2/17/2012
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING
DIGITAL COMMUNICATION
Spring 2010
Yrd. Doç. Dr. Burak Kelleci
OUTLINE
Baseband M-Ary PAM Transmission
| Tapped Delay-Line
Delay Line Equalization
|
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BASEBAND M-ARY PAM TRANSMISSION
Up to now for binary systems the pulses have two
possible amplitude levels.
| In a baseband M-ary PAM system, the pulse
amplitude modulator produces M possible
amplitude levels with M>2.
| In an M-ary system, the information source emits
a sequence of symbols from an alphabet that
consists of M symbols.
symbols
| Each amplitude level at the PAM modulator
output corresponds to a distinct symbol.
| The symbol duration T is also called as the
signaling rate of the system, which is expressed
as symbols per second or bauds.
|
BASEBAND M-ARY PAM TRANSMISSION
Let’s consider the following quaternary (M=4)
system.
| The symbol rate is 1/(2Tb), since each symbol
consists of two bits.
|
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BASEBAND M-ARY PAM TRANSMISSION
|
The symbol duration T of the M-ary system is
related to the bit duration Tb of the equivalent
binary PAM system as
T = Tb log 2 M
For a given channel bandwidth, using M-ary
PAM system, log2M times more information is
transmitted than binary PAM system.
| The price we paid is the increased bit error rate
compared binary PAM system.
| To achieve the same probability of error as the
binary PAM system, the transmit power in <-ary
PAM system must be increased.
|
BASEBAND M-ARY PAM TRANSMISSION
For M much larger than 2 and an average
probability of symbol error small compared to 1,
the transmitted power must be increased by a
factor of M2/log2M compared to binary PAM
system.
| The M-ary PAM transmitter and receiver is
similar to the binary PAM transmitter and
receiver.
| In transmitter, the M-ary pulse train is shaped
by a transmit filter and transmitted through a
channel which corrupts the signal with noise and
ISI.
|
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BASEBAND M-ARY PAM TRANSMISSION
The received signal is passed through a receive
filter and sampled at an appropriate rate in
synchronism with the transmitter.
| Each sample is compared with preset threshold
values and a decision is made as to which symbol
was transmitted.
| Obviously, in M-ary system there are M-1
threshold levels which makes the system
complicated.
| The raised cosine pulse shape, which is ISI-free
for binary signaling is also ISI-free for M-ary
signaling.
|
TAPPED DELAY-LINE EQUALIZATION
In theory, if the channel response is precisely
known, it is virtually possible to make the ISI
very small by using suitable transmit and receive
filters.
| In practice, the channel response is not exactly
known. Therefore, the channel effects which
creates ISI must be compensated.
| The process to mitigate ISI issue is called
equalization.
| The filter used to perform this operation is called
equalizer.
|
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TAPPED DELAY-LINE EQUALIZATION
A tapped delay-line equalizer is well suited to
compensate the channel response.
| For symmetry, the total number of taps is chosen
to be (2N+1) with weights denoted by w-N,…,
w-1,w0,w1,…,wN.
|
TAPPED DELAY-LINE EQUALIZATION
|
The impulse response of the tapped delay-line
equalizer is
h(t ) =
N
∑ w δ (t − kT )
k =− N
k
where δ(t) is the Dirac delta function and the
delay T is chosen equal to the symbol duration.
| Let
Let’ss assume that this equalizer is connected in
cascade with a LTI system with a impulse
response of c(t).
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TAPPED DELAY-LINE EQUALIZATION
|
The impulse response of the equalized system is
the convolution of c(t) and h(t)
p(t ) = c(t ) ∗ h(t )
N
= c(t ) ∗
∑ w δ (t − kT )
k
k =− N
=
N
∑ w c(t ) ∗ δ (t − kT )
k =− N
=
k
N
∑ w c(t − kT )
k =− N
k
TAPPED DELAY-LINE EQUALIZATION
|
Let’s evaluate p(t) at the sampling times t=nT
p (nT ) =
N
∑ w c((n − k )T )
k =− N
|
k
To eliminate ISI completely, the Nyquist
criterion for distortionless transmission must be
satisfied.
⎧1 n = 0
p(nT ) = ⎨
⎩0 n ≠ 0
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TAPPED DELAY-LINE EQUALIZATION
|
Since there are only (2N+1) adjustable
coefficients, the ideal condition can satisfied
approximately as follows.
n=0
⎧1
p(nT ) = ⎨
⎩0 n = ±1,±2,… ± N
|
To simplify the notation, let’s denote the impulse
response at nT as
c n = c(nT )
TAPPED DELAY-LINE EQUALIZATION
|
Imposing the distortionless transmission
condition to the convolution sum results in
(2N+1) equations
N
∑w c
k =− N
|
k
n−k
n=0
⎧1
=⎨
⎩0 n = ±1,±2,… ± N
In theory, the longer the equalizer is (N
approaches to infinity). the more closely will the
equalized system approach the ideal condition.
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TAPPED DELAY-LINE EQUALIZATION
|
These equations can also be written in matrix
form.
⎡ c0
⎢
⎢
⎢c N −1
⎢
⎢ cN
⎢c N +1
⎢
⎢
⎢
⎣ c2 N
c − N +1
c− N
c − N −1
c0
c −1
c−2
c1
c2
c0
c1
c −1
c0
c N +1
cN
c N −1
c − 2 N ⎤ ⎡ w− N ⎤ ⎡ 0 ⎤
⎥⎢
⎥ ⎢ ⎥
⎥⎢
⎥ ⎢ ⎥
c − N −1 ⎥ ⎢ w−1 ⎥ ⎢0⎥
⎥⎢
⎥ ⎢ ⎥
c − N ⎥ ⎢ w0 ⎥ = ⎢1⎥
c − N +1 ⎥ ⎢ w1 ⎥ ⎢0⎥
⎥⎢
⎥ ⎢ ⎥
⎥⎢
⎥ ⎢ ⎥
⎥
⎢
c0 ⎦ ⎣ w N ⎦⎥ ⎢⎣0⎥⎦
TAPPED DELAY-LINE EQUALIZATION
In practice, the channel varies with time and the
equalizer coefficients must be changed according
to the channel changes.
| This operation is called adaptive equalization.
| Majority of the equalizers used in practical
systems are adaptive.
|
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EFFECT OF ISI AND EQUALIZER IN
100 MBPS TRANSMISSION.
In 100Mbps ethernet communication, the signal
attenuates over 100 meters especially with
frequency.
| The magnetic devices in close proximity to the
twisted pair ethernet cable effects the channel
characteristics.
| There is also a potential echo from the opposite
end of the cable.
cable
| Since the system transmits and receives at the
same time, there is a possibility of crosstalk
between the transmit path and receive path.
|
EFFECT OF ISI AND EQUALIZER IN
100 MBPS TRANSMISSION.
|
The transmitted signal
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EFFECT OF ISI AND EQUALIZER IN
100 MBPS TRANSMISSION.
|
The received signal
EFFECT OF ISI AND EQUALIZER IN
100 MBPS TRANSMISSION.
|
The equalized signal
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