80-Matlab Digcomm Lab

8/19/2019 80-Matlab Digcomm Lab

1/40

Welcome to MATLAB DigComm LAB

1. Matlab Toutrial• http://www.math.utah.edu/lab/ms/matlab/matlab.h

tml#startig

!. LAB1 to LAB" : BA$C WA%&

'. L&CT()&: Comple* &*poetial +uctio• LAB, to LAB-

. Chael Modelig• LAB

". 0+DM modelig ad &rror )ate Measure• LAB to LAB11

,. )&20)T TA3

!41'/1!/1 !41' DigComm Lab 5+ire Tom Wada6

http://www.math.utah.edu/lab/ms/matlab/matlab.html#startinghttp://www.math.utah.edu/lab/ms/matlab/matlab.html#startinghttp://www.math.utah.edu/lab/ms/matlab/matlab.html#startinghttp://www.math.utah.edu/lab/ms/matlab/matlab.html#starting


2/40

LAB1 ： AM

• Write Amplitude Modulatio 5AM6 program

b7 MATLAB

• A 8 1 9 4."cos5!pi1t6

• ;c 8"uec7 ;s 8 144


3/40

LAB1 ： AM aswer

• 84:1444? @ 1441 poits

• ;c8"?

• ;s8144? @ amplig +re>uec7

• t 8 /;s? @ time ide*

• @ $2(T to Modulator

• A 8 1 9 4."cos5!pi1t6?

• @ 0(T2(T• * 8 A . si5!pi;ct6?

• @ +$()&

• ;igure516?

• subplot5!116?

• plot5A6?

•

subplot5!1!6?• plot5*6?



4/40

LAB!: AM Demodulatio

• (se LAB1 result * ad calculate 7 as each

* is s>uared.

• $; 7ou coect each pea o; 7 7ou ca rec

oEer origial A.



5/40

LAB! ： AM Demod aswer

• 84:1444? @ 1441 poits

• ;c8"?

• ;s8144? @ amplig +re>uec7


• @ $2(T to Modulator

• A 8 1 9 4."cos5!pi1t6?

• @ 0(T2(T• * 8 A . si5!pi;ct6?

• @@

• 7 8 * . *?

• @ +$()&

• ;igure5!6?

•

subplot5'116?• plot5A6?

• subplot5'1!6?

• plot5*6?

• subplot5'1'6?

• plot576?



6/40


7/40

LAB' ： pectrum aswer

• 81:1:4?

• * 8 F=eros51146 oes51146 =eros51146 o

es51146 =eros51146 oes51146 =eros511

46 oes51146G?

• ;igure5'6

• subplot5!116?

•

plot5*6?• a*is5F14H4." 1."G6?

• @@

• 7 8 ;;t5*6?

• subplot5!1!6?

• plot5abs5766?

• a*is5F14H14 "4G6?


Assume T 8 14 poits


8/40

LAB ： B23 waEe;orm

• Mae B23 waEe;orm as ;ollows


)2cos( φ π += ft A x

)2cos( ft A x π =

)2cos( π π += ft A x

Whe data84

Whe data81


9/40

LAB ： B23 aswer

• 84:'!?

• ;c8!?

• ;s8'!? @ amplig +re>uec7


• @ B23 waEe;orm

• *4 8 cos5!pi;ct6?

• *1 8 cos5!pi;ct 9 pi6?• @ +$()&

• ;igure5"6?

• subplot5!116?

• plot5*46?

• subplot5!1!6?

•

plot5*16?


4

5A4 I46851 46

5A1 I16

851 J6


10/40

LAB" ： K23 waEe;orm

• Mae K23 waEe;orm as ;ollows


)2cos( φ π += ft A x

)4/2cos( π π += ft A x

)4/32cos( π π += ft A x

)4/52cos( π π += ft A x)4/72cos( π π += ft A x

4

5A4 46

851 1J/65A1 16

851 'J/6

5A! !6

851 "J/65A! !6

851 -J/6


11/40

LAB" ： K23 aswer • 84:'!?

• ;c8!?



• @ K23 waEe;orm

• *4 8 cos5!pi;ct 9 1pi/6?

• *1 8 cos5!pi;ct 9 'pi/6?

• *! 8 cos5!pi;ct 9 "pi/6?• *' 8 cos5!pi;ct 9 -pi/6?

• @ +$()&

• ;igure5"6?

• subplot5116?

• plot5*46?

•

subplot51!6?• plot5*16?

• subplot51'6?

• plot5*!6?

• subplot516?

• plot5*'6?



12/40

LECTURE:

COMPLEX EXPONENTIAL FUNCTION



13/40

1. Comple* &*poetial +uctio

• )eal ad $magiar7 8comple* umber

• )eal part is same as preEious cosie waEe.

Real part Imaginary part

•

We will shi;t ;rom $ ad C0 toComple* &*poetial +uctio.


)2sin()2cos(

)(~ )2(

φ π φ π

φ π

+⋅++=

= +

ft A j ft A

Aet x ft j


14/40

!. )eal $magiar7 plae•

$K plae – $: $H2hase 8 )eal a*is

– K: KuadratureH2hase 8 $magiar7 a*is

• )ealH$magiar7 plae 5Comple* plae6 – Comple* umber ca be idicated as a poit

Complex plane

4Real axis (I

Imaginary axis (!

a

b

a 9 N b



15/40

Comple* &*poetial +uctio hows

)otatio i $HK plae

Real part Imaginary

4Real (I

Imaginary (!

A


)2sin()2cos(

)(~ )2(

φ π φ π

φ π

+⋅++=

= +

ft A j ft A

Aet x ft j

)(~ t x

)2cos( φ π + ft A

)2sin( φ π + ft A

φ π + ft 2


16/40

Comple* &*poetial +uctio

shows )otatio o T$M&O



17/40

Comple* Amplitude 52haser6

• P8*5t846 shows

startig poit 5t846 .

• P is called as

Comple* Amplitude 52haser6!41'/1!/1 !41' DigComm Lab 5+ire Tom Wada6

ft j j

ft j

e Ae

Aet x

π φ

φ π

2

)2()(~

⋅=

= +

t j

j

e X t x

f

Ae X

assume

0)(~

20ω

φ

π ω

⋅=

=

=


18/40

K23

b7 Comple* &*poetial +uctio

4

Real (I

Imaginary (!

Comple* Amplitude 52haser6 8 Costellatio poit


ft j j ft j

eeet x π π π

π 24

1)

4

12(

0 )(~

⋅==

+

ft j j ft j

eeet x π

π π π

24

3)

4

32(

1 )(~

⋅==

+

ft j j ft j

eeet x π π π

π 24

5)

4

52(

2 )(~

⋅==

+

ft j j ft j

eeet x π π π

π 24

7)

4

72(

3 )(~ ⋅==

+

4

1π j

e4

3π j

e

4

5π j

e 47π

je


19/40

CoEersio

;rom Comple* &*poetial +uctio

to )eal siusoid.


Tae )eal 2art

The

Qou ca coEertO

)2sin()2cos(

)(~ )2(

φ π φ π

φ π

+⋅++=

= +

ft A j ft A

Aet x ft j

]Re[)](~Re[)2cos()(

~

)2(

)2(

φ π

φ π

φ π +

+

==+

=

ft j

ft j

Aet x ft A Aet x


20/40

LAB, ： K23 waEe;orm

• Mae K23 waEe;orm as ;ollows usig


4

5A4 46

851 1J/65A1 16

851 'J/6

5A! !6

851 "J/65A! !6

851 -J/6

)2sin()2cos(

)(~ )2(

φ π φ π

φ π

+⋅++=

= +

ft A j ft A

Aet x ft j


21/40

LAB, ： K23 5!6 aswer • 84:'!? ;c8!?



• @ K23 2hasers

• P4 8 e*p51N1pi/6? P1 8 e*p51N'pi/6?

• P! 8 e*p51N"pi/6? P' 8 e*p51N-pi/6?

• @ +$()&

• ;igure5,16? plot5FP4 P1 P! P'G R9R6?

• a*is5FH1 1 H1 1G6?

• @• P4waEe 8 P4 e*p51N!pi;ct6? P1waEe 8 P1 e*p51N!pi;ct6?

• P!waEe 8 P! e*p51N!pi;ct6? P'waEe 8 P' e*p51N!pi;ct6?

• @

• ;igure5,!6?

• PP8real5P4waEe6? QQ8imag5P4waEe6? SS8t?

• plot'5PP QQ SS6? *label 5R$R6? 7label5RKR6? =label5RtimeR6?

• @

• ;igure5,'6?

• subplot5116? plot5real5P4waEe66?

• subplot51!6? plot5real5P1waEe66?

• subplot51'6? plot5real5P!waEe66?

• subplot516? plot5real5P'waEe66?



22/40

LAB- ： Draw B&) graph

• Mae ;ollowig graph b7 MATLAB



23/40

LAB- ： B&) graph aswer

• &B4dB 8 4:1:!4? @ &b4 i dB

• &B4 8 14 .5&B4dB/146?

• B&)UK23 8 4."er;c5s>rt5&B466?

• ;igure5-6?

• semilog75&B4dB B&)UK236?

• a*is5F4 !4 1&H, 1G6?

• *label5R &b/4 5dB6 R6?• 7label5R B&) o; 023R6?

• grid o?

• title5R K23 B&)R6?



24/40

LECTURE:

C"ANNEL MO#ELIN$



25/40

Multipath Chael•

Direct path ad Dela7ed paths



26/40

C%annel Mo&eling

'y Implse Response


27/40

Con+oltion operation

•

Chael $mpulse )espose851 4." 4.!6• ed 51 1 1 1 16 sigal

• The )eceiEed igal is 511."1.-1.-1.-4.-4.!6


•

$; 7ou multipl7 two pol7omial


28/40

Chael Modelig

b7 $mpulse )espose


29/40

LAB ： C


30/40

LAB ： C


31/40

LECTURE:

OF#M MO#ELIN$


OF#M &i it l i ti 0OR1 )"EET


32/40

OF#M &igital *ommni*ation 0OR1 )"EET

We are goig to sed bits b7 the ;ollowig 0+DM commuicatio s7stem

44411411 ①

44

41

14

②

M A

211

I

Q

4441

1411

d4819N

d18H19Nd!81HN

d'8H1HN

③

$+

+

T

u4

u1

u!

u'

④

$

add

u4

u1

u!

u'

u'

0+DM$

u4

u1

u!

u'

u'

⑤

$

rmE

u4

u1

u!

u'

⑥

+

+

T

d4819N

d18H19N

d!81HN

d'8H1HN

⑦

De

M

A

2

44

41

14

11

⑧ 44411411

u' u4 u1 u! u'


))()1()((4

1

))1()1((4

1

))()1()((4

1

)(41

)3,,2,1,0()(4

1

32103

32102

32101

32100

3

0

4

2

jd d jd d u

d d d d u

jd d jd d u

d d d d u

k d IFFT ed u nn

nk j

nk

⋅+−⋅+−⋅+=

−⋅++−⋅+=

−⋅+−⋅+⋅+=

+++=

==

⋅= ∑

=

π

)()1()(

)1()1(

)()1()(

)3,,2,1,0()(

32103

32102

32101

32100

3

0

4

2

juu juud

uuuud

juu juud

uuuud

nu FFT eud k k

nk j

k n

−⋅+−⋅+⋅+=−⋅++−⋅+=

+⋅+−⋅+−⋅+=+++=

==

⋅=∑=

−

π


33/40

LAB 0+DM1. 2lease draw 0+DM s7mbol comple* waEe ;orm icludi

g $ whe 7ou sed V44411411.!. 2lease draw 0+DM s7mbol comple* waEe ;orm icludi

g $ whe 7ou sed V14414411.'. 2lease draw 0+DM s7mbol comple* waEe ;orm icludi

g $ whe 7ou sed V44444444.

. Compare those ' waEe;orm. The Did 7ou ;id a7 problemX $; 7es please state the problem.

Time

Time

$

K

&;;ectiEe 7mbol$



34/40

LAB 16 aswer

• @@

• data8F41!'G? @ 4HY44 1HY41 !HY14 'HY11

• @ MA2

• mod>ps8 F19i H19i 1Hi H1HiG?

• cost 8mod>ps5data916?

• @ $++T

•uu 8 i;;t5cost6?

• @ $ ADD

• uuUg 8Fuu56 uuG?

• @ +$()&

• ;igure516

• subplot5'116? plot5real5uuUg6RHR6? a*is5F1 " H! !G6?

• subplot5'1!6? plot5imag5uuUg6RHR6? a*is5F1 " H! !G6?

• subplot5'1'6? plot5abs5uuUg6RHR6? a*is5F1 " H! !G6?



35/40

LAB14 0+DM

MA3& 144 s7mbol 0+DM sigal based o preEious poit0+DM 9 1 poit $.

Add oise o; )814dB



36/40

LAB14 0+DM aswer • @ imple 0+DM s7stem 5sed bits/s7mbol 144 s7mbol6

• @ +ire Wada

• clear all?• umUs7mbol 8 144? @ umber o; s7mbols

• Us7mbol 8 ? @ poits i s7mbol

• M 8 ? @ si=e o; sigal costellatio


•

• @@ 1 . create radom data

• data 8 ;loor5rad5Us7mbolumUs7mbol6M6?

•

• @@ !. mappig ito $HK costellatio• dataU1 8 mod>ps519data6?

•

• ;igure51446?

• subplot5!!16?

• plot5dataU1Rr.R6?

• a*is5FH' ' H' 'G6

• title5Rdata costellatioR6

•

• dataU! 8 dataU1?•

• @@ '. $++T

• dataU' 8 i;;t5dataU!6?

• subplot5!!!6?

• plot55real5dataU'66RHR6?

• title5R$++TR6?

• @@ . $ add

• dataU 8 FdataU'5Us7mbol:6?dataU'G?

•

• @@.1 Add oise

• sigpower8mea5mea5abs5dataU6.!66?

• s8 14? @@ 14dB

• awg 8 5rad5Us7mbol91umUs7mbol69irad5Us7mbol91umUs7mbol66?

• awgpower8mea5mea5abs5awg6.!66?

• awg 8 awg/s>rt5awgpower6145Hs/!46s>rt5sigpower6?

• dataU8dataU9awg?

•

• subplot5!!'6?

• plot5real5dataU6RHR6?

• title5R$ addR6?

•

• @@ ". $ remoEe

• dataU" 8 dataU5!:Us7mbol91:6?

•

• @@ ,. ++T

• dataU, 8 ;;t5dataU"6?

•

• subplot5!!6?• plot5dataU,Rb.R6?

• a*is5FH' ' H' 'G6

• title5RreceiEe data costellatioR6

• ;igure5!446

• plot5real5reshape5dataU5Us7mbol916umUs7mbol1666?



37/40

LAB14 0+DM aswer



38/40

LAB11 7mbol &rror )ateMeasure 7mbol &rror )ate ;or LAB14.

Add oise o; )84dB "dB 14dB.(se ZdemapK23.m[ ;uctio.2ut the mH;ile i same director7.

@ demapK23.m

@ The program demap to Comple* to umerical data.

;uctio gra7code 8 demapK235comp6

re 8 real5comp6?

im 8 imag5comp6?

i; 5re Y8 4 \ im Y8 4 6 gra7code84?

elsei; 5re ] 4 \ im Y8 4 6 gra7code81?

elsei; 5re Y8 4 \ im ] 4 6 gra7code8!?

else gra7code8'?

ed


LAB11 b l & ) t


39/40

LAB11 7mbol &rror )ate• @ imple 0+DM s7stem 5sed bits/s7mbol 144 s7mbol6

• @ +ire Wada

• clear all?

• umUs7mbol 8 144? @ umber o; s7mbols

• Us7mbol 8 ? @ poits i s7mbol

• M 8 ? @ si=e o; sigal costellatio


•

• @@ 1 . create radom data

• data 8 ;loor5rad5Us7mbolumUs7mbol6M6?

•

• @@ !. mappig ito $HK costellatio

• dataU1 8 mod>ps519data6?

•

• dataU! 8 dataU1?

•

• @@ '. $++T

• dataU' 8 i;;t5dataU!6?

•

• @@ . $ add

• dataU 8 FdataU'5Us7mbol:6?dataU'G?

•

• @@.1 Add oise

• sigpower8mea5mea5abs5dataU6.!66?

• s8 "? @@ 14dB

• awg 8 5rad5Us7mbol91umUs7mbol69irad5Us7mbol91umUs7mbol66?

• awgpower8mea5mea5abs5awg6.!66?

• awg 8 awg/s>rt5awgpower6145Hs/!46s>rt5sigpower6?

• dataU8dataU9awg?

• @@ ". $ remoEe

• dataU" 8 dataU5!:Us7mbol91:6?

•

• @@ ,. ++T

• dataU, 8 ;;t5dataU"6?

•

• ;igure5116

• plot5dataU,Rb.R6?

• a*is5FH' ' H' 'G6

• title5RreceiEe data costellatioR6

•

• @@ -. recoEer data

•

• rdata8=eros5Us7mbolumUs7mbol6?

• ;or s7m 8 1: umUs7mbol

• ;or ide* 8 1:Us7mbol

• rdata5ide* s7m6 8 demapK235dataU,5ide*s7m66?

• ed

• ed

•

• @@ . measure 7mbol &rror )ate b7 compare data ad rdat

a

•

• TotalUdata8 Us7mbolumUs7mbol?

• di;; 8 rdata H data?

• @ cout how ma7 ot =ero i di;;

• otSero 8 5di;; ^8 46?

• TotalUerror8sum5sum5otSero66?

• ;prit;5 R ) 8@.!; QMB0L &))0) )AT& 8 @.";

_R s TotalUerror/TotalUdata6?

• !41'/1!/1 !41' DigComm Lab 5+ire Tom Wada6


40/40


•

Mae a Matlab program to measure 7mbol &rror )ate Es ratioi 13 0+DM with K23 modulatio – ++T si=e 8 14! poits i 1 s7mbol – $ legth 8 1/++T si=e 8 1! poits – Total 144 s7mbol

• Write Mid )eport to e*plai 0+DM simulatio icludig1. Qour Matlab program!. Total 144 s7mbol waEe;orm

'. Costeratio with )84 ' , dB. 7mbol &rror )ate Es ) raph

– %ertical: &) i log scale –

80-Matlab Digcomm Lab

Documents