??f?a?? d?a

1
??f?a?? d?aµ??f?s?
2
???d???? d?a??aµµa ???/??? S?st?µat??
3
Ge???? µ??f? d?aµ??f?µe??? s?µat??
4
??aµ??f?t??S???es? µe ? ?a? Q s???st?se????ad???
pa?astas? t?? d?aµ??f?µe??? s?µat??
5
?pe????s? t?? µ??ad???? pa?astas??
6
?a?ade??µa d?aµ??f?s? µe pa?µ???t?? p?at???,
t?? fas?? ? t?? s????t?ta?
7
? d?aµ??f?s?-ap?d?aµ??f?s? st? ped?? t??
µ??ad???? s?µat??
8
??f?a?? d?aµ??f?s? PAM? d?aµ??f?t?? st? ped??
t?? µ??ad???? s?µat??
9
??f?a?? d?aµ??f?s?(µe p?a?µat??a s?µata)
10
ASK ?a? PSK
ASK bm1 ? cma bm0 ? cmb OOK cm bm
g(t)rectangular
BPSK cm expjpbm cos(jpbm)jsin(jpbm) s(t)c
os2pfctpbm ? cos2pfct
11
?? fasµa e??? pa?µ??a d?aµ??f?µe???
fe???t??S?es? fasµat?? µ??f?? pa?µ??
12
?? fasµa e??? pa?µ??a d?aµ??f?µe??? fe???t??
13
?a?ade??µata ßas???? pa?µ?? ?a? t?? fasµat?? t???
??a ???
G?a t?? pe?????sµ? t?? fasµat?? ep?d???eta? ?
???s? ßas???? pa?µ?? µe t?? µe??st? d??at?
d?a??e?a
14
?e????e? Nyquist
ISIIntersymbol interference
15
??a?e??? ISI µe pa?µ? µ??f?? sinc(?)
16
???t???a t?? Nyquist ??a µ?de???? ISI

• ?? ep??a??pt?µe??? pa?µ?? de? ?a d?µ??????s???
  p??ß??µa st?? ???? e?t?µ?s? e??? d?ad????
  s?µß???? a? e???? µ?de???? t?µ? t?? st??µ? p??
  ?a???µe de??µat?????a t?? ?aµßa??µe??? s?µat??.
• ?e µa??µat????? ?????, ?e???µe ? pa?µ?? ?a
  ??a??p??e? t?? s?es?
• ?p?? k e??a? a?e?a??? ?a? ? ? ap?stas? µeta??
  s?µß???? (1/R)
• ??a?? ?a? a?a??a?a s?????? ??a ?a ?s??e? ? p??
  pa?? s?es? e??a? ?

17
S??epe?e? t?? ???t????? Nyquist ??a pa?µ??? µe
fasµa a?st??a pe?????sµe??

• ? pa?µ?? e?e? fasµa ?(f) µe a?st??a
  pe?????sµe?? ?W.
• ?? BW lt (1/2T) de? ?pa??e? pa?µ?? p?? ?a
  ??a??p??e? t? ???t????
• d??t?...
• Rgt2BW
• ?? BW1/2T, t?te µ??? ? pa?µ?? µe fasµa
  X(f)sta?e?a ??a fltBW, ?a? X(f)0, a????
  ??a??p??e? t?? s?es?, d??t?...
• R 2BW
• ???ad? ? pa?µ?? p?? ep?t?epe? µetad?s?
  s?µß???? µe ???µ? 1/? ????? ISI ?a? e?e? e?a??st?
  e???? fasµat?? e??a? ? x(t) sinc(t/T) . ?
  pa?µ?? a?t?? e??a? µ? p?a?µat?p???s?µ?? (d??t?
  e?e? µ? µ?de-???? t?µ? ??a tlt0) a??a t??
  p??se??????µe µe µ?a ?a??ste??µe?? e?d??? t??,
  d?? t?? sinc(t-t)/T, ?p?? ? ?a??ste??s? t
  ep??e?eta? ets? ?ste ??a tlt0 ?a e???µe
  sinc(t-t)/T ? 0.

X(f)
S ?(fm/T)
...
...
-1/? -BW
BW 1/T f
S ?(fm/T)
...
...
-1/? -BW 0 BW 1/T f
18
S??epe?e? t?? ???t????? Nyquist ??a pa?µ??? µe
fasµa a?st??a pe?????sµe?? (2)

• 3. ?? BW gt (1/2T) ?pa????? ?????e?e?e? pa?µ??
  p?? ??a??p????? t? ???t????, d??t?...
• R lt 2BW
• ?a?ade??µa pa?µ?? p?? ??a??p????? ta ???t???a
  t?? Nyquist e??a? ? ?????e?e?a pa?µ??
  ?pe????µe??? s???µ?t???? µe fasµa ?p?? st?
  s??µa. G?a f? 0 e???µe t?? p??????µe??
  pe??pt?s? op?? BW1/2T.

S ?(fm/T)
...
...
-1/? -BW 0 BW
1/T f
1/2T


X(f)

?(f)
f0 1/2T R/2

BW
19
?????e?e?a pa?µ?? ?pe????µe??? s???µ?t????

• ?e????af? st? ped?? s????t?t??
• ?p?? BW e??a? t? ap???t? e???? fasµat?? t??
  pa?µ??
• f0 1/2T, f1 f0 f?, f? BW f0,
  
• ? r f?/f0 e??a? ? roll-off factor
  (s??te?est?? a?ad?p??s??)

r f?/f0 f0 1/2T R/2 BWf0f?f0(1r)
r0 r0.5 r1
f0
20
S??a?t?s? µetaf??a? t?? pa?µ?? ?pe????µe???
s???µ?t????
r f?/f0 f0 1/2TR/2 BWf0f?f0(1r)
(R/2)(1r)
fs
21
????? fasµat?? pa?µ?? ?pe????µe??? s???µ?t????

• G?a t? PCM s?st?µa µe ???µ? pa?a????? d?ad????
  s?µß???? R 1/T, e???µe
• BW (1r)/2 R Hz
• r "rolloff factor", 0 ? r ? 1,
• ??d??e? pe??pt?se??
• r 0, e??a? ap?a ? pa?µ?? sinc(.)
• r 1, e??a? ? µe??st? d??at? t?µ? t?? pa?aµet???
  r ?a? t? fasµa pa???e? t?? µ??f? ?pe????µe???
  s???µ?t????
• r 0.35, e??a? ? t?µ? p?? ???s?µ?p??e?ta? sta
  ???e??-?µe???a???a ??f?a?a s?st?µata ????t??
  t??ef???a? NA-TDMA ?a? CDMA (p??t?p? IS-54/136)

r f?/f0 f0 1/2TR/2 BWf0f?f0(1r)
22
?a?µ?? ?pe????µe??? s???µ?t???? - Fasµa

r f?/f0
23
?a?µ?? ?pe????µe??? s???µ?t????(Raised cosine)

• ?e????af? st? ped?? ??????

24
?a?µ?? ?pe????µe??? s???µ?t????
arrolloff factor
25
?a?µ??? d?aµ??f?s? fe???t?? µe p???ap???? pa?µ???
26
?a?µ??? d?aµ??f?s? s????t?ta? fe???t??
27
?a?µ??? d?aµ??f?s? s????t?ta? µe s??e?e?a fas??
(CPFSK)
The basis pulses follow each other in such a way
that the phase of the total signal is continuous
28
S?????? µ??f? ßas???? pa?µ????a CPFSK
29
????? s?µat??

• ?? d?a??aµµa st?? ???? s?µat?? e??a? ??a ap? ta
  p?? s?µa?t??a e??a?e?a ??a t?? a?a??s? t??
  s?st?µat?? d?aµ??f?s??.
• ?a? pa?e?e? µ?a ??af??? pa?astas? t??
  ???s?µ?p????µe??? ??µat?µ??f?? ? ?p??a ep?t?epe?
  µ?a ep?pt??? ?a? e??p???µe?? a?t?µet?p?s? t??
  d?af???? µe??d?? d?aµ??f?s??.

30
S??a?t?se?? ?as?? e??? s?????? s?µat??

• ????µe e?a s????? s?µat?? (??µat?µ??f??) s1(t),
  s2(t),,sM(t)
• p?????? ?, ?a? e?peµpeta? µ?a ap? a?te? ?a?e
  f??a.
• ?? s??a?t?se?? f1(t), f2(t),fK(t), ?p?? ? ? ?,
  ap?te???? µ?a p???? ?????a?????? ßas? ??a t?
  d??e? s????? t?? s?µat?? a?
• ?? s??a?t?se?? ßas?? e??a? ????????e? µeta??
  t???, d??ad?
• ?? s??a?t?se?? ßas?? e??a? ?a??????p???µe?e?
• ?a? ?a?e s?µa si(t) µp??e? ?a ??afte? sa?
  ??aµµ???? s??d?asµ??

31
S??a?t?se?? ?as?? ?a? ????? s?µat??

s1(t), s2(t),,sM(t)
s1(t) s2(t) . . . sM(t)
?a?e µ?a ap? t?? ??µat?µ??fe? si(t) µp??e? ?a
pa?asta?e? sa? e?a s?µe?? st?? K-d?astat? ????
p?? ap?te???? ?? s??a?t?se?? p?? µp????? ?a
pe????af??? ap? t?? s??a?t?se?? ßas?? fj(t)
f1(t), f2(t),fK(t)
f1(t) f2(t) . . fK(t)
????? s?µat??
32
?fa?µ??? st?? ??f?a?e? ep????????e?? ??aµ??f?t??

• Se e?a ??f?a?? t??ep????????a?? s?st?µa log2M
  bits p????f???a? µetad?d??ta? µe µ?a ap? t?? ?
  d?a?es?µe? ??µat?µ??fe? e??? s?????? SM. ?? ??
  ??µat?µ??fe? a?te? a?????? se ???? s?µat?? µe
  ???ste? s??a?t?se?? ßas?? t?te µp????µe ?a t??
  pe????a???µe ???s?µ?p????ta?
• ?? s????? t?? ? s??te?est?? t?? a?apt??µat?? ?a?e
  s??a?t?s??
• ??? ??af??? pa?astas? t?? ?-d?astat?? aste??sµ??
  s?µat?? ?p?? s?µe???eta? ? ?es? ?a?e s?µat??
  st?? ???? t?? s?µat??.
• ? ??af??? pa?astas? a?t? d??e? p?????a
  p????f????? ???s?µ?? ??a t?? d?aµ??f?s? ?a?
  ap?d?aµ??f?s? a?t?? t?? s?µat??
• ? e??s?s?-??e?d? e??a? ? e??s?s? s???es??
• ??aµ??f?s? e??a? ? d?ad??as?a ???p???s?? t??
  e??s?s?? a?t??

33
???s?s? s???es??Ge???? µ??f? ??aµ??f?t?
???a?? s?µß???sµ?? fk(t) ? fk(t) am,I ? sm,i
LUT Look-up-table
log2M bits address
s??te?este?
34
?e?t?????a t?? d?aµ??f?t?

• ?? ?e?e?, e?a? d?aµ??f?t?? µe ? s?µata
  ?-d?astase?? ??e?a?eta? ?a ap????e?se? t??? K x M
  s??te?este? (? s??te?este? ??a ?a?e e?a ap? ta ?
  s?µata) ?a? ?a pa?a???e? t?? ? s??a?t?se??
  ßas??.
• ?? s??te?este? ap????e???ta? se ? look-up tables
  (LUTs)p?? e???? log2M ??aµµe? d?e????se?? ?a? µ?a
  e??d?
• ?? ded?µe?a e?s?d?? ?µad?p?????ta? se ?µade? t??
  log2M bits ?a? ?a???????? t? e?peµp?µe?? s?µß???
  ?a? t?? ????? d?e????s? t?? LUTs.
• ?? e??d?? t?? LUTs e??a? ?? ? s??te?este? t??
  a?apt??µat?? t?? ep???µ?t?? s?µat??.
• ?? ? s??te?este? p???ap?as?a???? t?? ?
  s??a?t?se?? ßas?? ?a? ta ? ????µe?a a??????µe?a
  d????? t? ep???µ?t? s?µa p?? a?t?st???e? st?
  s???e???µ??? s?µß???.

35
??a?efa?a??s?

• ???s?s? s???es?? (d?aµ??f?t??)
• ???s?s? a?a??s?? (ap?d?aµ??f?t??)
• ??e??e?a s?µat??

36

• ???????G?? ?? d????? ta s?µata (BPSK)
• p?? ??????ta? st? 0lttlt?b , ?a? e???? e?e??e?a ?b
  t?te µ?a ?ata????? s??a?t?s? ßas?? e??a? ?
• ?? s????? t?? s?µat?? µp??e? ?a pa?asta?e? ap?
  ta a??a t?? d?a??sµat??, p?? ta a?t?p??s?pe????
  st?? d?a??sµat??? ????

37

• ?a d?? p??????µe?a s?µata e?f?a???ta? s??a?t?se?
  t?? s??a?t?s?? ßas?? ?? e???
• ?? ?e???s??µe t?? f(t) sa? t? µ??ad?a??
  d?a??sµa ???? a???a s??teta?µe???. ??te t? s?????
  µp??e? ?a pa?asta?e? ?p??
  p?? ?at?
• S??????, pa??sta???ta? µ??? ta a??a t??
  d?a??sµat??. ??t? t? d?a??aµµa ???µa?eta?
  signal constellation (aste??sµ?? s?µat??).

0
f(t)
?Eb
-?Eb
?
?
?Eb
-?Eb
f(t)
38
??aµ??f?s?

• Te???µe µe ta ??f?a?a ded?µe?a ?a d?aµ??f?s??µe
  ??µat?µ??fe? p?? ?a e??a?
• Fasµat??a ap?d?t??e?, ?a?
• ??e??e?a?a ??????µ??e?
• ? pa?astas? st?? ???? s?µat?? e??a? µ?a ß?????
  µe??d?? ?e???s?? t?? d?aµ??f?s?? ? ?p??a µa?
  ep?t?epe?
• ?a s?ed?a???µe fasµat??a ?a? e?e??e?a?a
  ap?d?t????? aste??sµ??? s?µat??.
• ?a ?a???????µe t?? µ??f? t?? ße?t?st?? de?t? ??a
  ded?µe?? d?a??aµµa aste??sµ??.
• ?a a????????µe t?? ep?d?se?? t?? ded?µe??? t?p??
  d?aµ??f?s??

39
?p?d?aµ??f?s? s?µat??

• ??peµp??µe e?a s?µa s(t) ? s1(t),
  s2(t),,sM(t), ?p?? t? s(t) e??a? µ?de???? ??a t
  ?0,T. G?a pa?ade??µa, e?peµp??µe t? sm(t) a?
  ?e???µe ?a µetad?s??µe t? m-st? ap? ? s?µß??a.
• ?a d?af??a s?µata e?peµp??ta? µe p??a??t?ta
• p1 Prs1(t),, pMPrsM(t)
• To ?aµßa??µe?? s?µa st?? de?t? e??a? a?????µ???
  ???? ????ß?? o ?p???? ?p?t??eta? p??s?et????
• r(t) s(t) n(t)
• ???e?t?? t?? r(t), ? de?t?? ?p??????e? µ?a
  e?t?µ?s? s(t) t?? s?µat?? s(t), µe st??? t??
  e?a??st?p???s? t?? p??a??t?ta? sfa?µat??
  e?t?µ?s?? e??? s?µß???? PsPr s(t) ? s(t)

40
To µ??te?? t?? ????ß??

• ?? s?µa ?f?stata? st? ?a?a?? a?????s? ????
  p??s?et???? ?e???? Gaussian T???ß??
• (?dditive White Gaussian Noise AWGN)
  n(t)
• St?? p?? ?at? ?e???s? ?p??et??µe ?t? ? ????ß??
  n(t) e?e? µes? t?µ? 0, s??a?t?s? a?t?s?s?et?s??
  Rnn(t) N0/2d(t) ?a? p????t?ta fasµat????
  ?s???? Snn(f) N0/2.
• ?a?e ??aµµ??? s??a?t?s? t?? n(t) e??a? ep?s??
  Gaussian st??ast??? d?ad??as?a.

?a?a??
r(t)
s(t)
S
n(t)
41
??aµ??f?s? - ?p?d?aµ??f?s?
n'(t)
f2(t)
?
s2
s3
?
?
s1
r1, r2
?
s4
f1(t)
42
?a?astas? st?? ???? t?? s?µat??

• ?? e?peµp?µe?? s?µa µp??e? ?a pa?asta?e? ?? e???
• ? ????ß?? µp??e? ?a pa?asta?e? ep?s?? µe t??
  ß???e?a t?? s??a?t?se?? ßas?? ?? e???
• ? s???st?sa n'(t) t?? ????ß?? e??a? t? µe??? t??
  ????ß?? p?? de? a???e? st?? ???? p?? pe????af???
  ?? s??a?t?se?? ßas?? (de? µp??e? ?a ??afe? sa?
  ??aµµ???? s??d?asµ?? t???).
• St? ep?µe?? slide ap?de????eta? ?t? t? n'(t)?
  sm(t) ?m?0,,M-1

43
H s???st?sa n'(t) e??a? ????????a p??? ??a ta
s?µata sm(t)

• ??a?µat?

44
?a?astas? ?aµßa??µe??? s?µat?? st?? ???? s?µat??

• ?? ?aµßa??µe?? s?µa µp??e? ???p?? ?a pa?asta?e?
  ?? e???
• ?p?? rk sm,k nk

n'(t)
f2(t)
r1, r2
f1(t)
45
O ????? ap?fase?? s????????eta? se ????
pepe?asµe??? d?astase??

• ??peµp??µe e?a s?µa t? ?p??? ape??????eta? µe t?
  d?a??sµa p????f???a? ? d?astase?? s s1,
  s2,, sK ?s1,s2,,sM
• ?aµßa???µe t? d?a??sµa r r1, r2,,rK sn, t?
  ?p??? e??a? t? a????sµa t?? e?peµp?µe???
  d?a??sµat?? s ?a? t?? d?a??sµat?? t?? ?e??ß?? n
  n1, n2,nK.
• ???e?t?? t?? r ?e???µe ?a ß???µe µ?a e?t?µ?s? s
  t?? e?peµp?µe??? d?a??sµat?? s ?ste ?a
  e?a??st?p??e?ta? ? p??a??t?ta sfa?µat??
  PsPrs?s
• 
  

s
?e?t??
r
46
?a???a? ?p?fas?? µe??st?? µetap??a??t?ta? MAP
(Maximum a posteriory Probability)

• ?p??et??µe ?t? ta d?a??sµata s1,s2,,sM µe ta
  ?p??a µetad?d??ta? ta ? d?af??et??a s?µß??a,
  e?peµp??ta? µe p??a??t?te? p1, p2,,pM
  a?t?st???a, ?a? ?t? ?aµßa?eta? t? d?a??sµa r.
• H p??a??t?ta sfa?µat?? e??? s?µß????
  e?a??st?p??e?ta? a? st?? de?t? ? e?t?µ?s? s e??a?
  t? d?a??sµa sm ??a t? ?p??? ?s??e?
• Prsm r ? Prsi r,
  ?m?i
• (???
  receiver)
• ?s?d??aµa (Bayes)

47
?a???a? ?p?fas?? µe??st?? p??a??fa?e?a?ML
(Maximum Likelihood)

• ?? p1p2p? 1/M, ? a? ?? p??a??t?te? e?p?µp??
  t?? s?µß???? e??a? a???ste? (?p?te ?p?t??eta?
  ?se?), t?te ? ?a???a? MAP ?s?d??aµe? µe t?? ML
• H p??a??t?ta sfa?µat?? e??? s?µß????
  e?a??st?p??e?ta? a? ep??e???µe ?? e?peµp?µe??
  s?µß??? t? sm t? ?p??? ??a??p??e? t?? s?es?
• p(rsm) ? p(rsi), ?m?i.
• (ML receiver)

48
?p?????sµ?? p??a??t?t??

• G?a ?a efa?µ?s??µe t??? ?a???e? ap?fas?? MAP ?a?
  ML ??e?a?eta? ? ?p?????sµ?? t?? p??a??t?t??
  p(rsm).
• ?pe?d? r sm n, ?p?? t? sm e??a? e?a sta?e??
  d?a??sµa, a??e? ?a ?p?????s??µe t?? p(n) p (n1,
  n2,,nK) p?? e??a? ? ap? ?????? pdf t?? ?
  t??a??? µetaß??t?? ni.
• ? ????ß?? n(t) e??a? µ?a Gaussian t??a?a
  d?ad??as?a
• ?p?µe??? ? s???st?sa t??
• e??a? µ?a Gaussian t??a?a µetaß??t?.
• ?ata s??epe?a ? p(n1, n2,,nK) e??a? ? ap? ??????
  pdf ? Gaussian µetaß??t??

49
?p?????sµ?? t?? pdf t?? ????ß??, p(n)

• ?? Gaussian µetaß??te? ni ?a? nk e??a?
  as?s?et?ste?
• ??a?µat?

50
?p?????sµ?? t?? pdf t?? ????ß??, p(n) (2)

• ?pe?d? ?nink0 ??a i?k, ?? s???st?se? t??
  ????ß?? e??a? as?s?et?ste? ?a? ep?µe???
  a?e?a?t?te?.
• ?pe?d? ?nk2 N0/2, ?a?e s???st?sa t?? ????ß??
  e?e? µetaß??t?t?ta (variance) ?s? µe ?0/2. ?ata
  s??epe?a

p(n)
51
? ?p? s?????? pdf t?? ?aµßa??µe??? s?µat?? r,
p(rsm)

• O? µese? t?µe? t?? s???st?s?? t?? ?aµßa??µe???
  s?µat?? e??a? o? a?t?st???e? s???st?se? t??
  e?peµp?µe??? d?a??sµat??,
• nkrk-sm,k ?a? ep?µe???

52
??µ? t?? ße?t?st?? ?e?t?

• ?a???a? ap?fas?? MAP

53
?a?astas? ?aµßa??µe??? s?µat?? st?? ???? s?µat??

• ?p? ta p?? pa?? p????pte? ?t? ep??e?eta? e?e??? ?
  ??µat?µ??f? sm(t) ap? t? s?µe?? t?? ?p??a? st??
  aste??sµ? t?? s?µat?? e?e? t?? µ????te??
  e???e?de?a ap?stas? t? s?µe?? p??ß???? t??
  ?aµßa??µe??? s?µat?? r(t).

n'(t)
f2(t)
?
?
? s1,1, s1,2
r1, r2
?
f1(t)
54
??µ? t?? ße?t?st?? ?e?t? (s??e?e?a)

• ?pa?e?f??ta? ????? ?? ?p???? e??a? ?????? ??a
  ??e? t?? ep????e? e???µe
• ????ap?as?a???µe ?a? µe t? ?0/2 ?a? e???µe t??
  te???? µ??f? t?? MAP receiver

55
F?s??? e?µ??e?a t?? ap?te?esµat??

• ?? (?0/2)lnpm de???e? t?? s?µas?a t??
  p??a??t?ta? e?p?µp?? e??? s?µß????.
• ?? ? ????ß?? e??a? µe?a???, ? pm e?e? µe?a??
  ßa??t?ta
• ?? ? ????ß?? e??a? µ?????, t? ?aµßa??µe?? s?µa ?a
  µ????e? p??? µe t? e?peµp?µe?? ?a? ? s?µas?a t??
  pm e??a? µ????.
• ??
  e??a? ? s?s?et?s? t?? e?peµp?µe???
  µe t? ?aµßa??µe?? s?µa.
• ??
  e??a? ? e?e??e?a t??
  e?peµp?µe??? s?µat??

56
??a ???p???s? t?? ße?t?st?? de?t?? Correlation
Receiver
??daµe ?t?
r(t)
?
S
S
-?1/2
(?0/2)ln(p1)
s1(t)
?p????? t?? µe?a??te???
. . . .
r(t)
?
S
S
-?m/2
(?0/2)ln(pm)
sm(t)
r(t)
?
S
S
-?M/2
(?0/2)ln(pM)
sM(t)
57
?p??p???se?? ??a e?d??e? pe??pt?se??

• ???t???? ML ?? ??a ta s?µata e??a? ?s?p??a?a
  (p1p2pM) ?? p??a??t?te? e?p?µp?? pm µp?????
  ?a a????????.
• ?? ??a ta s?µata e???? ?s? e?e??e?a
  (?1?2...??) ?? ???? e?e??e?a? µp????? ep?s??
  ?a a????????.
• ?e???a t? ???t???? ap?fas?? ap??p??e?ta? st?

G?a ?s?p??a?a s?µß??a ?a? ??µat?µ??fe?
?s?? e?e??e?a?
?e?t?? s?s?et?s?? Correlation Receiver
s?(t)
58
???p???s? µe??µe??? p???p????t?ta?i) ? ßa?µ?da
s?s?et?s??

• ?p????µe ?a e?att?s??µe t?? a???µ? t??
  s?s?et?st?? a? ???p???s??µe t?? e?f?as? t?? s
  s??a?t?se? t?? s??a?t?se?? ßas??

???ß??? t?? r(t) st?? s??a?t?se?? ßas??
(?p?????sµ?? t?? rk)
r(t)
r1
?

f1(t)
rr1,r2,,rK
s???st?se? t?? ?aµßa??µe??? s?µat?? st? s?st?µa
t?? s??a?t?se?? ßas??
r(t)
?
rK
fK(t)
59
???p???s? µe??µe??? p???p????t?ta?ii) ? ßa?µ?da
?pe?e??as?a?

S
S
?p????? t?? µe?a??te???
rr1,r2,,rK
-?1/2
(?0/2)ln(p1)

?
S
S
S
-??/2
(?0/2)ln(pM)
60
? ?e?t?? ???sa?µ?sµe??? F??t???Matched Filter
Receiver

• ?p??et??µe ?t? ?? s??a?t?se?? ßas?? fk(t) e??a?
  µ? µ?de???e? st? d?ast?µa 0,?, ?a? ??????µe t??
  hk(t) fk(T t) ? fk(t) hk(T t)
• ??te
• ?p?? t? r(t)?hk(t)tT s?µß????e? t??
  t?µ? t?? s??e????? t?? s?µat?? r(t) ?a? hk(t)
  ?ata t?? st??µ? tT.
• ?p????µe d??ad? ?a ???p???s??µe t?? s?s?et?s? t??
  r(t) µe t?? s??a?t?s? ßas?? fk(t) pe????ta? t?
  r(t) µesa ap? e?a ??aµµ??? f??t?? µe ????st???
  ap????s? hk(t) fk(T t). To f??t?? a?t?
  ???µa?eta? "p??sa?µ?sµe?? - matched"

61
???p???s? t?? correlator µe p??sa?µ?sµe?? f??t??

hk(t) fk(T t)
tT
h1(t)
r(t)
r1

?a?µ?da epe?e??as?a?
rr1,r2,,rK
tT
hK(t)
r(t)
rK
???sa?µ?sµe?? f??t??
62
???p???s? t?? correlator µe p??sa?µ?sµe?? f??t??
(2)

• ????? p??ß??? st?? s??a?t?se?? ßas??

tT
s1(?-t)
r(t)
S
S
-?1/2
(?0/2)ln(p1)
?p????? t?? µe?a??te???
. . . .
r(t)
S
S
sm(?-t)
-?m/2
hm(t)sm(T-t)
(?0/2)ln(pm)
r(t)
s1(?-t)
S
S
-?M/2
???sa?µ?sµe?a f??t?a
(?0/2)ln(pM)
63
?a?ade??µa s?ed?as?? ?e?t?st?? ?e?t?

• ?? s????? t?? s?µat?? µa? e??a? ?? a??????e?
  ??µat?µ??fe?, ?4
• s1(t)
  s2(t)
• s3(t)
  s4(t)

1
1
2
1
2
1
2
t
t
-1
1
1
1
1 2
1
2
1
2
t
t
T2, E1E2E3E42
64
?e?t?? s?s?et?s?? (Correlation Rx)

?pe?d? ta s?µata e???? ?se? e?e??e?e? µp????µe ?a
t?? a????s??µe
r(t)
?
S
S
-?1/2
(?0/2)ln(p1)
s1(t)
?p????? t?? µe?a??te???
. . . .

r(t)
?
S
S
-?4/2
(?0/2)ln(p4)
s4(t)
65
?e?t?? p??sa?µ?sµe??? f??t???(Matched Filter Rx)

hk(t) sk(2 t)
t2
h1(t)
r(t)
S

(?0/2)ln(p1)
?p????? t?? µe?a??te???
t2
h4(t)
r(t)
S
(?0/2)ln(p4)
66
S?ed?as? ße?t?st?? de?t? µe??µe??? p???p????t?ta?

• ?? p?? ?at? s????? s??a?t?se?? ap?te?e? µ?a p????
  ?????a?????? ßas? ??a t?? 4 ??µat?µ??fe? t??
  pa?ade??µat??
• f1(t)
  f2(t)
• s1(t) 1f1(t) 1f2(t), s2(t)
  1f1(t) - 1f2(t)
• s3(t) -1f1(t) 1f2(t), s4(t)
  -1f1(t) -1f2(t)

1
1
1 2
1 2
-1
-1
67
?e?t?? µe??µe??? p???p????t?ta??a?µ?da
s?s?et?sµ??

• ?e?t?? S?s?et?s??
• ?e?t?? p??sa?µ?sµe??? f??t???

r1
r(t)
?
rr1 r2
f1(t)
r(t)
?
r2
f2(t)
hk(t) fk(2 t)
h1(t)
r1
h1(t)
r(t)
t2
rr1 r2
1 2
h2(t)
h2(t)
r(t)
r2
1 2
68
?e?t?? s?s?et?s?? µe??µe??? p???p????t?ta??a?µ?da
?pe?e??as?a?
f2
s1
s3

f1
s4
s2
?p????? t?? µe?a??te???
rr1,r2
?
S
69
??a??s? ?e?t?????a? t?? de?t? s?s?et?s??
(????d?astat?? ????? s?µat??)
??peµp?µe?? s?µa (???)
?
r(t)
f(t)(1/?T) ??a 0tT 0 a????
trigger at tkT
70
??ad????e? ap?fase?? t?? de?t? s?s?et?s??
71
?e?t?????a de?t? p??sa?µ?sµe??? f??t???
(???)
r(t)
h(t)f(T-t)
?d? h(t) 1/?T ??a 0tT 0 a????
trigger at tkT
72
(No Transcript)
73
(No Transcript)
74
(No Transcript)
75
(No Transcript)
76
(No Transcript)
77
?a?astas? ?aµßa??µe??? s?µat?? st?? ???? s?µat??

• ?p? ta p??????µe?a p????pte? ?t? ? de?t?? MAP
  ep??e?e? e?e??? t?? ??µat?µ??f? sm(t) ? ?p??a
  e?e? t?? µ????te?? e???e?de?a ap?stas? ap? t?
  s?µe?? p??ß???? t?? ?aµßa??µe??? s?µat?? r(t)
  st?? ???? t?? s?µat??.

n'(t)
f2(t)
?
?
? s1,1, s1,2
r1, r2
?
f1(t)
78
?e?????? t?? s?ed?as?? t?? ße?t?st?? ?e?t?

• ? ße?t?st?? s?µf???? (coherent) de?t?? ??a t??
  AWGN e?e? t??a µe??
• ?? p??t? µe??? s?s?et??e? t? ?aµßa??µe?? s?µa µe
  ?a?e e?a ap? ta p??a?a ?a µetad????? s?µata
• ?? de?te?? ?a??????p??e? t?? s?s?et?s? e?s????ta?
  t?? ep?d?as? t?? e?e??e?a? ?a?e s?µat??.
• ?a? t? t??t? e?sa?e? t?? ep?d?as? t?? p??a??t?ta?
  e?p?µp?? e??? s?µß???? se s??a?t?s? µe t?? ?s??
  t?? ????ß??.
• ??t?? ? de?t?? e??a? ?e????? efa?µ???? ??a ?a?e
  s????? s?µat??.
• ?p??p???se?? e??a? d??ate? ?at? ap? d?af??e?
  s?????e?.

79
???t???a ep?d?se?? t??ep????????a??? s?st?µat??

• ? p??a??t?ta sfa?µat?? e??a? t? ßas??? ???t????
  ep?d?se?? e??? s?st?µat?? d?aµ??f?s??-ap?d?aµ??f?s
  ??.
• Sfa?µa e???µe ?ta? ? e?t?µ?s? e??? s?µß????
  e??a? d?af??et??? ap? t? p?a?µat??? s?µß??? d.
• ? ????? p?? e???µe sfa?µata fa??eta? sta p?? ?at?
  d?a??aµµata p??ß???? t?? ?aµßa??µe??? s?µat??
  st?? s??a?t?se?? ßas??

80
?e????e? ?p?fas??

• ?e?t?st?? ?a???a? ap?fas??
• ?st? ?t? ? e??a? ? pe?????
  ?p??
• ? j?m
• ??te a?t? ? pe????? Rm e??a? ? m-?st? "pe?????
  ap?fas??" ( ? pe????? ?p?? a? pese? t? r
  ap?fas??eta? ?t? sta????e t? m-?st? s?µß???)

81
?a?at???se?? ??a t?? pe????e? ap?fas??

• ?a ???a t?? pe?????? ap?fas?? e??a? ?a?eta st??
  ??aµµ? p?? s??dee? d?? s?µe?a t?? ????? s?µat??.
  (e??a? s?st????)
• ?? ta s?µata e??a? ?s?p??a?a, ta ???a ap?fas??
  e??a? a???ß?? st? µes?? t?? ap?stas?? µeta?? d??
  s?µe???.
• ?? ta s?µata de? e??a? ?s?p??a?a, ? pe????? t??
  ????te??? p??a??? s?µat?? s????????eta?.

82
???a??t?ta sfa?µat?? s?µß????

• ? Ps(e) Prs?s e??a? ? µes? p??a??t?ta
  sfa?µat?? s?µß????, d??ad?
• ?p?? Prs?sissi P(Esi) e??a? ? ?p? s??????
  p??a??t?ta ?a µ?? ap?fas?se? ? de?t?? ?t?
  sta????e t? si d??e?t?? ?t? sta????e t? si.
  ???a?
• P(Esi)
• ????µe p???ap?? ????????s? st?? pe????? Ri d??t?
  ? pdf e??a? ? d?astase??

83
?p?????sµ?? p??a??t?ta? sfa?µat??

• ?pe?d? ? p??a??t?ta sfa?µat?? e??? s?µß????
  e?a?tata? ap? t? µe?e??? t?? pe?????? ap?fas??
  ?a? ?? pe????e? ap?fas?? e??a? e? ?e?e?
  d?af??et??e? ??a ?a?e s?µe?? t?? aste??sµ??, ?a
  ?p?????s??µe a????a t?? p??a??t?ta sfa?µat??
  ?p??et??ta? ?t? e?peµf???e t? s?µß??? sm. ??
  ?p?????sµ?? ?a ?????? ??a m1,,M ?a? ?a
  ???s?µ?p???s??µe t? ?e???µa t?? ??????
  p??a??t?ta? ??a ?a s??d?as??µe ta ap?te?esµata.
• G?a d?ad??e? d?aµ??f?se?? ? d?ad??as?a e?e? ??
  e???
• ?p??et??µe ?t? ste??eta? t? s1 ?a? ?p????????µe
  t?? p??a??t?ta sfa?µat?? P(Es1).
• ?p??et??µe ?t? ste??eta? t? s2 ?a? ?p????????µe
  t?? p??a??t?ta sfa?µat?? P(Es2).
• ???s?µ?p????µe t? ?e???µa t?? ?????? p??a??t?ta?
  ??a ?a ?p?????s??µe t?? µes? p??a??t?ta
  sfa?µat??
• P(E) P(Es1 )Prsta????e t? s1
  P(Es2 )Prsta????e t? s2
• 4. ?a???µe t?? ?????? ?p??es? ?t?
• Prsta????e t?
  s1Prsta????e t? s21/2
• ?p?te P(E) (1/2)P(Es1) (1/2)P(Es2)
  (1/2)P(Es1) P(Es2)

84
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? s?µß????
??a t? BPSK

• ??? s?µata a?t??et?? p??s?µ?? ?2 (? ? ?s???
  t?? s?µat??)
• ??a s??a?t?s? ßas??
• ?a?astas? st?? ???? t?? s?µat??
• Prs1 Prs2 0.5 (?s?p??a?a s?µß??a)

?Eb
-?Eb
?
?
s2
s1
85
???a t?? pe?????? ap?fas?? ??a t? BPSK

• S?µf??a µe t?? ??? ?a???a ap?fas?? ep??e?eta? t?
  s1 a?
• p(rs1)Pr(s1) ? p(rs2)Pr(s2) ?

R2
R1
?
?
?
0
r
s1 ?Eb r
s2 - ?Eb
86
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? ??a t? BPSK

???ad?
87
(No Transcript)
88
???a??t?te? sfa?µat?? ??a t? BPSK

• St? p??????µe?? slide e?daµe ?t?
• ???? s?µµet??a?
• ??????t? t? ap?te?esµa e????? ??a t?? pe??pt?s?
  t?? BPSK, t? ?d?? ap?te?esµa ?s??e? ??a ?a?e
  s????? s?µat?? µe t? ?d?? d?a??aµµa aste??sµ??.
• Ps(e) Q(di,j /? 2N0) ?p??
  di,j e??a? ? e???e?de?a ap?stas? t??
  s?µe??? i ?a? j

89
G?af??? pa?astas? t?? p??a??t?ta? sfa?µat?? ??a
t? BPSK

90
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? ??a t?
d?ad??? s?µf??? (coherent) FSK

• ??? ????????a s?µata (?2)
• ta s?µata e??a? ????????a ??a f1-f2k/2T, ?p?? k
  sta?. (??at???).
• ??? s??a?t?se?? ßas??
• ?a?astas? st?? ???? t?? s?µat??

91
?e????e? ap?fas?? ??a t? d?ad??? s?µf??? FSK

f2(t)

R2
s2
R1
f1(t)
s1

?e pe??st??f? ?a? a??a?? a????? e???µe
R2
R1


s2' - ?Eb/2 s1' ?Eb/2
92
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? ??a t?
d?ad??? s?µf??? (coherent) FSK

• ?a?e µeta?es?, pe??st??f? ? a?a??as? t??
  s??teta?µe???, p?? de? a??a?e? t?? ap?stas?
  µeta?? t?? s?µat?? de? ep???ea?e? t?? p??a??t?ta
  sfa?µat??.
• ?pa?a?aµßa???ta? t??? ?p?????sµ??? p?? ?a?aµe ??a
  t? B?SK µe a?t??atastas? t?? ??b µe t? ?Eb/2
  ß??s???µe ?t?

93
??a??aµµa t?? BER (bit error rate) ??a t? BPSK
?a? FSK

• To FSK e??a? ?at? 3db ?e???te?? t?? BPSK
  (??e?a?eta? d?p?as?a e?e??e?a a?a bit ??a t??
  ?d?a p??a??t?ta sfa?µat??)

3db
94
?p?????sµ?? p??a??t?ta? sfa?µat?? ??a t? d?ad???
s?µf??? ASK

• ??? ??µat?µ??fe? (?2)
• ??a s??a?t?s? ßas??
• ?a?astas? st?? ???? s?µat??
• ?p?te
• ?? d?a??aµµa aste??sµ?? e??a? ?d?? µe t?? FSK
  ?p?te

µeta ap? a??a?? a????? gt
R2 R1
R2 R1
?
X
X
?
s20 ?Eb/2 s1?2Eb
s2-?Eb/2 0 s1?Eb/2
95
??aµ??f?s? p???ap??? ep?ped??

• ?st? m(t) t? µ???µa p????f???a?
• ??ad??? s?µat?d?s?a m(t) ? 0,1
• M-ary s?µat?d?s?a m(t) ? 0, 1,,M-1
• To s?µa p????f???a? pa???e? µ?a ap? ? t?µe?
• ?2k
• k a???µ?? bits/symbol.
• ?a?ade??µa
• ? d?af??et??e? fase?? (M-ary PSK)
• ? d?af??et??a p?at? (M-ary ASK)
• s??d?asµ?? ?p?? ? tet?a?????? d?aµ??f?s? p?at???
  (Quadrature Amplitude Modulation QAM)

96
?as??? p?e??e?t?µa t?? d?aµ??f?s?? p???ap???
ep?ped?? ??????µ?a fasµat??

• ?st?
• ?b ? d?a??e?a e??? bit
• Ts ? d?a??e?a e??? s?µß????
• ??te
• Rb 1/Tb e??a? ? ???µ?? µetad?s?? bits
• Rs 1/Ts e??a? ? ???µ?? µetad?s?? s?µß????
• ? p????f???a µetad?deta? µe t?? ???µ? µetad?s??
  t?? bits
• ?? e???? fasµat?? e??a? a?a???? t?? ???µ??
  µetad?s?? s?µß????
• e?a? µ??? pa?µ?? µetad?deta? ??a ?a?e s?µß???

97
M-ary PSK (MPSK)

• ?a?astas? µet??? ?a? fas??
• m(t) ? 0, 1,,M-1
• To Ac e??a? µ?a sta?e?a ?a? s?µß????e? t? p?at??
  t?? s?µat??.
• ??d??? pe??pt?s? ?2 p?? a?t?st???e? st? BPSK

98
M4 Quadrature PSK (QPSK)

• QPSK
• ??af??et??? fas? ??a ?a?e s?µß???
• ???s?µ?p??e?ta? e???tata
• ?a?astas? I/Q

99
??a??aµµa aste??sµ?? t?? QPSK

y(t)

?c


- ?c
?c
x(t)

- ?c
?a?at???s? ??af??et??e? µetat?p?se?? fas??
µp????? ?a pa?a???? d?a??aµµa aste??sµ?? p??
p????pte? ap? t? p?? pa?? µe pe??st??f? ?a?ade??µa

100
Fasµat??a ?a?a?t???st??a t?? MPSK

• ? p????t?ta fasµat???? ?s???? ?p??????eta? e????a
  a? ?e???s??µe t? MPSK ?? a????sµa M s?µat?? ASK.
• ?pe?d? ?s (log2M) Tb o ?????? ??ß?? t??
  fasµat?? t?? MPSK e??a? log2M f??e? µ????te???
  ap? t?? ??ß? t?? fasµat?? e??? s?µat?? BPSK µe
  t? ?d?? bit-rate

101
???a??t?ta sfa?µat?? s?µß???? ??a t? QPSK

• ?a 4 s?µata t?? QPSK e??a? ta a??????a
• ?a s?µata a?ta µp????? ?a pa?asta???? µe t??
  s??a?t?se?? ßas??
• ??t? ? pa?astas? d??e? ta a??????a d?a??sµata
  p????f???a?
• ?p?? ?s PT ? e?e??e?a e??? s?µß????

102
?? d?a??aµµa aste??sµ?? t?? QPSK ?a? ?? pe????e?
ap?fas??
f2

s2
?
s1
s3
?
?
f1
s4
?
103
To d?a??aµµa aste??sµ?? t?? QPSK µeta ap?
pe??st??f? 450

f2
s1
s2
?
?
s2-?Es/2, ?Es/2
f1
s3-?Es/2, -?Es/2
s4?Es/2, -?Es/2
?
?
s3
s4
104
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? s?µ???? ??a
t? QPSK

105
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? s?µ???? ??a
t? QPSK (2)

106
???a??t?ta sfa?µat?? s?µß???? ??a t? QPSK

• H ?p?-s?????? p??a??t?ta sfa?µat?? ?a? ??a ta 4
  s?µata e??a? ?d?a, d??ad?
• ? p??a??t?ta sfa?µat?? e??? s?µß???? t?? QPSK
  e??a? s?ed?? d?p?as?a e?e???? t?? BPSK
• ?ta? µ???s??µe p?? ?at? ??a t? BER (Bit Error
  Rate) ?a d??µe ?t? ta BPSK ?a? QPSK e???? t? ?d??
  BER.

107
??R d?a??aµµata ??a t? QPSK ?a? t? BPSK

108
?a?at???se?? ep? t?? d?ad??as?a? ?p?????sµ?? t??
p??a??t?t?? sfa?µat??

• ? p??a??t?ta sfa?µat?? e???s?eta? ???????????ta?
  t?? ?p?-s?????? p??a??t?ta sfa?µat?? st?? pe?????
  ap?fas??.
• ? ?p?????sµ?? a?t?? ???eta? d?s???a a? e???µe
  ???? p????? d?astase??
• ?e t?? ?ata????? pe??st??f?, µetaf??a ?a?
  a?a??as? t?? s??teta?µe???, µp????µe ?a
  ap??p???s??µe t??? ?p?????sµ???
• ? s?µpe??f??a e??? aste??sµ?? s?µat?? ?? p??? t??
  p??a??t?ta sfa?µat?? e?a?tata? ap???e?st??a ap?
  t?? ap?stase?? t?? s?µe??? t?? aste??sµ??
• ? µe??d?? t?? Union Bound µa? ep?t?epe? ?a
  e?att?s??µe t??? ?p?????sµ??? t?? p??a??t?ta?
  sfa?µat?? se µ?a se??a ?p?????sµ?? d?ad????
  sfa?µat??

109
?e??d?? Union Bound
110
?as??? ?dea ??a t?? ?p?????sµ? sfa?µat?? µe t??
µe??d? Union Bound
R2

• ??aµ??f?s? QPSK
• ?st? ?2,j ? ep?fa?e?a ?p??
• t? ?aµßa??µe?? s?µa r
• e??a? p??s?este?a st? sj,
• a? ?a? t? e?peµp?µe?? s?µa
• e??a? t? s2. Tote

????ß?? ?p?????sµ??
s2
?
r
?

?
?
s1
s3
s4
?
?
?
?
? r
? r
r
?
A2,3

?
?

?
?

?
?
s3
Pr(Z2?Z1)
Pr(Z2?Z4)
?
?
?
A2,4
A2,1
Pr(Z2?Z3)
111
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? a?a ?e????
s?µß????

• ??daµe p?? pa?? ?t? ? p??a??t?ta sfa?µat?? ??a t?
  ?e???? sj ?a? si ?s??ta? µe t?? p??a??t?ta ?t? t?
  ?aµßa??µe?? s?µa r e??a? p??s?este?a st? sj ap?
  ?t? st? si.
• ?e ?ata????e? pe??st??fe? ?a? µetaf??e? µp????µe
  pa?t?te ?a e?f?as??µe t? p??ß??µa t?? ap?fas??
  µeta?? e??? ?e????? s?µe??? µe t?? a???????
  µ??f?
• 
  e??a? ? ????e?de?a ap?stas? µeta?? t??
  s?µe??? sj ?a? si .
• ??t? s?µa??e? ?t?

Rj Ri
sj' - di,j/2 0
si' di,j/2
112
?? Union Bound (te???? µ??f?)
G?a ?s?p??a?a s?µß??a
????ßeste?? µ??f? t?? Union Bound
?p?? ?i e??a? t? s????? t?? ??µat?µ??f?? µe
pe????e? ap?fas?? efapt?µe?e? t?? Rj
113
?fa?µ??? t?? Union Bound st? QPSK
s2
?Es

• ?? ap?stase?? µeta?? s?µat?? e??a?
• d1,2 d1,4 d2,3 d3,4 ??2Es ?4Eb
• d1,3 d2,4 2?Es ??8Eb
• ????ß?? ?p?????sµ??
• Union Bound
• ?e?t??µe?? Union Bound

?
s1
s3

?
?
?Es
s4
?
114
? a???ße?a t?? Union Bound

• T? Union Bound e??a? ??a a?? ???? d??t? µp??e? se
  µe???e? pe????e? ?a ????????s??µe d?? f??e?.
• ?? Union Bound e??a? p??? a???ße?, ?d??? ??a
  ????e? s?µat?-????ß??e? s?ese?? ?b/N0

115
Union Bound ??a M-ary PSK

• S????? ??µat?µ??f??
• S??a?t?se?? ßas??
• ??a??sµat??? pa?astas? t?? s?µat??
• m 1,2,,M

116
????? s?µat?? t?? 8-ary PSK





??s



117
?p?????sµ?? t?? sfa?µat?? s?µß???? ??a t? M-ary
PSK

• ???e s?µa e?e? d?? ?e?t????e? pe????e? ap?fas??.
• ???? t?? s?µµet??a?, ? ap?stas? di,j µeta?? ????
  t?? ?e?t?????? pe?????? e??a? ?d?a ?a? ?s? µe
• Union Bound (Mgt2)

?
R2
s2
R1
?
s1?Es 0
G???a p/M
118
S?????s? ep?d?se?? ??a M-ary PSK
119
16- QASK
00 01 11 10
00 01 11 10
? aste??sµ?? s?µat?? ?a? ?? pe????e? ap?fas??
fa????ta? st? d?p?a?? s??µa. ??a??????µe 3
?at?????e? s?µe??? ?a ????a?a s0,
s3, s12, s15 ?a e??te???a s1, s2, s4,
s7, s8, s11, s13, s14 ?a es?te???a s5,
s6, s9, s10 G?a ?a?e ?at?????a e???µe a???
p??a??t?ta sfa?µat??. ?a? ed? ?a ?p?????s??µe
p??ta t?? p??a??t?ta s?st?? ap?fas?? P(Cm) 1
P(Em)

G???a?a s?µe?a ?p??et??µe ?t? ste??eta? t? s0
??te rn s0nwn ?a?
?ts?
?a? ep?µe???
120
16-QASK (s??e?.)
???te???a s?µe?a ?p??et??µe ?t? ste??eta? t? s1
??te rn s1nwn ?a?
?ts?
?a? ep?µe???
?s?te???a s?µe?a ?p??et??µe ?t? ste??eta? t? s5
??te rn s5nwn ?a?
?ts?
?a? ep?µe???
121
16-QASK (s??e?.)
??a?efa?a?????ta?
?a? epe?d? Eavg 10 ?2 ?a? s2 ?0/2
122
????????a s????a s?µat??

• ? s??a?t?se?? ßas?? f1(t),fM(t)
• M s?µata
• ?a?astas? st?? ???? s?µat??
• ?a?ade??µa ??a ?4 s1?Es 0 0 0, s20 ?Es 0
  0,
• s30
  0 ?Es 0, s40 0 0 ?Es
• ?a?ade??µa ??a M-ary FSK

123
?p?????sµ?? t?? Union Bound ??a M-ary ????????a
s?µat?d?s?a

• ?a?ade??µa 3-ary ?????????? ????? s?µat??

??s
?
?
??s
??s
?
124
?a?at???se?? ep? t?? p??a??t?ta? sfa?µat?? ??a
????????a s?µata

• ?? ep?d?se?? ße?t?????ta? ?a??? t? ? a??a?e?.
• St? ???? (?a??? ???), ? p??a??t?ta sfa?µat??
  µp??e? ?a ???e? a??a??eta µ????, ef' ?s?? ?b/?0 gt
  - 1.6db.
• Ta pe??ss?te?a s?st?µata ???s?µ?p????? µ?-s?µf???
  FSK (non-coherent FSK) a?t? t?? s?µf???? FSK.
• ? ????????a s?µat?d?s?a ep?t???a?e? ße?t?ste?
  ep?d?se?? ?a??? t? ???, a??a ?a? ??a pepe?asµe??
  ? ?pa??e? d??at?t?ta ße?t??se??.

125
S????? ??a t? Union Bound

• T? Union Bound ep?t?epe? t?? ?p?????sµ? t??
  p??a??t?ta? sfa?µat?? ??a a??a??eta d?a??aµµata
  aste??sµ??.
• ?ste??sµ?? s?µat?? p????? d?astase?? (?p?? t?
  FSK) µp????? ?a ?????? p??? ap?d?t????, ap?
  e?e??e?a?? ap???, ?a??? t? ? µe?a???e?.
• ?ste??sµ?? s?µat?? sta?e??? d?astase?? (p.?. ?2.
  ?p?? t? PSK ?a? t? QAM) de? ???s?µ?p?????
  ap?d?t??a t?? e?e??e?a ?a??? t? M µe?a???e?

126
?? s?µf???? ?e?te?(Noncoherent Rx)

• ?e??? t??a ?e???saµe ?t? ???? ?? de?te? e??a?
  s?µf???? (Coherent d??. e??a? se ?es? ?a
  a????e?s??? ?a? ?a pa?a???????s??? t?? fas? t??
  ?aµßa??µe??? s?µat??).
• G?a t?? t??ef????e? ??aµµe?, t?? µ??????µat??e?
  ?e??e??, ?a? ???sµ??e? d???f?????? ?e??e?? ?
  s?µf??? ???? e??a? ef??t?.
• ??????t? ?p?????? st?? p???? s?st?µata ??a?? ?a
  pa?a???????s??? t?? f?s? e??? s?µat?? (p.?. ??
  phase locked loops) se p????? pe??pt?se?? e??a?
  d?s????? ? a?st???? s???????sµ?? f?s??.
• G?a p???? s?st?µata as??µat?? ?a? ????t??
  ep??????????, ?? p???ap??? d??de?se?? ?a? ?
  ????s? t?? de?t? eµp?d????? t?? s???????sµ? fas??.

127
??p?? µ? s?µf???? de?t??

• ?a PSK ?a? QAM s?µata µetafe???? p????f???a µe
  t?? fas? t?? fe???t??.
• Se p???e? pe??pt?se??, µ?????t? de? e??a? d??at?
  ? a????e?s? t?? ap???t?? t?µ?? t?? fas?? e???
  s?µat??, e??a? ef??t? ? a????e?s? t?? d?af??a?
  fase?? ap? t? e?a s?µß??? st? ep?µe??.
• G?a t? FSK µe t????? (s????t?te? fe???t??) a??eta
  ap?µa???sµe?e? , ? ap?d?aµ??f?s? µp??e? ?a
  ep?te???e? ????? ?aµ?a p????f???a fas?? µe ???s?
  e??? µ? s?µf???? de?t?

128
??af????? ??d???p???s? ded?µe???

• Te????µe t?? d?aµ??f?s? BPSK
• 0 gt s(t) ?2P cos(2pfct), ??a t?0, T
• 1 gt s(t) ?2P cos(2pfctp) - ?2P
  cos(2pfct), ??a t?0, T
• ? d?af????? ??d???p???s? µetas??µat??e? ta
  p??t??e?? ded?µe?a
• ?a???a? ????µe a??a?? e?peµp?µe??? bit ?a?
  ep?µe??? ?a? t?? fas?? a? to bit e?s?d?? e??a? 1

di
bi
BPSK Mod.
?
1 bit delay
bi di ?bi-1 bi-1 a? di1, bi-1 a? di0
129
pa?ade??µa ??af?????? ??d???p???s??

• di 0 1 0 1 1 1 0 data
• bi-1 0 0 1 1 0 1 0
• bi 0 1 1 0 1 0 0 Tx symbol
• Fas? 0 0 p p 0 p 0 0

bi di ?bi-1 1 a? di ? bi-1 0
a? di bi-1
130
S?µf??? (coherent) ???? d?af????a ??d???p???µe???
ded?µe???

• ? d?af????? ??d???p???s? s???a ???s?µ?p??e?ta?
  a??µa ?a? a? e??a? ef??t? ? s?µf??? ????
• di 0 1 0 1 1 1 0
• bi-1 0 0 1 1 0 1 0
• bi 0 1 1 0 1 0 0 Rx symbol
• di 0 1 0 1 1 1 0

di
r(t)
bi
BPSK Demod.
?

1 bit delay
bi-1
bi di ?bi-1
Data


di bi ?bi-1(di ? bi-1)? bi-1di ? 0 di
131
??af????? ????

• ?p????µe ?a ?e???s??µe t?? d?af????? ???? sa?
  µe??d? ????? p?? ???s?µ?p??e? t? ?aµßa??µe?? s?µa
  r(t) st?? p??????µe?? pe???d? bit sa? s?µa
  a?af??a? fas?? ??a t?? ?p?????sµ? t?? s?s?et?s??.

132
S?????s? ep?d?se?? BPSK ?a? DPSK
?eta ap? p???p???? a?a??s? p????pte? ?t? ??a t?
DPSK ?s??e? Pb (1/2)exp(-Eb/N0)
DBPSK
H µe?a??te?? p??a??t?ta sfa?µat?? t?? DBPSK
?fe??eta? st?? a?????e?a?t?s? t?? s?µß????
133
??af????? ???? p???ap??? s?µat??

• Sta p??????µe?a as???????aµe µe t?? d?ad???
  pe??pt?s? t?? D?PSK, a??a e??a? fa?e?? ?t?
  µp????µe ?a ???s?µ?p???s??µe d?af?????
  ??d???p???s? ?a? ap???d???p???s? µe ???e t?p?
  d?aµ??f?s?? fas??.
• ?e t? DQPSK e???µe 4 d??ate? µetat?p?se?? fas??
  0, 90, 180 ?a? 270 µ???e?.
• ? p/4 DQPSK d?aµ??f?s? e?sa?e? µ?a ep?p?e??
  µetat?p?s? fas?? ?at? p/4 (450) µe ???e s?µß???
  ??a ?a e?att??e? ? p??a??t?ta sfa?µat?? ?????sµ??
  s?µß???? (p?? µp????? ?a eµfa??s???? a?
  µetad?deta? s??e??? fe??? µe sta?e?? fas? p.? a?
  ?pa??e? µ?a µa??a a???????a ap? 0 ? 1)
• ?? p/4 DQPSK ???s?µ?p??e?ta? st? s?st?µa ????t??
  t??ef???a? ??-?DMA t?? ???.

134
?? s?µf??? ???? FSK

• ?a s?µata FSK p?? e???? a??et? ap?stas? st? ped??
  s????t?t??, µp????? ?a ap?d?aµ??f????? ?????
  ?a????? p????f???a fas?? st?? d??t?.
• ? ße?t?st?? µ? s?µf???? ap?d?aµ??f?t?? ??a t? FSK
  µp??e? ?a ?e????e? sa? e?a? a????e?t?? e?e??e?a?.
• ? d?aµ??f?t?? FSK µe µ? s?µf??? ap?d?aµ??f?t?
  ap?te???? e?a f???? a??a e???st? s?st?µa
  ep????????a? ?ata????? ??a as??µate? efa?µ??e?.

135
??µ? t?? ße?t?st?? µ? s?µf???? de?t? ??a t?
d?ad??? FSK

r1c
(.)2
?
?p????? µe?a??te???
f1c(t)
S
r1s
(.)2
?
r(t)
f1s(t)
r2c
(.)2
?
f2c(t)
S
r2s
(.)2
?
f2s(t)
136
?p?d?se?? t?? ?-ary FSK ßase? t?? Union Bound

137
?e?????? ??a t??? µ?-s?µf????? de?te?

• ? d?af????? f??as? ( Differential detection)
  e??a? ?ata????? ??a t?? ap?d?aµ??f?s? fas??.
• ? µ?-s?µf??? f??as? e??a? ?ata????? ??a t??
  ap?d?aµ??f?s? s????t?ta?.
• ? pa?astas? st?? ???? t?? s?µat?? ?d??e? st??
  ße?t?st? d??t? ?a? se µe??d? a???????s??
  ep?d?se??.
• ?? µ?-s?µf??? FSK µp??e? ?a ???e? p??? a??e?t???
  st?? ????ß?.
• ?? FSK p???ap??? s????t?t?? e??a? p???
  ??????µ??? ap? e?e??e?a?? ap??? a??a de? e??a?
  ??????µ??? st?? e?µeta??e?s? t?? fasµat??.