United International University EEE 456 Digital Communication Lab
Group: 04 Eperiment!" Eperiment name: Under sampling in #D$ so%t&are de'ned radio
#ubmitted by:
Md. Tayebur AhmedID: 021 132 007 A.R.M. AtaharIshtiaq #ubmitted to:
Arifa u!ta"a
ID: 021 142 096
Date o% submission: (()04)*0(+ Under sampling in #D$ so%t&are de'ned radio #ft$are%De&"ed #ft$are%De&"ed Radi# 'DR( is a $ire!ess )#mmu"i)ati#"s system $here a!! #f the si*"a! +r#)essi"* is m+!eme"ted i" s#ft$are. It is a" ad,a")ed radi# te)h"#!#*y i" $hi)h the m#du!ati#" a"d dem#du!ati#" #f radi# si*"a!s is +erf#rmed e-)!usi,e!y e-)!usi,e!y by s#ft$are.
,-y is it used. A )#mmu"i)ati#" !i" )#"sists #f three )#m+#"e"ts: )#m+#"e"ts: the tra"smitter/ the )ha""e!/ a"d the re)ei,er. •
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T# T# +r#du)e +r#du)e a radi# that )a" re)ei,e re)ei,e a"d tra"smit tra"smit a "e$ f#rm f#rm #f radi# +r#t#)#! +r#t#)#! ust by ru""i"* ru""i"* "e$ s#ft$are. s#ft$are. A te)h"ique i" $hi)h a!! the +r#)essi"* is d#"e i" s#ft$are i.e./ mi-i"*/ &!teri"*/ dem#du!ati#" et). sed t# im+!eme"t diere"t dem#du!ati#" s)heme a"d diere"t sta"dards )a" be im+!eme"ted i" the same de,i)e. a" be u+dated s# that de,i)e d#es"t be)#me #bs#!ete $ith time.
I% so%t&are does everyt-ing &-at is t-e role o% -ard&are. A basi) DR system may )#"sist #f a +ers#"a! )#m+uter equi++ed )#m+uter equi++ed $ith a s#u"d )ard// #r #ther a"a!#*%t#%di*ita! )#",erter/ )ard )#",erter / +re)eded by s#me f#rm #f R5 fr#"t e"d. e"d . ard$are is sti!! "eeded f#r the R5 fr#"t e"d a"d A"a!#* t# Di*ita! #",ert#r 'AD( a"d Di*ita! t# A"a!#* )#",erter 'DA(.
Disadvantages o% #D$ • • •
The )h#i)e #f ar)hite)ture ar)hite)ture de+e"ds de+e"ds #" the a,ai!ab!e a,ai!ab!e te)h"#!#*y te)h"#!#*y. #m+!e-ity i" usi"* the s#ft$are. There are are te)h"#!#*y !imits !imits #" a)hie,ab!e a)hie,ab!e R5 +erf#rma")es. +erf#rma")es.
/pplications % #D$ 1ec-nology • •
e!! +h#"e te)h"#!#*y. Mi!itary a++!i)ati#"s. a++!i)ati#"s.
Undersampling under sampling sampling is a te)h I" si*"a! +r#)ess +r#)essi"* i"*// under e)h"iqu ique $her $here e #"e #"e sam+!es a ba"d+ass%&! ba"d+ass %&!ter tered ed si*"a si*"a!! at a sam+!e rate rate be!#$ be!#$ its yquist rate 't$i)e rate 't$i)e the u++er )ut# freque")y(/ freque")y (/ but but is sti!! sti!! ab!e ab!e t# re)# re)#"st "stru) ru)tt the si* si*"a "a!. !. 8a"d$i 8a"d$idth dth !imited !imited si*"a!s si*"a!s '!ie '!ie radi# radi# si*"a!s si*"a!s i" )#mmu"i)a )#mmu"i)ati#" ti#"s( s( d#"t d#"t ha,e freque" freque")y )y )#m+#"e"t )#m+#"e"ts s "ear D. That bei"* the )ase/ the ty+e #f a!iasi"* that the yquist am+!e Rate
attem+ts t# a,#id is"t is"t a +r#b!em. It is a!s# a!s# is "#$" as "dersam+!i"*/ "dersam+!i"*/ ba"d%+ass ba"d%+ass sam+!i"* a"d su+er%"yquist sam+!i"*. The a!iasi"* ee)t due t# the u"dersam+!i"* u"dersam+!i"* te)h"ique )a" be used f#r #ur ad,a"ta*e. he" a si*"a! is sam+! sam+!ed ed at a rate rate !ess !ess tha" tha" t$i)e t$i)e its ma-imu ma-imum m frequ freque") e")y/ y/ the the a!ias a!iased ed si* si*"a! "a! a++ears at 5s ; 5i"/ $here 5s is the sam+!i"* freque")y a"d 5i" i" the i"+ut si*"a! freque")y. If $e sam+!e the 70% M< si*"a! $ith 100 M= sam+!i"* rate/ the a!iased )#m+#"e"t $i!! a++ear at 30 M< '100 ; 70(. As $e "#$ i" ad,a")e that the si*"a! is a!iased/ $e )a" re)#,er the a)tua! freque")y by usi"* the 5s ; 5i" re!ati#"shi+. The u"der sam+!i"* te)h"ique a!!#$s the AD t# beha,e !ie a mi-er #r a d#$" )#",erter i" the re)ei,e )hai". 5#r a ba"d%!imited si*"a! #f 70 M< $ith a 20%M< si*"a! ba"d$idth/ if the sam+!i"* rate '5s( is 100 M=/ the a!iased )#m+#"e"t $i!! a++ear bet$ee" 20 M< t# 40 M< '30 >10 M<(.
1-e eperiment I" this e-+erime"t y#u!! use the ?m#"a Te!e)#ms%Trai"er 1@1 t# set u+ a ba"d$idth !imited si*"a!. #u!! the" use u"der sam+!i"* t# dem#du!ate the ba"d$idth !imited si*"a! a"d re)#,er the messa*e. 5i"a!!y/ y#u!! e-+!#re the ee)ts #" the re)#,ered messa* messa*e e #f mismat mismat)h )hes es bet$ee bet$ee" " the the m#du!a m#du!ated ted )arrie )arriers rs ba"d$i ba"d$idth dth a"d the the freque")y used f#r u"der sam+!i"*. It sh#u!d t#e y#u ab#ut 40 mi"utes t# )#m+!ete this e-+erime"t.
E2uipment . ?m#"a ?m #"a Te!e)#ms%T Te!e)#ms%Trai"er rai"er 101 '+!us '+ !us +#$er%+#)( +# $er%+#)( . Dua! )ha""e! 20M< #s)i!!#s)#+e #s)i!!#s)#+e . t$# ?m#"a Te!e)#ms%Trai"er 101 #s)i!!#s)#+e !eads . ass#rted ?m#"a Te!e)#ms%Trai"er 101 +at)h !eads
3art / ! #etting up a band&idt- limited signal T# T# e-+erime"t $ith u"der sam+!i"* y#u "eed a ba"d$idth !imited si*"a!. A"y #f the m#du!ati#" s)hemes )a" be used f#r this +ur+#se/ but f#r sim+!i)ity #f $iri"*/ $e!! use a D8 si*"a!. The &rst +#rt #f the e-+erime"t *ets y#u t# set #"e u+.
5i*ure
5i*ure Messa*e si*"a! ' b!ue ( a"d Mudu!ated 'red( The Mu!ti+!ier m#du!es #ut+ut sh#u!d sh#u!d be D8 si*"a! $ith a!ter"ati"* ha!,es #f its e",e!#+e f#rmi"* the s#me sha+e as the messa*e.
uestion ( 5#r the *i,e" i"+uts t# the Mu!ti+!ier m#du!e/ hat are the freque")ies #f the t$# si"e$a,es that mae u+ the D8 si*"a!B A"s: The freque")ies #f the t$# si"e$a,es that mae u+ the D8 si*"a! are 9C< a"d 102<.
uestion * hats the ba"d$idth #f the D8 si*"a!B A"s: The ba"d$idth #f the D8 si*"a! is 4<.
3art ! Direct do&n!conversion using under sampling am+!ed si*"a! the sam+!i"* si*"a! E the messa*e
As the sam+!i"* si*"a! is a di*ita! si*"a!/ the e-+ressi#" )a" be re$ritte" as: am+!ed si*"a! : 'D F fu"dame"ta! F harm#"i)s( harm#"i)s( E messa*e he" the messa*e si*"a! is m#du!ated )arrier !ie the D8 si*"a! that y#u ha,e set u+/ the e-+ressi#" )a" be re$ritte" as: am+!ed si*"a! : 'D F fu"dame"ta! E harm#"i)s( harm#"i)s( - 'G8 F 8( #!,i"* the e-+ressi#" '$hi)h "e)essari!y i",#!,es tri*#"#metry that is "#t sh#$" here( *i,es: % Du+!i)ates #f the G8 a"d 8 'due t# their mu!ti+!i)ati#" $ith sam+!i"* si*"a!s D )#m+#"e"t( % A!iases #f the G8 a"d 8 at freque")ies equa! t# the sum a"d diere")e #f their freque")ies a"d the sam+!i"* si*"a!s fu"dame"ta! freque")y %umer#us #ther a!iases #f the G8 a"d 8 at freque")ies equa! t# the sum a"d diere")e #f their freque")ies a"d the sam+!i"* si*"a!s harm#"i) freque")ies
5i*ure
5i*ure Messa*e si*"a! 'b!ue( a"d sam+!e a"d h#!d #ut+ut 'red(
1unable lo& pass 'lter output
5i*ure Messa*e si*"a! 'bue( Demudu!ated 'red(
uestion hats the si*"i&)a")e #f the si*"a! #" the 8aseba"d G=5s #ut+utB A"s: The A"s: The si*"i si*"i&)a &)a")e ")e #f the the si*"a! si*"a! #" the the 8aseba 8aseba"d "d G=5s G=5s #ut+ut #ut+ut is the u"der% u"der% sam+!ed D8 si*"a! !##s a !itt!e !ie a" i",erted ,ersi#" #f the #ri*i"a! si*"a!.
uestion 4 Hi,e" the sam+!i"* freque")y is C.3332 'the si*"a!s s+e)i&ed ,a!ue #f C< is r#u"d #u"ded ed d#$" d#$" f#r f#r sim+ sim+!i !i)i )ity ty(/ (/ $hi) $hi)h h har harm#"i m#"i) ) i" the the sam+ sam+!i !i"* "* si*" si*"a! a! is dem#du!ati"* the D8 si*"a!B A"s: 13th harm#"i) i" the sam+!i"* si*"a! is dem#du!ati"* the D8 si*"a!.
3art C ! #ync-roni7ation Re)a!! that tra"smitter a"d re)ei,er )arrier sy")hr#"i
5i*ure This m#di&)ati#" m#di&)ati#" substitutes substitutes the Master i*"a!s i*"a!s m#du!es m#du!es C< DIHITAG DIHITAG #ut+ut
5i*ure @ di*ita! #ut+ut 'red( a"d baseba"d #ut+ut 'b!ue(
5i*ure 8aseba"d !#$ +ass Jter #ut+ut 'red( 'red( Messa*e si*"a! 'b!ue( The freque")y freque")y #f the di*ita! di*ita! +u!se i" K )#"tr#! $as e tried t# )#rre)t the freque")y err#r by tur"i"* the 0 m#du!es 5reque")y Adust )#"tr#! ,ery s!i*ht!y t# the !eft a"d ri*ht.
uestion 5 hy d#es"t d#es"t this this s#!,e s#!,e the +r#b! +r#b!em em a"d a!!#$ the the dem#du dem#du!at !at#r #r t# re)#, re)#,er er the messa*eB A"s: i")e it is hi*h!y u"!ie!y that the @ m#du!es #ut+ut $i!! e-a)t!y the ri*ht freque")y at e-a)t the ri*ht +hase f#r su))essfu! dem#du!ati#"/ this d#es"t s#!,e the +r#b!em a"d a!!#$ the dem#du!at#r t# re)#,er the messa*es.
Discussion e !ear"ed that if a si*"a! is ba"d!imited $e )a" )a+ture a!! the i"f#rmati#" by sam+!i"* it !ess tha" yquist rate. The Mu!ti+!ier m#du!es #ut+ut sh#u!d be D8 si*"a! si* "a! $ith $ith a!ter a!ter"at "ati"* i"* ha!,e ha!,es s #f its e",e!# e",e!#+e +e f#rmi" f#rmi"* * the s#me s#me sha+e sha+e as the messa*e.
The Fourier transforms of real-valued functions are symmetrical around the 0 Hz Hz axis. axis. After sampling, only a periodic a periodic summation of the Fourier transform (called discrete-time Fourier transform is still availa!le. The individual, fre"uency-shifted copies of the original transform are transform called aliases. aliases. The fre"uency offset !et#een ad$acent aliases is the sampling-rate, denoted !y f !y f s. %hen the aliases are mutually exclusive (spectrally, the original transform and the o riginal continuous function, or a fre"uency-shifted version of it (if desired, can !e recovered from the samples. The first and third graphs of Figure & depict a !ase!and a !ase!and spectrum spectrum !efore and after !eing sampled at a rate that completely separates the aliases. The second graph of Figure & depicts the fre"uency profile of a !andpass function occupying the !and ( A ( A,, A' A' B B (shaded !lue and its mirror image (shaded !eige. The condition for a nondestructive sample rate is that the aliases of !oth !ands do not overlap #hen shifted !y ! y all integer multiples of f of f s. The fourth graph depicts the spectral result of sampling at the same rate as the !ase!and function. The rate #as chosen !y finding the lo#est rate that is an integer su!-multiple su!-multiple of A of A and and also satisfies the !ase!and y"uist !ase!and y"uist criterion) criterion) f + B.. onse"uently, the !andpass s * + B function has effectively !een converted to !ase!and . All the other rates that avoid overlap are +/ + / given !y these more general criteria, #here A #here A and and A A' ' B are B are replaced !y f !y f and f L and f H , respectively:
The t#+ 2 *ra+hs *ra+hs de+i)t 5#urier 5#urier tra"sf#rms tra"sf#rms #f 2 diere"t fu")ti#"s fu")ti#"s that that +r#du)e +r#du)e the same resu!ts $he" sam+!ed at a +arti)u!ar rate. The baseba"d fu")ti#" is sam+!ed faster tha" its yquist rate/ a"d the ba"d+ass fu")ti#" is u"dersam+!ed/ ee)ti,e!y )#",erti"* it t# baseba"d. The !#$er *ra+hs i"di)ate h#$ ide"ti)a! s+e)tra! resu!ts are )reated by the a!iases #f the sam+!i"* +r#)ess.
