©2000 bg mobasseri where am i?. ©2000 bg mobasseri basic isdea for a receiver to demultiplex a tdm...
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![Page 1: ©2000 BG Mobasseri Where am I?. ©2000 BG Mobasseri BASIC ISDEA For a receiver to demultiplex a TDM signal, it must know where the beginning of a frame](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f395503460f94c560cb/html5/thumbnails/1.jpg)
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Where am I?
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BASIC ISDEA
For a receiver to demultiplex a TDM signal, it must know where the beginning of a frame is
To do this, transmitters embed a special N-bit sync word called marker
Initially, several repetitions of the sync word precedes the data
message
start of messageN-bit sync
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SLIDING CORRELATOR
Knowing the synchronization codeword, the receiver constantly “looks” for it in the data
This task is accomplished by a correlation or matched filter detector. Let’s look at a 4-bit sync: {c1,c2,c3,c4}
AkAk-1 Ak-2 Ak-3 Ak-4
frameindicator
V
Vk+
-
c1 c2 c3 c4
data bits slide in and out
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WORKINGS OF A SLIDING CORRELATOR
AkAk-1 Ak-2 Ak-3 Ak-4
frameindicator
V
Vk+
-
c1 c2 c3 c4
{C1, C2, C3,C4} define the frame marker. Then
vk = cii=1
N
∑ ak−i
N : (4 )frame marker length here
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HOW FRAME BEGINNING IS SENSED?
As data slides by the N-bit synch word, Vk takes on different values
There comes a time when the N-bit sync word fills the N-stage shift register. In this case, Vk achieves its maximum=N
If the register word differs from the sync word in just one bit, then Vk=N-2(assuming 1 pulses)
To sense the frame beginning, therefore, set the threshold voltage to slightly below N-2
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CASE OF FALSE FRAME
False synchronization is sensed when N or N-1 successive message bits match the sync-word bit
Can this happen?. Yes, question is with what probability?
Assuming equally likely +1’s and -1’s
Pff =P falseframe{ } =12 ⎛ ⎝ ⎞ ⎠
N
+ 12 ⎛ ⎝
⎞ ⎠
N−1
=3×2−N
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T1 SYNCHRONIZATION
T1 line uses a single bit per frame but framing bit sequence is known, i.e. if many individual framing bits are strung along, they form a known pattern
To acquire sync, several frames must be buffered, framing bits extracted and matched against the known pattern
1 0 1 0
frame
1 0 1 0 ...
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PROPERTIES OF GOOD SYNC WORDS
Since large false correlations result in wrong synchronization, synch word pattern must have several important properties
One such property is that they should have very small partial correlation with their shifted versions
The reason is that at certain times the shift register contains a part of the sync word as data is passing through
buffer
sync word
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AN EXAMPLE
buffer
sync word
buffer
sync wordMATCH
partial crosscorrelationshould be small
ShiftedVs. sync
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DESIRABLE CROSS CORRELATIONS
1 lag
N
1/N
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LENGTH-5 SYNC WORD
Ck = xjj=1
N−k
∑ xj+k
C0=5
C1=0
+1
-1
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BARKER SYNC CODES
Barkers sequences have the property that their largest sidelobes have a magnitude of 1.
N(length of code) Barker sequence(+/- are pulse ampl.)
1 +2 ++ or + -3 + + -4 + + + - or + + - +5 + + + - +7 + + + - - + -11 + + + - - - + - - + -13 + + + + + - - + + - + - +