Channel Equalization Techniques Fernando Gregorio Based on: 1-Adaptive Signal Processing, Benesty-Huang 2-Fundamentals of Adaptive Filtering, Ali H. Sayed

Outline Introducction Channel equalization Linear equalizers Decision feedback equalizers Adaptive algorithms for channel equalization Adaptive linear equalizer Adaptive DFE Training and tracking Simulations Static channel Time varying channel S88-4221 Seminar

Introduction In a communication system, the transmitter sends the information over an RF channel. The channel distorts the transmitted signal befores it reaches the receiver. The receiver ”task” is to figure out what signal was transmitted Turn the received signal in understandable information. S88-4221 Seminar

Introduction Intersymbol Interference (ISI) Noise ISI Noise Channel desired signal noise S88-4221 Seminar

Introduction Equalizer The purpose of an equalizer is to reduce the ISI as much as possible to maximize the probability of correct decisions Noise Channel Equalizer S88-4221 Seminar

Linear Equalizers The current and the past values of the received signal are linearly weigthed by equalizer coefficients and summed to produce the output. The ISI can be completely removed, without taking in consideration the resultanting noise enhacement  Zero forcing equalizer. A substantial increment of the noise power is created using ZF equalizer. S88-4221 Seminar

Linear Equalizers Mean-Square Error equalizer From the point-of-view of minimizing error probability, it is adventageous to allow some residual ISI if this can reduce the noise power. The MSE criterion attempts to minimize the total error between the slicer input and the transmitted data symbol. Transmit signal Power noise S88-4221 Seminar

Decision-Feedback Equalizers Simple nonlinear equalizer which is particulary useful for channel with severe amplitude distortion. DFE uses desicion feedback to cancel the interferfence from symbols which have already have been detected. The basic idea is that if the values of the symbols already detected are known (past decisions are assumed correct), then the ISI contributed by these symbols can be canceled exactly. S88-4221 Seminar

Decision-Feedback Equalizers Decision feedback equalizer structure The forward and feedback coefficients may be adjusted simultaneously to minimize the MSE. Feed back filter (FBF) Input Output Feed forward filter (FFF) + + Symbol decision Adjustment of filter coefficients S88-4221 Seminar

Adaptive Equalization The object is to adapt the coefficients to minimize the noise and intersymbol interference (depending on the type of equalizer) at the output. The adaptation of the equalizer is driven by an error signal. The aim is to minimize: Error signal + Channel Equalizer S88-4221 Seminar

Adaptive Equalization There are two modes that adaptive equalizers work; Decision Directed Mode: The receiver decisions are used to generate the error signal. Decision directed equalizer adjustment is effective in tracking slow variations in the channel response. However, this approach is not effective during initial acqusition . Training Mode: To make equalizer suitable in the initial acqusition duration, a training signal is needed. In this mode of operation, the transmitter generates a data symbol sequence known to the receiver. Once an agreed time has elapsed, the slicer output is used as a training signal and the actual data transmission begins. S88-4221 Seminar

Stochastic gradient algorithm The main idea is to minimize the mean square error between the output of the equalizer, and the transmitted signal. Since the number of samples that the receiver observe is finite, mean square is calculated by using time averages instead of ensemble averages. The resulting adaptation algorithm becomes; Error signal Received signal S88-4221 Seminar

Stochastic gradient algorithm Error signal LINEAR EQUALIZER Trainning mode Decision directed mode + Channel Equalizer S88-4221 Seminar

Decision-Feedback Equalizers Decision feedback equalizer structure The forward and feedback coefficients may be adjusted simultaneously to minimize the MSE. Feed forward C(z) Feedback F(z) Adjustment of filter coefficients Output + Symbol decision Input S88-4221 Seminar

Decision-Feedback Equalizers Feed forward C(z) Feedback F(z) Adjustment of filter coefficients Output + Symbol decision Input S88-4221 Seminar

Evaluation 1 Linear equalizer LMS Wiener solution Scenarios Channel 1 Channel 2 ( Time varying channel) S88-4221 Seminar

Evaluation 1- Linear Equalizer Static Channel h = [0.2, -0.15, 1.0, 0.21, 0.03] Lf=5 Delay=4 SNR=30dB S88-4221 Seminar

Evaluation 1- Linear Equalizer Static Channel h = [0.2, -0.15, 1.0, 0.21, 0.03] Lf=12 Delay=11 SNR=30dB S88-4221 Seminar

Evaluation 1 - Linear Equalizer Time varying channel Rayleigh 5 taps, fd=10 Hz , Ts=0.8us Lf=8 , mu=0.1 Delay=7 SNR=30dB S88-4221 Seminar

Evaluation 1 - Linear Equalizer Time varying channel Rayleigh 5 taps, fd=80 Hz , Ts=0.8us Lf=8 , mu=0.1 Delay=7 SNR=30dB S88-4221 Seminar

Evaluation 2 Desicion feedback equalizer LMS Decision direct mode and trainning mode Scenarios Channel 1 h = [0.2, -0.15, 1.0, 0.21, 0.03] Channel 2 h = [0.2, -0.35, 1.0, 0.51, 0.03] S88-4221 Seminar

Evaluation 2 Decision Feedback equalizer (static channel) Channel 2 Severe ISI Channel 1 S88-4221 Seminar

Evaluation 3 Decision Feedback equalizer Rayleigh 5 taps, fd=20 Hz , Ts=0.8us Lf=8 , mu=0.015 ,Lfeed=5 Delay=7 SNR=30dB S88-4221 Seminar

Evaluation 3 Decision Feedback equalizer Rayleigh 5 taps, fd=80 Hz , Ts=0.8us Lf=8 , mu=0.015 ,Lfeed=5 Delay=7 SNR=30dB S88-4221 Seminar

Conclusions Adaptive equalizer is an essential component of communication systems. Low complexity implementation with a good performance in channel with low levels of ISI is obtained using linear equalizers. In case of channels with severe ISI, DFE is the best option. S88-4221 Seminar