprovide alternative compromises between performance and complexity, Compared withthe LE, NN based equalizers have the same architecture of making decisions symbol bysymbol, but can handle a hypersurface decision boundary rather than the hyperplanedecision boundary of the LE, thus achieve superior performance. In particular, Bayesian
Equalizer (BE), a.k.a. Radial Basis Function (RBF) equalizer because of the perfect
implementation by RBF networks, is the error probability optimized solution forsymbol-decision equalization. The BE presents slightly poorer performance then MLSE
but has significantly lower complexity and shorter delay. Therefore, it is regarded as avery promising equalization technique.
The conventional equalization is purchased with the assistance of pilot sequence, which
is known at the receiver and sent before the information-bearing signal sequence beingsent. In contrast to pilot-aided equalization, the equalizer without the benefit of a pilot
sequence is said to be self-recovering or blind equalizer. In blind equalization, theBussgang statistics approaches are based on a LE, thus they inherit the noise
enhancement characteristic; the Second Order Statistics (SOS) and Higher Order
Statistics (HOS) based approaches are essentially channel identification solutions,which do not directly give equalization solution. Furthermore, these three classes ofblind equalization approaches are not suitable for nonlinear channel. For blind MLSE,
although theoretically it can be applied on nonlinear channel, it suffers from not only
the difficulty of nonlinear channel identification but also the high complexity and longdecision delay like the MLSE. On the other hand, since BE is designed in accordancewith the channel output states (COSs), the channel identification and the noise
enhancement can be avoided. Due to these attractive characteristics, naturally , it isdesirable to develop the blind equalization techniques based on BE.
So far the Bayesian family equalizers are developed for single channel, while that formultichannel case has not been discussed yet. Aiming at performance improvement andwide-range application, this thesis focuses on two topics, one is Bayesian Decision
Feedback Equalizer (BDFE) with receiver diversity combining and another one is blind
equalization using BE. The major contributions of this thesis lie on two proposed
combining schemes for BDFE with receiver diversity and the proposal of three kinds ofBlind Bayesian Equalizers (BBEs) . The main components of this thesis and the major
results of the presented work can be summarized as follows:
Chapter 1 introduces the history of the equalization research and gives an overview ofthis thesis.
Chapter 2 describes the mathematical model of baseband communication system,
explains the reason of ISI and derives the BE and the BDFE.
Chapter 3 investigates the problem of BEFE with receiver diversity combining andproposes two combining schemes. In the first combining scheme, Bayesian Decision
Variable Combining (BDVC), we employ several BDFEs corresponding to the same
numbers of receivers, and the decision variable is defined as the product of the Bayesian
Decision Variables (BDVs) in the corresponding BDFE of each sub-channel. Since theBDVC exploits the maximum diversity at BDV level, we give the optimal solution formultichannel. However, this optimal solution is computationally expensive. To make acompromise between performance and complexity, a complexity reduced linear
combining is proposed, where a linear combiner is used to combine the received signalsof each subchannel before being fed to a BDFE. This eigenvector based Maximal Delay
span channel energy Combining (MDC) maximizes the desired part energy of the
combined channel, which the performance of the followed BDFE mainly depends on.
Consequently , the significant complexity reduction is achieved, at a price of light
performance loss. Although the MDC based BDFE shows somewhat worse performance
than that based on BDVC, it is more practical due to its simplicity . The validity andperformance superiority of these two combining schemes are demonstrated by thesimulations.
Chapter 4 focuses on the proposed first approach to blind equalization using BE, blind
BDFE with channel estimators. For the challenging blind equalization problem, due tothe lack of channel information, a straightforward idea is to employ a cannel estimator.
Chen et al. have proposed a blind BDFE (BBDFE) , where the channel and the signal
are estimated in a joint sense. However, this decision-directed based approach suffersfrom the incorrect convergence, without the suitable initialization corresponding to thesmall ISI. How to find a suitable initialization becomes a key problem. Chen et al. havesuggested an initialization according to the partial information of the channel. In
contrast, with no any knowledge of the channel, a “start” vector that has several states
is used to obtain several channel estimates, which are the initial channel estimates in
the proposed method. Then the decision-directed algorithm is individually purchasedfrom these initializations with the corresponding BDFEs. By evaluating the Bayesianlikelihood which is defined as the accumulation of the natural logarithm of themaximum BDV decision variable at each instant, the optimal channel estimatescorresponding to the maximum Bayesian likelihood can be found, as well as the optimal
BDFE. Compared with Chen’s BBDFE, the proposed one not only presents better
convergence performance with less computational complexity, but also is able to deal
with the channel having severe ISI and in-band spectral null satisfactorily.
Chapter 5 develops the received signal constellation (RSC) estimation based BBE, theproposed second approach to BE based blind equalization. Since BE is based on theclassification viewpoint, it essentially depends on the COSs, rather than the channel
itself. In other words, only the RSC, which composes the COSs, is important. Based on
this property, we develop a BBE and highlight its application in nonlinear channel.
Usually, most of the algorithms for blind equalization are developed on linear channel
models because of the simplicity. The difficulty in nonlinear case is that not only thechannel parameters but also the channel model is not known exactly. Fortunately, a BE
cares about the RSC only, so it is very suitable for nonlinear channel. Using theBayesian likelihood cost function which has been defined in the last chapter, theproblem becomes to maximize the Bayesian likelihood cost function with respect to theRSC, and the complex channel modeling is avoided. For this high dimensional complex
optimal problem, a hybrid simplex genetic algorithm, in which the simplex operator isincorporated with genetic algorithm, is proposed. Furthermore, this RSC estimation
based BBE is extended to couple with adaptive array antenna, and by employing theabove mentioned BDVC, we propose a Blind Spatial and Temporal Bayesian Equalizer(BSTBE). Also simulation results are given to evidence the validity of the proposedBBEs.
Chapter 6 discusses the last kind of the proposed BBEs, Cluster Map based Blind RBF
Equalizer (CM-BRE), which highlights a new cluster matching consideration of blind
equalization problem. Without channel estimator, the desired numbers of COSs (RBFcenters) can be obtained by an unsupervised clustering algorithm, Neural Gas
Algorithm (NGA). Based on the cluster matching viewpoint, which comes from theclassification nature of the BE, a cluster map generated from the known RBF equalizer
structure is used to partition the unlabeled RBF centers into appropriate subsets
merely by several simple sorting operations, which corresponds to the weightinitialization. Finally, the weights are adjusted iteratively by an unsupervised Least
Mean Squares (LMS) algorithm. Since the weights are initialized according to theunderlying structure of RBF equalizer, the proposed CM-BRE can achieve almost
identical performance with the optimal BE and avoid the calculation of the complex costfunction, for example, the above mentioned Bayesian likelihood. Moreover, by further
exploration on the COSs, CM-BRE is extended to a Cluster Map based Blind RBF
Decision Feedback Equalizer (CM-BRDFE), in which not only the determination
method of the feedback vector is given, but also the high computational load mainly
caused by NGA is reduced by a downsizing method that employs the inter-relation
among RBF centers. The proposed CM-BRDFE also has the close performance to theoptimal RBF decision feedback equalizer, which is demonstrated by the simulations.
Chapter 7 concludes this thesis and gives some topics for future research.

List of Publications
No.
1

Article’s Title
Blind

Equalization

Using

ParallelBayesian

Decision

Author(s)CorrespondingVol., Pages (Year).

Chapter

H. LinMathematicsandK. Yamashita

Computers

inSimulation,

Feedback Equalizer
2

Journal’s Name,Vol.

Chapter 456,

pp.247-257 (2001).

Fractionally Spaced

H. LinProc. of Int. Conf. On

Bayesian Equalizer

K. Yamashita

NeuralChapter 3

Information

Processing,pp.81-84(Shanghai, China, 2001).
3HybridSimplex

Genetic

Algorithm

H. LinMathematics

andK. Yamashita

Computers

infor

Blind

Simulation,

Equalization

Using

pp.293-304 (2002).

Vol.

Chapter 559,

RBF Networks
4

Blind RBF Equalizer

H. LinProc. of IEEE Int. Conf.

for Received Signal

K. Yamashitaon

Chapter 6

Communication

Constellation

Systems,

Independent(Singapore, 2002).

pp.82-86

Channel5

Fractionally Spaced

K. Yamashita

IEICE

Bayesian

H. LinFundamentals,

Decision

Feedback Equalizer

Trans.

E86-A,

on

Chapter 3

Vol.

pp.215-220(2003).
6Cluster Map Based

H. Lin

IEICE

Trans.

Blind RBF Equalizer

K. Yamashita

Fundamentals,
E86-A,

on

Chapter 6Vol.

pp.2822-2829(2003).
7A Design Method ofK. Watanabe

IEEJ

BlindandH. LinElectronics, Information

Temporal

RBF

K. Yamashita

and Systems, Vol. 124-C,

Equalizer

Using

SpatialTrans.

onChapter 5

pp.941-946 (2004).

Genetic Algorithm
8

Blind RBF Equalizer

H. LinProc.

withK. Yamashita

Conf.

Decisionof

IASTED Int.
on

Artificial

Chapter 6

FeedbackIntelligenceandApplication,

pp.645-650(Innsbruck,

Austria,2004).
No.
9

Article’s Title
AClusterBasedBlindAuthor(s)Journal’s Name,

CorrespondingVol., Pages (Year).

Chapter

Map

H. LinIEICE

RBF

K. Yamashita

Fundamentals,

Decision

Feedback

E87-A,

Equalizer

with(2004).

Trans.

on

Chapter 6Vol.

pp.2755-2760

ReducedComputational
Complexity
10

BayesianDecision

Feedback Equalizer
withReceiver

Diversity Combining

H. Lin

IEICE

Trans.

K. Yamashita

Fundamentals,

on
Vol.

E88-A, (2005) (in press).

Chapter 3

審査結果の要旨
本論文は、デジタル通信システムにおけるチャネル等化の Bayesian 手法に関する一連の研究をまとめたものであり、以下の成果を得ている。
（1）受信機ダイバーシチ技術を Bayesian 等化器の設計に導入し、各受信機で設計した Bayesian 等化器の判定変数を合成する方法を提案している。提案手法の特徴
は、各 Bayesian 等化器で判定するよりも、合成した等化結果の誤差確率が低減化し得る点にあり、このことを数学的および実験的に明らかにしている。
（2）上記の Bayesian 等化器における、判定変数決定の計算負荷を軽減化するため、各受信機の信号を重み付け合成した信号を用いる Bayesian 帰還型等化器を提案している。この重み付け係数の決定アルゴリズムは、Bayesian 帰還型等化器の性能を向上することに目的を置いている。
（3）線形チャネルのブラインド等化問題に対して、チャネル推定アルゴリズムとBayesian 等化技術を結合した、パラレル型ブラインド Bayesian 帰還型等化器を提案している。提案した等化器は、従来のブラインド Bayesian 帰還型等化器に比較して、良い初期条件が得られることと Bayesian 尤度関数を評価関数に用いていることから、ヌル特性をもつ取扱いが非常に困難なチャネルに対しても、優れた特性をもつことを明らかにしている。
（4）非線形チャネルのブラインド等化問題は、非線形チャネルの推定が困難であることから非常に難しい問題とされてきた。Bayesian 等化器は基本的に、チャネル特性を直接利用せず、送信信号と Bayesian 等化器において重要な役割を担うセンタ要素間の関係より構築することができる。ここでは、最尤法に基づいた評価関数を定義し、センタ要素を大域的探索法である遺伝的アルゴリズムを用いて決定している。
（5）教師なしクラスター学習方法は、受信信号からラベルなしクラスターを抽出できる。この点に注目し、受信信号から抽出したクラスターと Bayesian 等化器固有の構造から得たクラスターマップをマッチさせることにより、送信信号を復元し得る新たなブラインド Bayesian 等化器を提案している。提案した等化器は、簡単な並び替えの操作で、線形と非線形チャネルにおいて、最適 Bayesian 等化器に近い性能を得ている。
以上の諸成果は、デジタル通信システムでの Bayesian 等化技術の実用化のための基礎的な知見や基盤を与えるものであり、この分野の技術の発展に貢献するところ大である。また、申請者が自立して研究活動を行うに十分な能力と学識を有することを証したものである。

3．審査委員会の所見
本委員会は、本論文の審査ならびに学力確認試験の結果から、博士（工学）の学位を授与することを適当と認める。