S?ed?as?

1
S?ed?as? ße?t?st?? de?t??e?t?? s?s?et?s???e?t??
p??sa?µ?sµe??? f??t??????a??t?ta sfa?µat??
??430 ??f?a?e? ?p????????e?
2
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?e s?µa µp??e? ?a ??afte? sa? ??aµµ????
  s??d?asµ??

3
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??
4
?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? t?? 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?
• ??? ?ata???? 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??

5
???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?
6
?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???.

7
??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??

8
??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??

9
?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)

10
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)
• O ????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)
11
?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

12
H s???st?sa n'(t) e??a? ????????a p??? ??a ta
s?µata sm(t)

• ??a?µat?

13
?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)
14
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
15
?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)

16
?a???a? ?p?fas?? µe??st?? p??a??fa?e?a?ML
(Maximum Likelihood)

• ?? p1p2pm 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)

17
?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??

18
?p?????sµ?? t?? pdf t?? ????ß??, p(n)

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

19
?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)
20
? ?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???

21
??µ? t?? ße?t?st?? ?e?t?

• ?a???a? ap?fas?? MAP

22
?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)
23
??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

24
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??

25
??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)
26
?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?

?e?t?? s?s?et?s?? Correlation Receiver
s?(t)
27
???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)
28
???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)
29
? ?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"

30
???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??
31
???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)
32
?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
33
?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)
34
?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)
35
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
36
?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
37
?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
38
??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
39
??ad????e? ap?fase?? t?? de?t? s?s?et?s??
40
?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
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46
?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)
47
?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?.

48
???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??

49
?e????e? ?p?fas??

• ?e?t?st?? ?a???a? ap?fas??
• ?st? ?t? ? e??a? ? pe?????
  ?p??
• ? j?m
• ??te ? 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???)

50
?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??.
• ?? 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?.

51
???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 ?ta? p?a?µat? ste??eta? t? si.
  ???a?
• P(Esi)
• ????µe p???ap?? ????????s? st?? pe????? Ri d??t?
  ? pdf e??a? ? d?astase??

52
?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 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)

53
?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
54
???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
s1 ?Eb r
s2 - ?Eb
55
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? ??a t? BPSK

???ad?
56
(No Transcript)
57
???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

58
G?af??? pa?astas? t?? p??a??t?ta? sfa?µat?? ??a
t? BPSK

59
?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??

60
?e????e? ap?fas?? ??a t? d?ad??? s?µf??? FSK
f2(t)

R2
s2
R1
f1(t)
s1

?e pe??st??f? ?a? µeta????s? t?? a????? e???µe
R2
R1


s2' - ?Eb/2 s1' ?Eb/2
61
?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??? ??a t? BFSK µe
  a?t??atastas? t?? ??b µe t? ?Eb/2 ß??s???µe
  ?t?

62
??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
63
?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? µeta?es? a????? gt
R2 R1
R2 R1
?
X
X
?
s20 ?Eb/2 s1?2Eb
s2-?Eb/2 0 s1?Eb/2
64
??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)

65
?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???

66
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

67
M4 Quadrature PSK (QPSK)

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

68
??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?? d?a pe??st??f?? ?a?ade??
µa
69
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.

70
???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????

71
?? d?a??aµµa aste??sµ?? t?? QPSK ?a? ?? pe????e?
ap?fas??
f2

s2
?
s1
s3
?
?
f1
s4
?
72
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
73
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? s?µ???? ??a
t? QPSK

74
?p?????sµ?? t?? p??a??t?ta? sfa?µat?? s?µ???? ??a
t? QPSK (2)

75
???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? e??a? ta BPSK ?a? QPSK e????
  ?d?? BER.

76
??R d?a??aµµata ??a t? QPSK ?a? t? BPSK

77
?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??