baseband system

DIGITAL COMMUNICATION
SYSTEMS (ECE4001)
Dr. Arvind Kumar | School of Electronics Engineering, VIT Vellore |
https://sites.google.com/view/arvindk

BASEBAND SYSTEM
| School of Electronics Engineering, VIT Vellore |

|Dr. Arvind Kumar| https://sites.google.com/view/arvindk
Reference Book
3

Module 4: Baseband System
1. Inter
Symbol
Interference
(ISI).
2. Nyquist
criterion for
distortion less
trans.
3. Raised
cosine
spectrum
4. Correlative
coding
5. Eye pattern 6. Equalization
The objective here is that of signal design, whereby the effect of symbol interference is reduced to zero.
4

Signaling over Band-Limited Channels
|Dr. Arvind Kumar| https://sites.google.com/view/arvindk 5

Signaling over Band-Limited Channels
• The important point to note here is that if, for example, a rectangular pulse, representing one
bit of information, is applied to the channel input, the shape of the pulse will be distorted at
the channel output.
• Typically, the distorted pulse may consist of a main lobe representing the original bit of
information surrounded by a long sequence of sidelobes on each side of the main lobe.
• The sidelobes represent a new source of channel distortion, referred to as Inter Symbol
Interference, so called because of its degrading influence on the adjacent bits of information.
There is a fundamental difference between ISI and channel noise.
• Channel noise is independent of the transmitted signal; its effect on data transmission over the
band-limited channel shows up at the receiver input, once the data transmission system is
switched on.
• Inters-symbol interference is signal dependent; it disappears only when the transmitted signal is
switched off.
6

1. Inter
Symbol
Interference
(ISI).
2. Nyquist
criterion for
distortion less
trans.
3. Raised
cosine
spectrum
4. Correlative
coding
7

1. Inter-Symbol Interference (ISI)
• ISI is the interference of the adjacent bits (in terms of pulses) into the desired pulse shape.
• This is a form of distortion of a signal, causing noise or delivering a poor output.
Causes of ISI
 Multi-path Propagation
 Non-linear frequency in channels
• The ISI is unwanted and should be completely eliminated to get a clean output.
• The causes of ISI should also be resolved in order to lessen its effect.

Baseband System and ISI
• Consider a baseband binary PAM system, The term “baseband” refers to an information-
bearing signal whose spectrum extends from (or near) zero up to some finite value for positive
frequencies.
• Thus, with the input data stream being a baseband signal, the data-transmission system is said
to be a baseband system.

Cont’d
• The pulse-amplitude modulator changes the input binary data stream {bk} into a new
sequence of short pulses, short enough to approximate impulses.
• More specifically, the pulse amplitude ak is represented in the polar form:
• The sequence of short pulses so produced is applied to a transmit filter whose impulse
response is denoted by g(t). The transmitted signal is thus defined by the sequence:
form of linear modulation
13

• The signal s(t) is naturally modified as a result of transmission through the channel whose
impulse response is denoted by h(t).
• The noisy received signal x(t) is passed through a receive filter of impulse response c(t).
• The resulting filter output y(t) is sampled synchronously with the transmitter, with the
sampling instants being determined by a clock or timing signal that is usually extracted from
the receive-filter output.
• Finally, the sequence of samples thus obtained is used to reconstruct the original data sequence
by means of a decision device.
• The amplitude of each sample is compared with a zero threshold
If the sample amplitude equals the zero threshold exactly, the receiver simply makes a random guess. 14

• we express the receive filter output as:
To be precise, an arbitrary time delay t0 should be included in the argument of the pulse p(t –kTb) to represent
the effect of transmission delay through the system. we have put this delay equal to zero. We assume that
the pulse p(t) is normalized by setting
where P(f), G(f), H(f), and C(f) are the Fourier transforms of p(t), g(t), h(t), and c(t), respectively.
• The receive filter output y(t) is sampled at time ti= iTb, where i takes on integer values.

• This residual effect due to the occurrence of pulses before and after the sampling instant ti is
called intersymbol interference(ISI).
• In the absence of ISI—and, of course, channel noise
under these ideal conditions, ith transmitted bit is decoded correctly
The first term ai represents the contribution of the ith trans. bit.
The second term represents the residual effect of all other
transmitted bits on the decoding of the ith bite.
where i takes on integer values
16

Signal Design for Zero ISI
• In effect, signaling over the band-limited channel becomes distortionless; hence, we may refer
to the pulse-shaping requirement as a signal-design problem.
• Whereby overlapping pulses in the binary data-transmission system are configured in such a
way that at the receiver output they do not interfere with each other at the sampling times ti=
iTb.
• So long as the reconstruction of the original binary data stream is accomplished, the behavior
of the overlapping pulses outside these sampling times is clearly of no practical consequence.
• Such a design procedure is rooted in the criterion for distortionless transmission, which was
formulated by Nyquist (1928b).
The primary objective of this chapter is to formulate an overall pulse shape p(t) so as to mitigate the ISI problem
17

Cont’d
• akp(iTb– kT, must be zero for all k except for k= 1 for binary data transmission across the
band-limited channel to be ISI free.
• In other words, the overall pulse-shape p(t) must be designed to satisfy the requirement
It is called a Nyquist pulse, and the condition itself is referred to as Nyquist’s criterion for
distortionless binary baseband data transmission.
where p(0) is set equal to unity (normalization condition)
18

1. Inter
Symbol
Interference
(ISI).
2. Nyquist
criterion for
distortion less
trans.
3. Raised
cosine
spectrum
4. Correlative
coding

2. Ideal Nyquist Pulse for Distortionless Baseband Data
Transmission
• Note: sampling in the time domain produces periodicity in the frequency domain. In
particular, we may write

Ideal Nyquist Pulse
• The simplest way of satisfying is to specify the frequency function P(f)
to be in the form of a rectangular function, as shown by:

Cont’d
• We find that a signal waveform that produces zero ISI is defined by the sinc function (FT of
rect func):
The special value of the bit rate Rb= 2W is called the Nyquist rate and W is itself
called the Nyquist bandwidth.
 The baseband pulse p(t) for distortionless transmission is called the ideal Nyquist pulse,
 Ideal in the sense that the bandwidth requirement is one half the bit rate.
24

Cont’d
25

 The function p(t) can be regarded as the impulse response of an ideal low-pass filter
with passband magnitude response 1/2W and bandwidth W.
 The function p(t) has its peak value at the origin and goes through zero at integer
multiples of the bit duration Tb.
 It is apparent, therefore, that if the received waveform y(t) is sampled at the instants of
time t= 0,  Tb,  2Tb, ………., then the pulses defined by ai p(t –iTb) with amplitude
ai and index i= 0,  1,  2, …………. will not interfere with each other.
Cont’d
26

• Ideal Nyquist pulse does indeed achieve economy in bandwidth, in that it solves the
problem of zero ISI with the minimum bandwidth possible.
• There are two practical difficulties that make it an undesirable objective for signal design:
 It requires that the magnitude characteristic of P(f) be flat from –W to +W, and
zero elsewhere.
 The pulse function p(t) decreases as 1/|t| for large |t|, resulting in a slow rate of
decay. This is also caused by the discontinuity of P(f) at  W.
 Accordingly, there is practically no margin of error in sampling times in the
receiver.
Cont’d
-W W 28

• The first term on the right-hand side the desired symbol, whereas the remaining
series represents the ISI caused by the timing error in sampling the receiver output
y(t).
• Unfortunately, it is possible for this series to diverge, thereby causing the receiver to
make erroneous decisions that are undesirable.
32

1. Inter
Symbol
Interference
(ISI).
2. Nyquist
criterion for
distortion less
trans.
3. Raised
cosine
spectrum
4. Correlative
coding

3. Raised-Cosine Spectrum
• We may overcome the practical difficulties encountered with the ideal Nyquist pulse by
extending the bandwidth from the minimum value W= Rb/2 to an adjustable value between
W and 2W.
• In effect, we are trading off increased channel bandwidth for a more robust signal design
that is tolerant of timing errors.
• The overall frequency response P(f) is designed to satisfy a condition more stringent than that
for the ideal Nyquist pulse, in that we retain three terms of the summation on the left-hand side
of (8.15) and restrict the frequency band of interest to [–W, W], as shown by
where, on the right-hand side, we have set
Rb= 1/2W in accordance with
34

• A particular form of P(f) that embodies many desirable features is provided by a raised-cosine
(RC) spectrum. This frequency response consists of a flat portion and a roll-off portion that
has a sinusoidal form, as shown by:

Cont’d
• The parameter α is commonly called the roll-off factor; it indicates the excess bandwidth
over the ideal solution, W.
• Specifically, the new transmission bandwidth is defined by:

The time response p(t) is naturally the inverse
Fourier transform of the frequency response P(f).
The time response p(t) consists of the product of two
factors:
1. Factor sinc(2Wt) characterizing the ideal Nyquist
pulse and
2. A second factor that decreases as 1/|t|2 for large |t|.
39

1. Inter
Symbol
Interference
(ISI).
2. Nyquist
criterion for
distortion less
trans.
3. Raised
cosine
spectrum
4. Correlative
coding

4. Correlative coding
• So far, ISI is an unwanted phenomenon and degrades the signal.
• But the same ISI if used in a controlled manner, is possible to achieve a bit rate of 2W bits per
second in a channel of bandwidth W Hertz.
• Such a scheme is called as Correlative Coding or Partial response signaling schemes.
• Since the amount of ISI is known, it is easy to design the receiver according to the
requirement so as to avoid the effect of ISI on the signal.
• The basic idea of correlative coding is achieved by considering an example of Duo-binary
Signaling.

baseband system

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