Digital communication

Digital CommunicationBaseband Shaping for Data Transmission

Discrete PAM Signals

PAM

Unipolar Polar Bipolar Manchester

Factors:

DC Component Transmission Bandwidth Bit Synchronization Error Detection

Polar Quaternary format

Differentially Encoded Polar Waveform

Inter Symbol Interference (ISI)

Intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbol.

Causes:

1. Multipath propogation.

2. Bandlimited channels

Pulse generator

HT(f)

Hr(f)

Hc(f)

Y(t)

Transmission filter Channel

Receiving filter

Decision device

Baseband Binary Data Transmission System

Hr(f)

Nyquist’s Criterion for zero ISI

The pulse shaping function p(t) with a fourier transform P(f) is given by

∑P(f-nRb)=Tb has

p(iTb-kTb)=1 for i=k

P(iTb-kTb)=0 for i≠k this condition is knows as Nyquist criterion for zero ISI.

Ideal solution:

PRACTICAL SOLUTIONS

The frequency response of an ideal low pass filter decreases towards zero abruptly which is practically unrealizable.

To overcome this problem raised cosine-roll off Nyquist filter is used.

The amplitude response is as shown:

The raised cosine spectrum is mathematically defined as:

The frequency f1 and B0 are related by

a is called the roll-off factor.

14 𝐵0 [1+𝑐𝑜𝑠(П (|𝑓 |− 𝑓 1)

2𝐵0−2 𝑓 1 ) ] , 𝑓 1≤|𝑓 |<2𝐵0− 𝑓 1

1𝐵0

,|𝑓 |< 𝑓 1

0,

P(f) =

Specifically, α governs the bandwidth occupied by the pulse and the rate at

which the tails of the pulse decay.

A value of α = 0 offers the narrowest bandwidth, but the slowest rate of

decay in the time domain.

When α = 1, the transmission bandwidth is 2B0, which is twice that of ideal solution.

Conversely, inverse when α = 0, the bandwidth is reduced to B0, implying a factor-of-two increase in data rate for the same bandwidth occupied by a rectangular pulse. But there is a slow rate of decay in the tails of the pulse.

Thus, the parameter α gives the system designer a trade-off between increased data rate and the tail suppression.

P(t)=

When α=1 we have:

p(t) = ) ) 0≤|f|<2B0

0 |f|>2B0

Inverse FT of the above equation yields:

p(t) =

Time Response

Transmission Bandwidth Requirement

From the earlier figure we know that the transmission bandwidth is:

B = 2B0 - f1 ………………(1)

where B0 =1 / 2Tb

Also,

a = 1- (f1/B0)

» f1= B0(1-a)

Therefore (1) becomes,

B= 2B0- B0(1-a)

» B= B0(1+a)

When a=1

B = 2B0

When a=0

B=B0

Eye Diagram

Information given by Eye Diagram

The width of the eye opening defines the time interval over which the received wave can be sampled without error from ISI. It is apparent that the preferred time for sampling is the instant of time at which the eye is open widest.

The sensitivity of the system to timing error is determined by the rate of closure of the eye as the sampling time is varied.

The height of the eye opening, at a specified sampling time, defines the margin over noise.