digital transmission s-72.1140 transmission methods in telecommunication systems (5 cr)
Post on 27-Dec-2015
215 Views
Preview:
TRANSCRIPT
Digital Transmission
S-72.1140 Transmission Methods in Telecommunication Systems (5 cr)
2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
I Baseband Digital Transmission
Why to Apply Digital Transmission? Digital Transmission Symbols and Bits
– M-level Pulse Amplitude Modulation (PAM)– Line codes (Binary PAM Formats)
Baseband Digital Transmission Link– Baseband Unipolar Binary Error Probability – Determining Decision Threshold – Error rate and Q-function – Baseband Binary Error Rate in Terms of Pulse Shape and
Pulse Shaping and Band-limited Transmission– Signaling With Cosine Roll-off Signals– Matched Filtering– Root-raised cos-filtering
Eye diagram
3 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
II Carrier Wave Digital Transmission
Waveforms of Digital Carrier Wave Communications Detection of Digital CW
– Coherent Detection• Error rate; General treatment
– Non-coherent Detection• Example of error rate determination (OOK)
Timing and Synchronization Error rate for M-PSK Error rate for M-QAM Comparison of digital CW methods
4 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Why to Apply Digital Transmission? Digital communication withstands channel noise, interference
and distortion better than analog system. For instance in PSTN inter-exchange STP*-links NEXT (Near-End Cross-Talk) produces several interference. For analog systems interference must be below 50 dB whereas in digital system 20 dB is enough. With this respect digital systems can utilize lower quality cabling than analog systems
Regenerative repeaters are efficient. Note that cleaning of analog-signals by repeaters does not work as well
Digital HW/SW implementation is straightforward Circuits can be easily configured and programmed by DSP
techniques Digital signals can be coded to yield very low error rates Digital communication enables efficient exchange of SNR to
BW-> easy adaptation into different channels The cost of digital HW continues to halve every two or three
years
STP: Shielded twisted pair
5 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
DigitalTransmission
‘Baseband’ means that no carrier wave modulation is used for transmission
Information:- analog:BW & dynamic range- digital:bit rate
Information:- analog:BW & dynamic range- digital:bit rate
Maximization of information transferred
Maximization of information transferred
Transmitted power;bandpass/baseband signal BW
Transmitted power;bandpass/baseband signal BW
Message protection & channel adaptation;convolution, block coding
Message protection & channel adaptation;convolution, block coding
M-PSK/FSK/ASK..., depends on channel BW & characteristics
M-PSK/FSK/ASK..., depends on channel BW & characteristics
wireline/wirelessconstant/variablelinear/nonlinear
wireline/wirelessconstant/variablelinear/nonlinear
NoiseNoise
InterferenceInterference
ChannelChannel
ModulatorModulator
ChannelEncoder
ChannelEncoder
Source encoder
Source encoder
Channel decoder
Channel decoder
Source decoder
Source decoder
DemodulatorDemodulator
Information sink
Information sink
Information source
Information source
Message Message estimate
Received signal(may contain errors)
Transmitted signal
InterleavingInterleaving
Fights against burst errors
Fights against burst errors
DeinterleavingDeinterleaving
In baseband systemsthese blocks are missing
6 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Symbols and Bits – M-ary PAM
1 1 00 1 11 110 1 0
bi ( 1/ ) ts/sb b bT r Tbitrate
( 1/ )D r Dsymbol rate baud
2nM
:
:
:
number of bits
: number of levels
Symbol duration
Bit duaration
b
n
M
D
T
2logn M
( ) ( ) k
ks t a p t kD
For M=2 (binary signalling):
For non-Inter-Symbolic Interference (ISI), p(t) mustsatisfy:
This means that at the instant of decision, received signal component is
( ) ( ) k b
ks t a p t kT
1, 0( )
0, , 2 ...
tp t
t D D
( ) ( ) ( )k K K K
ks t a p t kD a p t a
Generally: (a PAM* signal)
( )s t
*Pulse Amplitude Modulation
7 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Binary PAM Formats (1)
Unipolar RZ and NRZ
Polar RZ and NRZ
Bipolar NRZ or alternate mark inversion (AMI)
Bit stream
Split-phase Manchester
8 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Binary PAM Formats (2)
Unipolar RZ, NRZ:– DC component has no information, wastes power– Transformers and capacitors in route block DC– NRZ, more energy per bit, synchronization more difficult
Polar RZ, NRZ:– No DC term if ´0´and ´1´ are equally likely
Bipolar NRZ– No DC term
Split-phase Manchester – Zero DC term regardless of message sequence– Synchronization simpler– Requires larger bandwidth
9 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Baseband Digital Transmission Link
( ) ( ) ( ) k d
ky t a p t t kD n t
( ) ( ) ( )
K k kk K
y t a a p KD kD n t
message reconstruction at yields K d
t KD t
message ISI Gaussian bandpass noise
Uni
pola
r P
AM
original message bits
decision instances
received wave y(t)
Dt
10 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Baseband Unipolar Binary Error Probability
r.v. : ( ) ( ) k k k
Y y t a n t
The sample-and-hold circuit yields:
0
0
: 0,
( | ) ( )
k
Y N
H a Y n
p y H p y
Establish H0 and H1 hypothesis:
1
1
: 1,
( | ) ( )
k
Y N
H a Y A n
p y H p y A
and
pN(y): Noise probability density function (PDF) at the time
instance of sampling
Assume binary & unipolar x(t)
11 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Determining Decision Threshold0
0
: 0,
( | ) ( )
k
Y N
H a Y n
p y H p y
1
1
: 1,
( | ) ( )
k
Y N
H a Y A n
p y H p y A
Choose Ho (ak=0) if Y<VChoose H1 (ak=1) if Y>V
The comparator implements decision rule:
1 1 1
0 0
( | ) ( | )
( | ) ( | )
V
e Y
Veo Y
p P Y V H p y H dy
p P Y V H p y H dy
Average error error probability: 0 0 1 1
e e eP PP PP
120 1 0 1
1/ 2 ( ) e e e
P P P P P
Channel noise is Gaussian with the pfd:2
2
1( ) exp
22N
xp x
Transmitted ‘0’but detected as ‘1’
12 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Error rate and Q-function
21( ) exp
22 k dQ k
x m
0( )
Ve N
Vp p y dy Q
2
0 2
1exp
22Ve
xp dx
This can be expressed by using the Q-function
by
and also
0( )
Ve Np p y dy
1( )
V
e N
A VP p y A dy Q
m: mean2: variance
0ep
1ep
13 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Assigment
14 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Solution
15 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Baseband Binary Error Rate in Terms of Pulse Shape
12 0 1 0 1( )
2e e e e e e
Ap p p p p p Q
for unipolar, rectangular NRZ [0,A] bits
setting V=A/2 yields then
2 2 21 1( ) (0) / 2
2 2RS A A
for polar, rectangular NRZ [-A/2,A/2] bits
2 2 21 1( / 2) ( / 2) / 4
2 2RS A A A
and hence
2 2
2
/(2 ),unipolar
/ ,polar2 4R R
R RRRN
S NA AS NN
probability of occurrence for bits ’0’ and ’1’
16 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Assignment Determine average power for the following signals
T
T
A
-A
A
-A
A/2
-A/2
17 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Solution
T
A
-A
A
-A
A/2
-A/2
2 2 21 1( ) ( )
2 2RS A A A
T
2 2 21 1 5( ) ( / 2)
2 2 8RS A A A
18 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Pulse Shaping and Band-limited Transmission
In digital transmission signaling pulse shape is chosen to satisfy the following requirements:– yields maximum SNR at the time instance of decision
(matched filtering)– accommodates signal to channel bandwidth:
• rapid decrease of pulse energy outside the main lobe in frequency domain alleviates filter design
• lowers cross-talk in multiplexed systems
19 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Signaling With Cosine Roll-off Signals
Maximum transmission rate can be obtained with sinc-pulses
However, they are not time-limited. A more practical choice is the cosine roll-off signaling:
( ) sinc sinc /
1( ) [ ( )]
p t rt t D
fP f F p t
r r
2
2( ) sinc
1 (4 )
cos tp t rt
t
2
/ 2
1( ) cos ( / 2 )
2
r
fP f f r
r r
for raised cos-pulses =r/2
20 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Unipolar and Polar Error Rates in Terms of Eb/No
Eb/No is often indicated by
For sinc- pulse signalling the transmission BW is limited toand therefore noise before decision is limited to
and therefore
0 0/ /
b R bbNE S rN
0 0/ 2
R N bN N B N r
/ 2N b
B r
2
0 0
0 0
/(2 ) 2 /(2 ) ,unipolar
/( ) 2 / 2 ,polar2R R b b b b
R R b b b b
S N N r N rAS N N r N r
( ) ( )2 ,
2e e polar b e unipolar b
Ap Q p Q p Q
21 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Matched Filtering
( ) ( )exp( ) ( ) ( )d d
H f KP f j t h t Kp t t ( ) ( )exp( ) ( ) ( )d d
H f KP f j t h t Kp t t
0
0
( ) ( )
( ) ( )exp( )R R
R R
x t A p t t
X f A P f j t
0
1[ ( ) ( )]
( ) ( )exp
dR
R d
t t tA F H f X f
H f P f j t dfA
2 22 ( ) ( ) ( )2n
H f G f df H f df
2
2
2
2
( ) ( )exp
( )2
d
R
H f P f j t dfAA
H f df
H(f)H(f)++( )
Rx t
( )2n
G f
( )D
y t
Should be maximized
Post filter noise
Peak amplitude to be maximized
Using Schwartz’s inequality2
2 2
( ) * ( ) ( ) ( )V f W f df W f df V f df
22 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Assignment
What is the impulse response of the matched filter for the following signaling waveform?
How would you determine the respective output signal (after the matched filter)?
T
A
23 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Avoiding ISI and enabling band-limiting inradio systems
Two goals to achieve: band limited transmission & matched filterreception
Hence at the transmitter and receiveralike root-raised cos-filtersmust be applied
TXfilt.
RXfilt.
Decisiondevice
noise
data
( )T f ( )R f
( ) ( ) ( ), raised-cos shaping
( ) *( ), matched filteringN
T f R f C f
T f R f
( ) ( ) ( )N
R f T f C f
raised cos-spectra CN(f)
24 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
25 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Assignment
How many eye/openings you have in an M-level signaling?
S-72.1140 Transmission Methods in Telecommunication Systems (5 cr)
Digital Bandpass Transmission
27 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Binary Waveforms in Carrier Wave Communications
ASK
FSK
PSK
DSB
28 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Carrier Wave Communications
Carrier wave modulation is used to transmit messages over a distance by radio waves (air, copper or coaxial cable), by optical signals (fiber), or by sound waves (air, water, ground)
CW transmission allocates bandwidth around the applied carrier that depends on– message bandwidth and bit rate– number of encoded levels (word length) – source and channel encoding methods
Examples of transmission bandwidths for certain CW techniques:
MPSK, M-ASK Binary FSK (fd=rb/2)
MSK (CPFSK fd=rb/4), QAM:
2/ / log ( 2 )
T b b
nB r r n r M M T b
B r/ 2
T bB r
FSK: Frequency shift keyingCPFSK: Continuous phase FSK
29 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Digital CW Detection
At the receiver, detection can be– coherent (carrier phase information used for detection)– non- coherent (no carrier phase used for detection)– differentially coherent (‘local oscillator’ synthesized from
received bits) CW systems characterized by bit or symbol error rate (number
of decoded errors(symbols)/total number of bits(symbols)) Number of allocated signaling levels determines constellation
diagram (=lowpass equivalent of the applied digital modulation format)
30 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Coherent Detection by Integrate and Dump / Matched Filter Receiver Coherent detection utilizes carrier phase information and requires in-
phase replica of the carrier at the receiver (explicitly or implicitly) It is easy to show that these two techniques have the same
performance:
( )s t
( ) ( )h t s t
0( ) ( ) ( )v t s t y d
0
( ) ( ) ( )
( ) ( )
v t s t y t
s t y d
( )s t
( )y t
( )y t ( )v T
( )v T
31 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Non-coherent Detection
2-ASK
2-FSK
Base on filtering signal energy on allocated spectra and using envelope detectors
Has performance degradation of about 1-3 dB when compared to coherent detection (depending on Eb/N0)
Examples:
32 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Coherent (Optimum) Binary Detection
Received signal consists of bandpass filtered signal and noise that is sampled at the decision time instants tk yielding decision variable:
Quadrature presentation of the signaling waveform is
Assuming that the BPF has the impulse response h(t), signal component at the sampling instants is then expressed by
( )k m
Y y t z n
( 1)
0
( ) ( ) ( ) ( )
( ) ( )
b
b
b
m m b m k
m b
bk
k T
kT
T
t tz s t kT h t s h t d
s h d
kT
T
( ( ) x( ) ( ) )A
x y t y t d
0,1m
( ) ( )cos( ) ( )sin( )m C k i C k q C
s t A I p t t Q p t t
33 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Optimum Binary Detection - Error Rate Assuming ‘0’ and ‘1’ reception is equally likely, error happens
when H0 (‘0’ transmitted) signal hits the dashed region or for H1 error hits the left-hand side of the decision threshold that is at
1 0( ) / 2optV z z
2 020 0
0 1 1 0
1exp / 2
2
( ) / 2 / 2
opt
opte
e e e
V
V zp z d Q
p p p Q z z
Errors for ‘0’ or/and ‘1’ are equal alike, for instance for ‘0’:
For optimum performancewe have the maximized
SNR that is obtainedby matched filtering/
integrate and dump receiver
2
1 0 / 2z z
xQ
34 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Optimum Binary Detection (cont.)
Express energy / bit embedded in signaling waveforms by
Therefore, for coherent CW we have the SNR and error rate
2
1 0
2
0 0 1
2
1
0 10
0 0
1
0 0
( ) ( )
( ) 2 ( ) ( )
( )b b
b b
T T
T T
E
E E
s s d d
s d s s d
s
Note that the signaling waveform correlation greatly influences the SNR!
2
1 0 1 0 10 1 0 10 10
2
2 / 2
2 2
4 2 2b
e
z z E E E E E E E Ep Q Q
1 0 / 2ep Q z z 1 0 / 2ep Q z z
2max / 2
/ 2b b
o
o
E ESNR N
N
35 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example: Coherent Binary On-off Keying (OOK)
For on-off keying (OOK) the signaling waveforms are
and the optimum coherent receiver can be sketched by
1 0( ) ( )cos , ( ) 0
C Tb Cs t A p t t s t
2 2
1 1 0 10 1 00 0
( ) / 2, 0, ( ) ( ) 0b b
C b
T T
E s d A T E E s s d 2
0 1( ) / 2 / 4
b C bE E E A T 10b b
e b
E E Ep Q Q Q
1/( )R R R b b
b
bW T
S S S T E
36 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Timing and Synchronization Performance of coherent detection is greatly
dependent on how successful local carrier recovery is Consider the bandpass signal s(t) with width Tb rectangular
pulses pTb(t), that is applied to the matched filter h(t): ( ) ( )cos( ),
( ) ( ) ( )cos( )C Tb C
b Tb b C
s t A p t t
h t Ks T t Kp T t t
( )s t( )h t
( )z t
( ) ( ) ( )
cos cos 2b
c c c
b
z s t h t
TKA t
T
2
0
2
( )
/ 2
bT
C b
E s t dt
A T
2
0
2
( )
/ 2
bT
C b
E s t dt
A T
k
t
2 2
1 0 0 0 1
2
1
0 10
0 0 0 0
1
( ) ( ) ( ) 2 ( ) ( )( )b b b bT T T T
E E E
s s d d s d s s ds 2 2
1 0 0 0 1
2
1
0 10
0 0 0 0
1
( ) ( ) ( ) 2 ( ) ( )( )b b b bT T T T
E E E
s s d d s d s s ds
cT
cosb
c
b
TKA
T
( )c
yelding after filtering:
nominal point of inspection at Tb
37 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Analyzing phase error by Mathcad
210 cosb
e
c
E Ep Q
Therefore, due to phase mismatch at the receiver, the error rate is degraded to
38 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example Assume data rate is 2 kbaud/s and carrier is 100 kHz for an BPSK
system. Hence the symbol duration and carrier period are
therefore the symbol duration is in radians
Assume carrier phase error is 0.3 % of the symbol duration. Then the resulting carrier phase error is
and the error rate for instance for is
that should be compared to the error rate without any phase errors or
Hence, phase synchronization is a very important point to remember in coherent detection
1/ 2kbaud/s = 0.5msS
T 31/ 1/100 10 10C C
T f s
10 2314.2rad
0.5ms xs
x
o0.003 0.94 rad 54x
8 9dB 2 2 2( 2 cos ( 16cos 54) 10
ep Q Q
5( 16) 3 10e
p Q
(or carrier cycles)
39 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Error rate for M-PSK
In general,PSK error rate can be expressed by
where d is the distance between constellation points (or a=d/2 is the distance from constellation point to the decision region border) and is the average number of constellation points in the immediate neighborhood. Therefore
Note that for matched filter reception
2e n n
d ap n Q n Q
nn
qn
decision region
000
001
011111
101
100
110
010
d
2 sin( / 2)2 2 2 sin( / )
2 2e
d A Ap Q Q Q M
2
0
2, log ( )
b b
A EE nE M E
N
2M
2nM
/ 2sin( / 2)
d
A
A
40 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Error rate for M-QAM, example 16-QAM
2e n n
d ap n Q n Q
2 2 22 2
4 4 8 3 4 23
4 8 4
4 2 8 10 4 1810
16
nn
a a aA a
2
20
23 3 3
10 10e
a A Ep Q Q Q
N
symbol error rate
Constellation follows from 4-bit words and therefore
0 04
43 2 3
4 10 4 5b
bb
E E
EEp Q Q
N N
2
0
log ,
( ) /
/ 2 /
b
e
n M E nE
p p E n
A E N
2
2
2 3
18
a
a
2 2
2
3
10
a a
a
22a
2a
41 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Non-coherent Detection
42 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example: Non-coherent On-off Keying (OOK)
Bandpass filter is matched to the signaling waveform (not to carrier phase), in addition fc>>fm, and therefore the energy for ‘1’ is simply
Envelopes follow Rice and Rayleigh distributions for ‘1’ and ‘0’ respectively:
2
1( / 2)
b CE T A
distribution for "1"
distribution for ”0”"
43 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Noncoherent OOK Error Rate
The optimum decision threshold is at the intersection of Rice and Rayleigh distributions (areas of error probability are the same on both sides of decision threshold)
Usually high SNR is assumed and hence the threshold is approximately at the half way and the error rate is the average of '0' and '1' reception probabilities
Therefore, error rate for noncoherent OOK equals
0 11
2e e eP P P
2 2
0 0
1 10
/2
/2
( | ) exp /8 exp / 2
( | ) ( / 2 ) ( )
C
C
e Y C b
e Y C b
A
A
P p Y H dy A
P p Y H dy Q A Q
probability to detect "0" in error
probability to detect "1" in error
1 1exp( / 2) ( ) exp( / 2), 12 2e b b b bP Q
44 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Comparison
45 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Error Rate Comparison
a: Coherent BPSKb: DPSKc:Coherent OOKd: Noncoherent FSKe: noncoherent OOK
a: Coherent BPSKb: DPSKc:Coherent OOKd: Noncoherent FSKe: noncoherent OOK
46 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Comparison of Quadrature Modulation Methods
Note that still the performance is good, envelope is not constant. APK (or M-QASK) is used for instance in modems
APK=MQASK
(pe=10-4)
M-APK: Amplitude Phase Shift Keying
(pe=10-4)
PRK BPSK
APK M QASK M QAM
top related