A Simple Communication System Design Lab #3 with MATLAB Simulink

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Instructor : Jaewook KangAt CSNL-GISTE-mail: [email protected], Apr. 1st

A Simple Communication System Design Lab with MATLAB Simulink

- Lab #3: - Phase splitter- up conversion and down conversion

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Next time…

v Place: IC203

Weeks Time Hour Instructor

1 weekLab. #0 3.11

(13:00~16:00)

3- Overview of Development with Simulink

- QPSK Model with AWGN Channel/ Rayleigh FadingChannel

- Development Example: Interference Cancellation for Satellite CommuniJunil Ahn

2 weeksLab. #1

3.18(13:00~14:20)

1.5 - Basic OFDM Junil Ahn

3.18(14:30~16:00)

1.5- Introduction - How to use Simulink with interleaver

implementationJaewook Kang

3 weeksLab. #2

3.25(13:00~16:00)

3- How to use S-function builder- PSF and Matched filter design- Concept of upsampling and downsampling

Jaewook Kang

4 weeksLab. #3

4.1(13:00~16:00)

3 - Phase splitter - Up conversion and down conversion Jaewook Kang

5 weeksLab. #4

4.8(13:00~16:00)

3 - How to make subsystem- Channel implementation using Jaewook Kang

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Reviewv Q1) Why ?

v Q2) What is happen in freq. domain if sampling rate is up ?

v Q3) What about down case?

v Q4)Why PSF ?

v Q5) calculate bandwidth when Rsym=1 sym/sec and L=4.

dw p£

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Today’s main pointsv Understand up/down sampling

v Understand characteristic of complex exponential signal

v Learn about Hilbert transform

v Implement Phase splitter using FIR filter

v Understand up/down conversion

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Our target systemvTx part

vRx part

Tx Source Interleaver QAMMapper PSF X

NCO

↑4

PhaseSplitter

Matchedfilter

QAMDemapperX

NCO

↓4 De-Interleaver Rx Source

:Real:Complex

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up conversionvWhy upconvert to IF ?

§ 1) To reduce the work of D/A and A/D convertor.

§ 2) To bring the signal only using Inphase channel.

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up conversion§ As a result, rotational transform of basis in s plane

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up conversion

Re[ ( )] cos(2 ) sin(2 )

Im [ ( )] sin(2 ) cos(2 )shift shift

shift shift

s t x f t y f tag s t x f t y f t

p p

p p

= -

= +

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up conversion§ When baseband is up-converted to Fs/2

Re[ ( )] cos(2 )shifts t x f tp=

cos(2 ) sin(2 ) cos( )2 2s s

s sf fx nT y nT x np p p= - =

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up conversion§ NCO (Numerically Controlled Oscillator ) implementation

§ - Carrier frequency is determined by adjusting ‘k’§ In general k=4à Then, IF is pi/4§ - Thus, higher Fs should be required in order to up-convert

baseband into higher band

02s

shiftff< £ (s

shiftff kk

= ³ is positive number and k 2.0)

2

( ) ( ) ( )

( ) cos(2 ) sin(2 )

1cos(2 ) cos(2 ) cos(2 )

shift s

s s sj f nT

s shift s shift s

sshift s

s

s nT g nT c nT

c nT e f nT j f nTf nf nT nk f k

p p p

p p p

=

= = +

= =

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up conversion

§ The relationship between up-sampling rate and up-conversion

§ In this case, Fs is sampling rate of baseband signal, g(t)§ Usually g(t) is the output of PSF, so Fs is up-sampling rate

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Phase splitterv Purpose of the phase splitter

§ Since Tx only transmit real part of signals, we have to recover the full complex signal from real part of the received signal.

§ When using FIR filter to implement Phase splitter, we have to consider the delay of the filter (N-1)/2.

(N- 1)/2 sampledelay

N tap Hilbert Transform FIR filter

Xr(t) Xr(t)

Xi(t)

Xc(t)

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Phase splitterv Basic of complex exponential

§ What is shape of ?§ Can you draw Xc(t) in 3D domain ?

Ø (Hint: real imag, and time axis)

02c

0

0 fourier transform

x ( )( ) cos(2 )( ) sin(2 )

( ) ( ) ( ) ( ) ( ) ( )

j f t

r

i

c r i c r i

Let t Aex t A f tx t A f t

x t x t jx t X f X f jX f

p

pp

===

= + ¾¾¾¾¾® = +

02cx ( )

j f tt Ae p=

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§ As t increase, (+) freq. component rotates with CCW and (-) freq. component rotates with CW.

§ Sine and cosine is the same signal without phase. § Real part : even symmetric§ Imaginary part: odd symmetric

Imag

- f

Re

Acos(2* pi* f0* t)

- f0

f0

Imag

- f

Re

Asin(2* pi* f0* t)

- f0

f0

0

( 0)cos(2 0)rx tA f t Ap

= == = 0

( 0)sin(2 0) 0ix tA f tp

= =

= =

Conjugate symmetric

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§ Why cosine and sine are real ?Ø Imaginary component of (-) and (+) freq. are cancelled each other.

§ Such a fact implies that real and imag components co-exists in real periodic signal.

Imag

- f

Re

Acos(2* pi* f0* t)

- f0

f0

Imag

- f

Re

Asin(2* pi* f0* t)

- f0

f0

0

( 0)cos(2 0)rx tA f t Ap

= == = 0

( 0)sin(2 0) 0ix tA f tp

= =

= =

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§ Phase: The angle between real and imag component.§ Magnitude: The sum of real part of two freq component.

Ø According to time, the phase and magnitude is changing.

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§ Complex exp. signal has only one frequency component such that imaginary part exists.

§ How to extract real/imaginary part of Xc(t) ?

02cx ( )

j f tt Ae p=

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Phase splitterv Hilbert transform

§ Find imaginary part of Xc(t) from real part only when Xc(t) is complex exponential. Imag

- f

Re

- f0

f002j f tAe p

Imag

- f

Re

Acos(2* pi* f0* t)

- f0

f0

Re[]

Imag

- f

Re

Asin(2* pi* f0* t)

- f0

f0

Hilbert TR

+

Imag

- f

Re

- f0

f002j f tAe p

Xc Xr

Xi_hatXc_hat

X

j

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Phase splitterv Transfer function of Hilbert transform

§ The transfer function have sign shape on imaginary axis.

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Phase splitterv Impulse response of Hilbert transform

§ The discrete form can be obtained by sampling such that

22

2

0 2 220

2

( ) ( )

1 [1 cos( )]

s

s

s

s

fft

f

fft ft

f

s

h t H f e df

je df je df

f tt

p

p p

pp

-

-

=

= + -

= -

ò

ò ò

:apply iFT to H(f) of HF

1 [1 cos( )]nn

pp

-h(n)=

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Phase splitterv Implementation of Hilbert transform using FIR filter

§ 1) Determine the number of taps, NØ The larger, the nicer. But it cause longer delay.Ø The delay should be multiple of up sampling rate for synchronization.Ø Let N

§ 2) Generate h(n) : N=25 à delay =12§ 3) put h(n) into FIR filter as coefficient.

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Phase splitterv allclearv fs=1;%fs musthave'1'togetnomalized magnitude

responsev TapNum=73;%thenumberofFIRfilterv n=0:(TapNum-1);v delay=(TapNum-1)/2%thedelayofFIRfiltervv %generateHilberttransformImpulseresponsev ht=fs./(pi*(n-delay)).*[1-cos(pi*(n-delay))];v %alternateformv %H=2*sin(pi*(n-10)/2).^2./(pi*(n-10))vv ht(delay+1)=0;%//byL'Hopital's rulevv %Impulseresponseofhilbert tansform FIRfilterv figure(1);v stem(ht);v xlabel('Xaxis-Time-index(n)','fontsize',12);v ylabel('Yaxis-Magnitudeofh(n)','fontsize',12);v title('\bf{ImpulseresponseofHilberttansform,

h(n)}','fontsize',12);v %obtainthemagnituderesponseofHilberttransformv Hf=abs(fft(ht));

v %Magnituderesponseofhilbert transformFIRfilter

v figure(2);v stem(Hf);v xlabel('Xaxis-Frequency-index(m)','fontsize',12);v ylabel('Yaxis-Magnitude,|H(m)|','fontsize',12);v title('\bf{MagnituderesponseofHibert

transform,|H(m)|}','fontsize',12);vv Hf(TapNum-delay+1:TapNum)=Hf(TapNum-

delay+1:TapNum).*-1;vv figure(3);v stem(Hf);v xlabel('Xaxis-frequency-index(m)','fontsize',12);v ylabel('Yaxis-imaginaryaxis,jH(m)

','fontsize',12);v title('\bf{Hilberttransforminfrequency

domain}','fontsize',12);

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Phase splitterv Implementation of Hilbert transform using FIR filter

§ 1) Determine the number of taps, NØ The larger, the nicer. But it cause longer delay.Ø The delay should be multiple of up sampling rate for synchronization.Ø Let N

§ 2) Generate h(n) : N=25 à delay =12§ 3) put h(n) into FIR filter as coefficient.

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Next time…

v Place: IC203

Weeks Time Hour Instructor

1 weekLab. #0 3.11

(13:00~16:00)

3- Overview of Development with Simulink

- QPSK Model with AWGN Channel/ Rayleigh FadingChannel

- Development Example: Interference Cancellation for Satellite CommuniJunil Ahn

2 weeksLab. #1

3.18(13:00~14:20)

1.5 - Basic OFDM Junil Ahn

3.18(14:30~16:00)

1.5- Introduction - How to use Simulink with interleaver

implementationJaewook Kang

3 weeksLab. #2

3.25(13:00~16:00)

3- How to use S-function builder- PSF and Matched filter design- Concept of upsampling and downsampling

Jaewook Kang

4 weeksLab. #3

4.1(13:00~16:00)

3 - Phase splitter - Up conversion and down conversion Jaewook Kang

5 weeksLab. #4

4.8(13:00~16:00)

3 - How to make subsystem- Channel implementation using Jaewook Kang

A Simple Communication System Design Lab #3 with MATLAB Simulink

Engineering