©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 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

©2000 BG Mobasseri

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

©2000 BG Mobasseri

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

©2000 BG Mobasseri

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

©2000 BG Mobasseri

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

©2000 BG Mobasseri

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 ...

©2000 BG Mobasseri

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

©2000 BG Mobasseri

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

©2000 BG Mobasseri

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 + + + + + - - + + - + - +