siskom2 matched filter

7/26/2019 Siskom2 Matched Filter

1/17

Modul #02

TE3223TE3223

SISTEM KOMUNIKASISISTEM KOMUNIKASI 22

MATCHED FILTER

b Budi Praset aProgram Studi S1 Teknik Telekomunikasi

Jurusan Teknik Elektro - Sekolah Tin i Teknolo i Telkom

Bandung 2008


2/17

Today we are going to talk about:

ece ver s ruc ure

Demodulation (and sampling)

e ec on

First step for designing the receiver

atc e ter rece ver

Correlator receiver

space), an important tool to facilitate:

,Detection operations

2Modul 2 - Siskom 2 - Matched Filter


3/17

Demodulation and detection

FormatPulse

modulate

Bandpass

modulate

)(tsi)(tgiim

channelMi ,,1K=

M-ary modulation

)(thc

)(tn

transmitted symbol

estimated symbol

Ma or sources of errors:

Format Detect.

& sampleim )(tr)(Tz

Thermal noise (AWGN) disturbs the signal in an additive fashion (Additive)

is modeled by Gaussian random process (Gaussian Noise)

Inter-Symbol Interference (ISI) Due to the filtering effect of transmitter, channel and receiver,

symbols are smeared. 3Modul 2 - Siskom 2 - Matched Filter


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Example: Impact of the channel



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Example: Channel impact

)75.0(5.0)()( Tttthc =



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Receiver job:

Demodulation and sampling:

Waveform recovery and preparing the received

signal for detection: Improving the signal power to the noise power (SNR)

us ng ma c e er

Reducing ISI using equalizer

Detection:

received sample



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Receiver structure

Step 1 waveform to sample transformation Step 2 decision making

Demodulate & Sample Detect

Frequency

down-conversion

Receiving

filter

Equalizing

filter

Threshold

comparison)(tr

)(Tzim)(tz

For bandpass signals Compensation for

channel induced

ISI

Baseband pulse(possibly distored)

Sample

(test statistic)Baseband pulse

Received waveform



8/17

Baseband and bandpass

Bandpass model of detection process is

equivalent to baseband model because:

The received bandpass waveform is firsttransformed to a baseband waveform.

Equivalence theorem:

Performing bandpass linear signal processingo owe y e ero yn ng e s gna o e ase an ,

yields the same results as heterodying the bandpass

signal to the baseband, followed by a baseband linear

signal processing.



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Steps in designing the receiver

Find optimum solution for receiver designwith the following goals:

1. Maximize SNR2. Minimize ISI

eps n es gn: Model the received signal

.

First, we focus on designing a receiverwhich maximizes the SNR.



10/17

Design the receiver filter to

Model the received signal

)(thc)(tsi )(tr )()()()( tnthtstr ci +=

Simplify the model:

)(tnAWGN

Received signal in AWGN

)(tr)(tsiIdeal channels)()( tthc = )()()( tntstr i +=

AWGN



11/17

Matched filter receiver

Design the receiver filter such that the SNR is

maximized at the sam lin time when

)(thits ...1=

is transmitted.

Solution:

The optimum filter, is the Matched filter, given by

)()()( * tTsthth io t ==

which is the time-reversed and dela ed version of the con u ate of the

)2exp()()()( *

fTjfSfHfH iopt ==

transmitted signal

)(tsi )()( thth opt=

T0 t T0 t



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Example of matched filter

)()()( thtstz opti 2

A)(tsi )(thopt

T

A

T

A

)()()( thtt

2Atsi topt

T

A

T

A

T t T t T t0 2TT/2 3T/2T/2 TT/2

2

2TAAA



13/17

Properties of the matched filter

. signal as input is, except for a time delay factor, proportional to theESD of the input signal.

2

2. The output signal of a matched filter is proportional to a shiftedversion of the autocorrelation function of the input signal to which

exp =

e er s ma c e .

sss ERTzTtRtz === )0()()()(

. signal energy to the PSD of the white noise at the filter input.

ES s=

4. Two matching conditions in the matched-filtering operation:

2/0NN T

.

spectral amplitude matching that gives optimum SNR to the peak value.



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Correlator receiver

The matched filter output at the sampling

time T, can be realized as the correlator

output.

)()()( TrThTz opt

>

siskom2 matched filter

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