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- 1/16 -
Instructor : Junil Ahn and Jaewook Kang
At CSNL-GIST
E-mail: jwkkang@gist.ac.kr
2011, Mar. 11th~ Apr. 8th
A Simple Communication System
Design Lab with MATLAB Simulink
- Syllabus
- 2/16 -
PurposesPurposes
v 1) To understand how a basic communication system works.
v 2) To know how to use MATLAB Simulink to implement
communication systems.
v 3) To train your communication signal processing skill.
- 3/16 -
SchedulesSchedules
Place: IC203
Weeks Time Hour Instructor
1 week
Lab. #0
3.11
(13:00~
16:00)
3
- Overview of Development with Simulink
- QPSK Model with AWGN Channel/ Rayleigh Fading
Channel
- Development Example: Interference Cancellation for Satellite Communi
Junil Ahn
2 weeks
Lab. #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
implementation
Jaewook Kang
3 weeks
Lab. #2
3.25
(13:00~
16:00)
3
- QAM mapper and demammper
- Upsampling and Downsampling
Jaewook Kang
4 weeks
Lab. #3
4.1
(13:00~
16:00)
3
- PSF and Matched filter design
- Phase splitter
Jaewook Kang
5 weeks
Lab. #4
4.8
(13:00~
16:00)
3
- Up conversion and down conversion
- BER evaluation
Jaewook Kang
- 4/16 -
Instructor : Jaewook Kang
At CSNL-GIST
E-mail: jwkkang@gist.ac.kr
2011, Mar. 18th
A Simple Communication System Design
Lab with MATLAB Simulink
- Lab #1: - Introduction
- How to implement S-function blocks
- Convolutional-Interleaver block implementation
- 5/16 -
Properties of SimulinkProperties of Simulink
v 1) Schematic based language.
v 2) Simulink process signal/data dynamically like hardware.
v 3) Provide various kind of toolsets for the programming (Each is not
free).
v 4) Simulink can immediately generate HDL codes for
implementations.
v 5) Compatible with M-code, C/C++ as S- function.
- 6/16 -
Order of today’s proceedingOrder of today’s proceeding
v An example: A conventional QAM system (10 min)
v Preliminary : A (7,4) Hamming coded QPSK system using the
communi. blockset ( 1 hour )
§ How to use scope blocks ? (scope, scatter plot, and spectrum scope)
§ To understand signal type and framing
§ How to deal with the simulink using M-file.
v Our target system (15 min)
v Lab #1: Convolutional interleaver block implementation (2 hours)
§ Why interleaver ?
§ Operation of Convolutional interleaver
§ How to use S-function ?
- 7/16 -
Conventional PAM/QAM transmission systemsConventional PAM/QAM transmission systems
vTransmitter part
vReceiver part
The figure is borrowed
from Konkon univ.
- 8/16 -
An exampleAn example
v Basic communication system using the Simulink blockset
v Let’s run the simulink !
- 9/16 -
Before starting..Before starting..
vMex setup
- 10/16 -
Before starting..Before starting..
- 11/16 -
Preliminary (1/12)Preliminary (1/12)
vUseful hot keys
§ R: magnifying
§ F: focusing
§ V: reducing
§ Crtl-R: rotate block
§ Ctrl-I: filp blcok
- 12/16 -
Preliminary (2/12)Preliminary (2/12)
v A (7,4) Hamming coded QPSK system Implementation
using the given communi. Blockset
§ 1) Let’s compose the simplest testbench of QPSK system first.
Let’s make it !!
- 13/16 -
Preliminary (3/12)Preliminary (3/12)
v Some notice when you make it
1) At random integer block
§ Determine “M-ary number” according to the
system specification.
§ In this case, QPSK àM= 4 à 2^BitperSym
§ Check “Frame-based output”
2) Error rate calculation block
§ Receive delay: Total latency in the
received signal via signal processing
§ Check a condition to stop the simulation
§ Select output data as “Port”
§ Target number of error =200 is enough
- 14/16 -
Preliminary (4/12)Preliminary (4/12)
v Some notice when you make it
3) Discrete- time scatter plot scope block
§ Specify the block setup
according to your taste.
- 15/16 -
Preliminary (5/12)Preliminary (5/12)
vLet’ see the signal flow
§ At the scope block: integer from {0,1,2,3} are randomly generated.
§ The QAM modulator maps those integer to symbols in the constellation.
§ After AWGN channel, the points are scattered.
Mapping
AWGN
- 16/16 -
Preliminary (6/12)Preliminary (6/12)
v Let’s add (7,4)-Hamming code to the testbench
§ Change the source block to “Bernoulli Binary block”
§ Add a pair of Hamming en- and de-coder.
§ Change to frame-based processing
§ Change AWGN block and QAM block pair setup
- 17/16 -
Preliminary (7/12)Preliminary (7/12)
v With respect to (7,4) Hamming codes
§ A linear block channel codes
§ Perfect codes
§ The codes can correct 2^4-1 kinds of error pattern in codeword.
§ The codes have all 7 error patterns on Hamming sphere of radius t=1.
§ No performance loss even with bounded distance decoder.
§ The input message bit is k=4 and length of the codewords is n=7.
(6,3) linear block codes (7,4) Hamming codes
t=1 Hamming sphere
t=2 Hamming sphere
Cannot be corrected
Using t=1 bounded
Distance decoder
C C
- 18/16 -
Preliminary (8/12)Preliminary (8/12)
v Frame-based processing
§ Simulink supports the frame-based processing which makes
simulations faster as increasing the signal dimension.
§ Ex) <1x1> à <n X 1>
§ Some blocks only support the frame-based processing.
§ By using “buffer” and “un-buffer” block, we can control the dimension
size of the flowing signal.
Block Block
< Sample-based proc. > < Frame-based proc. >
- 19/16 -
Preliminary (9/12)Preliminary (9/12)
v Frame-based processing
§ Check “frame-based outputs” in the source block and specify the number of the
sample per a frame.
v Change the SNR expression in AWGN block based on
v Change the input and output type of the QAM block pair to “BIT”.
2logb c
o
E R MS
N N W
=
- 20/16 -
Preliminary (9/12)Preliminary (9/12)
v Buffer and unbuffer block
§ Very important block to adjust rate in the frame-based processing.
§ Let Mi denote the size of input and Mo denote the size of output.
§ 1) Buffer block
Ø If Mi < Mo the latency is Mo.
Ø In case of Mi > Mo
– 1) When Mi is mutiple of Mo à No latency
– 2) otherwise, à the latency is Mo.
§ 2) Un-buffer block
Ø No latency
§ But, sometime the latency calculation is not useful.
§ In such case, check the latency directly using scope block.
- 21/16 -
Preliminary (10/12)Preliminary (10/12)
v Draw BER curve using Simulink with M-file
§ Let’s make a comparison of the coded and uncoded system.
§ 1) Use simout block to output the result to workspace.
§ 2) Put all parameter using variable in workspace.
- 22/16 -
- 23/16 -
Preliminary (12/12)Preliminary (12/12)
v Result
0 1 2 3 4 5 6 7 8 9
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
EbNo
BER
Curve
Coded(7,4)Hamming-4QAM
Uncoded-4QAM
- 24/16 -
Our target systemOur target system
vTx part
vRx part
Tx Source Interleaver
QAM
Mapper
PSF X
NCO
↑4
Phase
Splitter
Matched
filter
QAM
DemapperX
NCO
↓4
De-
Interleaver
Rx Source
:Real
:Complex
- 25/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
v Why do we employ interleaver ?
§ Error usually occurs in burst manner.
§ Conventionally, channel coder is designed against a random and independent
error.
§ Interleaver is introduced to scatter the burst or packetized data in a time domain.
§ Deinterleaved data show almost random and independent errors.
§ Channel Decoder can handle such error.
v Two type of interleanver
§ Block interleaver:
Ø Simple concept, easy to implement.
Ø Needs more memory, and cause a large latency
§ Convolutional interleaver:
Ø Require half memory of block interleaver, causing a small memory.
Ø Most communication system employs this for its attractive features.
- 26/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
v Why do we employ interleaver ?
§ Error usually occurs in burst manner.
§ Conventionally, channel coder is designed against a random and independent
error.
§ Interleaver is introduced to scatter the burst or packetized data in a time domain.
§ Deinterleaved data show almost random and independent errors.
§ Channel Decoder can handle such error.
v Two type of interleanver
§ Block interleaver:
Ø Simple concept, easy to implement.
Ø Needs more memory, and cause a large latency
§ Convolutional interleaver:
Ø Require half memory of block interleaver, causing a small memory.
Ø Most communication system employs this for its attractive features.
- 27/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
v Example of convolutional Interleaver/Deinterleaver operation
Block
0 0 2 5 0 0 0 18 7 6 5 4 3 2 1… …
10 10
10
- 28/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
v Specification of Conv.-interleaver
§ The Number of row : R
§ Interleaver length: L
§ The latency through inter and de-interleaver:
§ The required memory for each block :
L=2
R=4
< Interleaver side > < De-interleaver side >
2
( )R R L- ´
2
( )
2
R R L- ´
- 29/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
v Testbench using simulink blocks
§ Ex) R=4, L=1
§ Latency: 2
(4 4) 1 12- ´ =
Latnecy:12
- 30/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
vS-function builder block
§ Let’s make R=4, L=1 convolutional interleaver.
§ The size of the required buffer:
2
( ) (16 4) 2
6
2 2
R R L- ´ - ´
= =
The Size of the memory
And the initial condition
- 31/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
vS-function builder block
§ Date properties
R
L
- 32/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
vS-function builder block
§ Output – specify what the current output data is in C language
- 33/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
vS-function builder block
§ Discrete Update – Describe operation for memory inside the block, such as
buffer shift at each time instance.
§ Array wrt. the memory denoted by xD[]
- 34/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
vSimulation
§ You can check your block using interleaving block given by MATLAB
simulink.
- 35/16 -
Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation
v What about de-interleaver block ?
§ Implementation of de-inleaver block is assignment of this week.
§ I’ll provide the code at next lecture.
§ It’s very similar with conv-inverleaver block.
§ Make it by yourself !!!
§ Does it work correctly ? Check by yourself like the below figure.
- 36/16 -
Wrapping upWrapping up
v How to implement a simple coded QAM system using the given
blocks
v Learned about way to use some block in simulink
§ Scope, Digital scatter, Random sources, AWGN, error rate calculation, Buffer etc.
v How to simulate BER performance with M-file in simulink.
v How to use S-function builder block
v Convolutional interleaving and de interleaving block pair.
- 37/16 -
Next weekNext week
v I’ll provide the source code of de-interleaving block
v Please do the assignment to be good at S-function.
Weeks Time Hour Instructor
1 week
Lab. #0
3.11
(13:00~
16:00)
3
- Overview of Development with Simulink
1) QPSK Model with AWGN Channel/ Rayleigh Fading
Channel
2) Basic OFDM
3) Development Example: Interference Cancellation for Satellite Communi.
Junil Ahn
2 weeks
Lab. #1
3.18
(13:00~
16:00)
3
- Introduction
- How to use Simulink with interleaver
implementation
Jaewook Kang
3 weeks
Lab. #2
3.25
(13:00~
16:00)
3
- QAM mapper and demammper
- Upsampling and Downsampling
Jaewook Kang
4 weeks
Lab. #3
4.1
(13:00~
16:00)
3
- PSF and Matched filter design
- Phase splitter
Jaewook Kang
5 weeks
Lab. #4
4.8
(13:00~
16:00)
3
- Up conversion and down conversion
- BER evaluation
Jaewook Kang

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A Simple Communication System Design Lab #1 with MATLAB Simulink

  • 1. - 1/16 - Instructor : Junil Ahn and Jaewook Kang At CSNL-GIST E-mail: jwkkang@gist.ac.kr 2011, Mar. 11th~ Apr. 8th A Simple Communication System Design Lab with MATLAB Simulink - Syllabus
  • 2. - 2/16 - PurposesPurposes v 1) To understand how a basic communication system works. v 2) To know how to use MATLAB Simulink to implement communication systems. v 3) To train your communication signal processing skill.
  • 3. - 3/16 - SchedulesSchedules Place: IC203 Weeks Time Hour Instructor 1 week Lab. #0 3.11 (13:00~ 16:00) 3 - Overview of Development with Simulink - QPSK Model with AWGN Channel/ Rayleigh Fading Channel - Development Example: Interference Cancellation for Satellite Communi Junil Ahn 2 weeks Lab. #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 implementation Jaewook Kang 3 weeks Lab. #2 3.25 (13:00~ 16:00) 3 - QAM mapper and demammper - Upsampling and Downsampling Jaewook Kang 4 weeks Lab. #3 4.1 (13:00~ 16:00) 3 - PSF and Matched filter design - Phase splitter Jaewook Kang 5 weeks Lab. #4 4.8 (13:00~ 16:00) 3 - Up conversion and down conversion - BER evaluation Jaewook Kang
  • 4. - 4/16 - Instructor : Jaewook Kang At CSNL-GIST E-mail: jwkkang@gist.ac.kr 2011, Mar. 18th A Simple Communication System Design Lab with MATLAB Simulink - Lab #1: - Introduction - How to implement S-function blocks - Convolutional-Interleaver block implementation
  • 5. - 5/16 - Properties of SimulinkProperties of Simulink v 1) Schematic based language. v 2) Simulink process signal/data dynamically like hardware. v 3) Provide various kind of toolsets for the programming (Each is not free). v 4) Simulink can immediately generate HDL codes for implementations. v 5) Compatible with M-code, C/C++ as S- function.
  • 6. - 6/16 - Order of today’s proceedingOrder of today’s proceeding v An example: A conventional QAM system (10 min) v Preliminary : A (7,4) Hamming coded QPSK system using the communi. blockset ( 1 hour ) § How to use scope blocks ? (scope, scatter plot, and spectrum scope) § To understand signal type and framing § How to deal with the simulink using M-file. v Our target system (15 min) v Lab #1: Convolutional interleaver block implementation (2 hours) § Why interleaver ? § Operation of Convolutional interleaver § How to use S-function ?
  • 7. - 7/16 - Conventional PAM/QAM transmission systemsConventional PAM/QAM transmission systems vTransmitter part vReceiver part The figure is borrowed from Konkon univ.
  • 8. - 8/16 - An exampleAn example v Basic communication system using the Simulink blockset v Let’s run the simulink !
  • 9. - 9/16 - Before starting..Before starting.. vMex setup
  • 10. - 10/16 - Before starting..Before starting..
  • 11. - 11/16 - Preliminary (1/12)Preliminary (1/12) vUseful hot keys § R: magnifying § F: focusing § V: reducing § Crtl-R: rotate block § Ctrl-I: filp blcok
  • 12. - 12/16 - Preliminary (2/12)Preliminary (2/12) v A (7,4) Hamming coded QPSK system Implementation using the given communi. Blockset § 1) Let’s compose the simplest testbench of QPSK system first. Let’s make it !!
  • 13. - 13/16 - Preliminary (3/12)Preliminary (3/12) v Some notice when you make it 1) At random integer block § Determine “M-ary number” according to the system specification. § In this case, QPSK àM= 4 à 2^BitperSym § Check “Frame-based output” 2) Error rate calculation block § Receive delay: Total latency in the received signal via signal processing § Check a condition to stop the simulation § Select output data as “Port” § Target number of error =200 is enough
  • 14. - 14/16 - Preliminary (4/12)Preliminary (4/12) v Some notice when you make it 3) Discrete- time scatter plot scope block § Specify the block setup according to your taste.
  • 15. - 15/16 - Preliminary (5/12)Preliminary (5/12) vLet’ see the signal flow § At the scope block: integer from {0,1,2,3} are randomly generated. § The QAM modulator maps those integer to symbols in the constellation. § After AWGN channel, the points are scattered. Mapping AWGN
  • 16. - 16/16 - Preliminary (6/12)Preliminary (6/12) v Let’s add (7,4)-Hamming code to the testbench § Change the source block to “Bernoulli Binary block” § Add a pair of Hamming en- and de-coder. § Change to frame-based processing § Change AWGN block and QAM block pair setup
  • 17. - 17/16 - Preliminary (7/12)Preliminary (7/12) v With respect to (7,4) Hamming codes § A linear block channel codes § Perfect codes § The codes can correct 2^4-1 kinds of error pattern in codeword. § The codes have all 7 error patterns on Hamming sphere of radius t=1. § No performance loss even with bounded distance decoder. § The input message bit is k=4 and length of the codewords is n=7. (6,3) linear block codes (7,4) Hamming codes t=1 Hamming sphere t=2 Hamming sphere Cannot be corrected Using t=1 bounded Distance decoder C C
  • 18. - 18/16 - Preliminary (8/12)Preliminary (8/12) v Frame-based processing § Simulink supports the frame-based processing which makes simulations faster as increasing the signal dimension. § Ex) <1x1> à <n X 1> § Some blocks only support the frame-based processing. § By using “buffer” and “un-buffer” block, we can control the dimension size of the flowing signal. Block Block < Sample-based proc. > < Frame-based proc. >
  • 19. - 19/16 - Preliminary (9/12)Preliminary (9/12) v Frame-based processing § Check “frame-based outputs” in the source block and specify the number of the sample per a frame. v Change the SNR expression in AWGN block based on v Change the input and output type of the QAM block pair to “BIT”. 2logb c o E R MS N N W =
  • 20. - 20/16 - Preliminary (9/12)Preliminary (9/12) v Buffer and unbuffer block § Very important block to adjust rate in the frame-based processing. § Let Mi denote the size of input and Mo denote the size of output. § 1) Buffer block Ø If Mi < Mo the latency is Mo. Ø In case of Mi > Mo – 1) When Mi is mutiple of Mo à No latency – 2) otherwise, à the latency is Mo. § 2) Un-buffer block Ø No latency § But, sometime the latency calculation is not useful. § In such case, check the latency directly using scope block.
  • 21. - 21/16 - Preliminary (10/12)Preliminary (10/12) v Draw BER curve using Simulink with M-file § Let’s make a comparison of the coded and uncoded system. § 1) Use simout block to output the result to workspace. § 2) Put all parameter using variable in workspace.
  • 23. - 23/16 - Preliminary (12/12)Preliminary (12/12) v Result 0 1 2 3 4 5 6 7 8 9 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 EbNo BER Curve Coded(7,4)Hamming-4QAM Uncoded-4QAM
  • 24. - 24/16 - Our target systemOur target system vTx part vRx part Tx Source Interleaver QAM Mapper PSF X NCO ↑4 Phase Splitter Matched filter QAM DemapperX NCO ↓4 De- Interleaver Rx Source :Real :Complex
  • 25. - 25/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation v Why do we employ interleaver ? § Error usually occurs in burst manner. § Conventionally, channel coder is designed against a random and independent error. § Interleaver is introduced to scatter the burst or packetized data in a time domain. § Deinterleaved data show almost random and independent errors. § Channel Decoder can handle such error. v Two type of interleanver § Block interleaver: Ø Simple concept, easy to implement. Ø Needs more memory, and cause a large latency § Convolutional interleaver: Ø Require half memory of block interleaver, causing a small memory. Ø Most communication system employs this for its attractive features.
  • 26. - 26/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation v Why do we employ interleaver ? § Error usually occurs in burst manner. § Conventionally, channel coder is designed against a random and independent error. § Interleaver is introduced to scatter the burst or packetized data in a time domain. § Deinterleaved data show almost random and independent errors. § Channel Decoder can handle such error. v Two type of interleanver § Block interleaver: Ø Simple concept, easy to implement. Ø Needs more memory, and cause a large latency § Convolutional interleaver: Ø Require half memory of block interleaver, causing a small memory. Ø Most communication system employs this for its attractive features.
  • 27. - 27/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation v Example of convolutional Interleaver/Deinterleaver operation Block 0 0 2 5 0 0 0 18 7 6 5 4 3 2 1… … 10 10 10
  • 28. - 28/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation v Specification of Conv.-interleaver § The Number of row : R § Interleaver length: L § The latency through inter and de-interleaver: § The required memory for each block : L=2 R=4 < Interleaver side > < De-interleaver side > 2 ( )R R L- ´ 2 ( ) 2 R R L- ´
  • 29. - 29/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation v Testbench using simulink blocks § Ex) R=4, L=1 § Latency: 2 (4 4) 1 12- ´ = Latnecy:12
  • 30. - 30/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation vS-function builder block § Let’s make R=4, L=1 convolutional interleaver. § The size of the required buffer: 2 ( ) (16 4) 2 6 2 2 R R L- ´ - ´ = = The Size of the memory And the initial condition
  • 31. - 31/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation vS-function builder block § Date properties R L
  • 32. - 32/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation vS-function builder block § Output – specify what the current output data is in C language
  • 33. - 33/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation vS-function builder block § Discrete Update – Describe operation for memory inside the block, such as buffer shift at each time instance. § Array wrt. the memory denoted by xD[]
  • 34. - 34/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation vSimulation § You can check your block using interleaving block given by MATLAB simulink.
  • 35. - 35/16 - Lab #1: Convolutional interleaver block implementationLab #1: Convolutional interleaver block implementation v What about de-interleaver block ? § Implementation of de-inleaver block is assignment of this week. § I’ll provide the code at next lecture. § It’s very similar with conv-inverleaver block. § Make it by yourself !!! § Does it work correctly ? Check by yourself like the below figure.
  • 36. - 36/16 - Wrapping upWrapping up v How to implement a simple coded QAM system using the given blocks v Learned about way to use some block in simulink § Scope, Digital scatter, Random sources, AWGN, error rate calculation, Buffer etc. v How to simulate BER performance with M-file in simulink. v How to use S-function builder block v Convolutional interleaving and de interleaving block pair.
  • 37. - 37/16 - Next weekNext week v I’ll provide the source code of de-interleaving block v Please do the assignment to be good at S-function. Weeks Time Hour Instructor 1 week Lab. #0 3.11 (13:00~ 16:00) 3 - Overview of Development with Simulink 1) QPSK Model with AWGN Channel/ Rayleigh Fading Channel 2) Basic OFDM 3) Development Example: Interference Cancellation for Satellite Communi. Junil Ahn 2 weeks Lab. #1 3.18 (13:00~ 16:00) 3 - Introduction - How to use Simulink with interleaver implementation Jaewook Kang 3 weeks Lab. #2 3.25 (13:00~ 16:00) 3 - QAM mapper and demammper - Upsampling and Downsampling Jaewook Kang 4 weeks Lab. #3 4.1 (13:00~ 16:00) 3 - PSF and Matched filter design - Phase splitter Jaewook Kang 5 weeks Lab. #4 4.8 (13:00~ 16:00) 3 - Up conversion and down conversion - BER evaluation Jaewook Kang