BLIND EQUALIZATION: ASPECTS OF COMMUNICATION

OUTLINEWireless Channel The Multipath ProblemFading CharacteristicsBasic Idea of EqualizationRole of EqualizationChallenges in designing Channel EqualizerShortcomings of non-adaptive EqualizerThe Adaptive EqualizerOperation of Adaptive EqualizerBasics of Blind DeconvolutionThe Bussgang TheoremBussgang Algorithm in Blind deconvolutionAssumptions in applying Bussgang AlgorithmIterative Deconvolution processConvolution NoiseNon-convexity of cost functionAdvantages & Disadvantagesheading to next development

WIRELESS CHANNEL

Received Information

THE MULTIPATH PROBLEM

FADING CHARACTERISTICS

Basic Idea of Equalization

•In telecommunication, the equalizer is a device that attemptsto reverse the distortion incurred by a signal transmittedthrough a channel.• Heq(f) = 1/H(f)• Goal is to mitigate the effects of ISI due to system behavior,multipath fading & attenuation.• The thumb rule: If

Coherence Time(Tc)> Symbol Duration(Tm) --Equalization is mandatory

Role of Equalization

Challenges to design Equalizer Equalizing process to mitigate ISI effect sometimes

enhance the noise power (shortcoming of the ZF equalizer)

Introduction of MMSE Equalizer Introduction of cost function Derivation of Wiener-Hoff equations

Shortcomings of Non-adaptive equalizers Since in wireless channels are time varying in

nature, non-adaptive equalizers can only perform well for a very limited period of time

Periodically estimation the channel andupdate of the equalizer coefficients accordingly are required in real-time commercial communication system leading to training & tracking modes of adaptive equalizers

THE ADAPTIVE EQUALIZERS

2 modes of operation:(a)Training Mode(b)Tracking Mode

Operation of Adaptive Filters:- The standard adaptive approach, though attractive

in handling time-variant channels, has to waste a fraction of the transmission time for a training sequence.

Even the so-called decision feedback equalization (DFE), which does not explicitly use a training sequence, requires sending known training sequences periodically to avoid catastrophic error propagation

Operation of Adaptive Filters(contd.)

The GSM Frame Structure

Nearly 17% resource is wasted in sending the training bits to configure the equalizers which is not cost-effective. A special equalization process is needed where the use of “training bits” are avoided causing efficient use of channel- vision to “BLIND EQUALIZATION”

BASICS OF BLIND EQUALIZATION Blind equalization is a digital signal processing technique in

which the transmitted signal is inferred (equalized) from the received signal, while making use only of the transmitted signal statistics. Hence, the use of the word blind in the name

Both the channel model & Transmitted signal is to be determined by observing the received signal characteristics.

The concept of Unsupervised learning

Use of higher order statistics- BUSSGANG STATISTICS

THE BUSSGANG THEOREM A theorem of Stochastic analysis

Statement: The cross-correlation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant

It was first published by Julian J. Bussgang in 1952 while he was at the Massachusetts Institute of Technology

Illustration… Let {X(t)} be a zero-mean stationary Gaussian random

process and {Y(t)}=g(X(t)) where g(.) is a nonlinear amplitude distortion

If is the autocorrelation function of X(t) , then the cross-correlation function of X & Y is:

where C is a constant that depends only on g(.)

BUSSGANG ALGO. IN BLIND DECONVOLUTION PROCESS

atbt

yt=b1at+b2at-1+…….+bnat-n-1

=B(q)* at

yt= Φt,n*bΦt,nToeplitz matrix with n columns containing

thc input sequence at

Necessary Assumptions for Bussgang Algorithm The data sequence x(n) is white; i.e. data symbols are

i.i.d random variable with zero mean & unit variance:E[x(n)]=0

AndE[x(n)x(k)]=1, k=n

=0, k n The pdf of x(n) is to be uniformly distributed as follows:

Iterative deconvolution Process

**Governing Equations

The Convolution Noise

Convolutional Noise

Basic block diagram of the Blind equalizer

Non-convexity of Cost Function

The Error performance surface of the Iterative deconvolution process may have local minima in addition to a global minima

Non-convergence form of the Cost function results in Ill-Convergence

Advantages & Disadvantages

.

HEADING TO NEXT DEVELOPMENT:- To overcome the problems, explicit algorithms

using cyclostationary statistics through tricepstrum calculation is developed where no minimization of cost function is required though computational complexity increases.

References1. Adaptive Filter Theory by S. Haykin, PHI2. Wireless Communications, Andrea Goldsmith, Stanford University3. Adaptive Filters: Theory & Applications, B.Farhang-Boroujeny, Wiley4. Wireless Communication: Principles & Practice, T.S. Rappaport, Pearson5. Adaptive Filtering Primer with MATLAB, A.D. Poularikas & Z.M.Ramadan, CRC

Publication6. Blind Identification and Equalization Based on Second-Order Statistics: A Time

Domain Approach, Lang Tong, Member, IEEE, Guanghan Xu, Member, IEEE, andThomas Kailath, Fellow, IEEE

7. BLIND DECONVOLUTION BY MODIFIED BUSSGANG ALGORITHM, Sirnone Fiori,Aurelio Uncini, and Francesco Piaua, Dept. Electronics and Automatics - University ofAncona (Italy)

8. Least Squares Approach to Blind Channel Equalization, Kutluyl Dogancay, Member,IEEE, and Rodney A. Kennedy, Member, IEEE

9. Blind Equalization by Direct Examination of the Input Sequences, Fredric Gustafsson,Member, IEEE, and Bo Wahlberg, Member, IEEE

10. Self-Recovering Equalization and Carrier Tracking in Two-Dimensional DataCommunication Systems, DOMINIQUE N. GODARD, MEMBER, IEEE