s-72.245 transmission methods in telecommunication systems (4 cr)
DESCRIPTION
S-72.245 Transmission Methods in Telecommunication Systems (4 cr). Review. 25. Filt. Phase detector. VCO. Divide by 10. PLL based frequency synthesizer. Reference signal f in is locked for instance to the fundamental frequency of a crystal oscillator. By adjusting the - PowerPoint PPT PresentationTRANSCRIPT
S-72.245 Transmission Methods in Telecommunication Systems (4 cr)
Review
2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen25
3 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
4 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
5 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
6 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
PLL based frequency synthesizer
VCOVCO
Filt.Filt.Phasedetector
Phasedetector
Divide by10
Divide by10
10out in
f f
inf
By adjusting thedivider differentfrequencies can be producedwhose phase is locked into fin
Reference signal fin
is locked for instanceto the fundamental frequency of a crystal oscillator
7 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Detecting DSB using PLL-principle
An important application for PLLs is in synchronization of receiver local oscillator in synchronous detection
In the Costas PLL (below) two phase discriminators are used to:– cancel out DSB modulation x(t) in the driving signal– synchronize the output frequency to the center frequency of the
DSB spectra (the suppressed carrier)– to detect the DSB signal
Cos
tas
PL
L d
etec
tor
for
DS
B
PD: phase detector (=multiply+LPF)
Loop drives phase error to zero
LPF yields constant (zero) output when loop is locked to carrier
1sin cos sin 2 sin 02ss ss ss ss
8 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
PAM Power Spectral Density (PSD) PSD for PAM can be determined by using a general expression
For uncorrelated message bits
and therefore
on the other hand and
21( ) ( ) ( )exp( 2 )
x an
G f P f R n j nfDD
Amplitude autocorrelation
2 2
2
, 0( )
, 0
a a
a
a
m nR n
m n
2 2( )exp( 2 ) exp( 2 )
a n an n
R n nfD m j nfD
1exp( 2 )
n n
nj nfD f
D D
2 22 2 2( ) ( ) ( ) ( )
x a an
G f r P f m r P nr f nr
1/r D
Total power
DC power
9 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
PAM Power Spectral Density (PSD) PSD for PAM can be determined by using a general expression
For uncorrelated message bits
and therefore
on the other hand and
21( ) ( ) ( )exp( 2 )
x an
G f P f R n j nfDD
Amplitude autocorrelation
2 2
2
, 0( )
, 0
a a
a
a
m nR n
m n
2 2( )exp( 2 ) exp( 2 )
a n an n
R n nfD m j nfD
1exp( 2 )
n n
nj nfD f
D D
2 22 2 2( ) ( ) ( ) ( )
x a an
G f r P f m r P nr f nr
1/r D
Total power
DC power
10 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example For unipolar binary RZ signal:
Assume source bits are equally alike and independent, thus
1( ) sinc
2 2
b b
fP f
r r
/ 22 2 2 2 2
0
(1/ 2 ) / 4,bT
a b a aT A dt A m
2 2
2 2( ) sinc ( )sinc16 2 16 2x b
nb b
A f A nG f f nr
r r
22
22 2
( ) ( )
( ) ( )
x a
an
G f r P f
m r P nr f nr
22 1
4 2b
b
Ar
r
11 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Equalization: Removing Residual ISI Consider a tapped delay line equalizer with
Search for the tap gains cN such that the output equals zero at sample intervals D except at the decision instant when it should be unity. The output is (think for instance paths c-N, cN or c0)
that is sampled at yielding
( ) ( ) N
eq nn N
p t c p t nD ND
( ) ( ) ( )N N
eq n nn N n N
p kD ND c p kD nD c p D k n
k
t kD ND
( ) ( 2 )N N
p t c p t ND
( ) ( )N N
p t c p t
0( ) ( )
Np t c p t ND
12 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Tapped Delay Line: Matrix Representation
At the instant of decision:
That leads into (2N+1)x(2N+1) matrix where (2N+1) tap coefficients can be solved:
1, 0
( ) ( )0, 1, 2,...,
N N
eq k n nn N n N k n
kp t c p D k n c p
k N
0 2
1 1 1
0
1 1 1
2 0
... 0
...
... 0
... 1
... 0
... 0
N N
N N
N N
N N
N N
p p c
p p c
p p c
p p c
p p c
0 1 1 2
1 0 1 2 1
1 1
2 2 1 1 0
... 0
... 0
... 1
... 0
n n n n
n n n n
n n n n n n
n n n n n
p c p c p c
p c p c p c
p c p c p c
p c p c p c
0 1 2
1
n
n n n
p p p
c c c
+( )
eqp t
( )p t
13 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example of Equalization
Read the distorted pulse values into matrix from fig. (a)
and the solution is
1
0
1
1.0 0.1 0.0 0
0.2 1.0 0.1 1
0.1 0.2 1.0 0
c
c
c
1
0
1
0.096
0.96
0.2
c
c
c
Zero forced values
0p
1p
2p
1p
2p
Question: what does thesezeros help because they don’texist at the sampling instant?
14 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Monitoring Transmission Quality by Eye Diagram
Required minimum bandwidth is
Nyqvist’s sampling theorem:
/ 2T
B r
Given an ideal LPF with thebandwidth B it is possible totransmit independent symbols at the rate:
/ 2 1/(2 )T b
B r T