Inter symbol Interference

The spreading and smearing of the signal such that the energy from one symbol effects the next ones in such a way that the received signal has higher probability of being interpreted incorrectly is called Inter symbol interference.

Pulse generator

Decision device

Receiving Filter

Channel 1Transmitted filter +

White gaussian

noise

x(t)

y(t)yi(t)

Clock pulses

Sample at time t= nTb

Causes of ISI

• Imperfections in the overall frequency response of the system.

• When short pulse is transmitted, frequency components are differentially attenuated and differentially delayed by the system.

• Pulse appears to be dispersed.

How it actually effects us now?

Each symbol spread by the medium

Actual signal seen by the receiver

What can be done to solve it?

• Simplest thing can be to slow down the signal.

• If delay spread is less than or equal to symbol time, there will be no ISI.

• But slowing down the data rate is very unacceptable in today’s time.

What else can be done?

• Pulse shaping.

How it helps?

• When timing pulse slices the signal to determine the value of signal at that instant, digital demodulator does not care about shape of the pulse.

We only care about what signal does at moment of sampling

Using a square pulse

• Ts is the symbol time.

• Rs is the symbol rate.

Square pulse in frequency domain

Bandwidth

• Bandwidth of the signal is equal to symbol rate for low pass signals twice of the symbol rate for band pass

signals

Disadvantages of Square pulse

• Square pulse is difficult to crate in time domain because of the rise time and decay time.

• Its frequency response goes on forever and decays slowly. Its second lobe is only 13dB lower than the first lobr.

• Very sensitive to ISI.

• If the square pulse gives sinc function in frequency domain, then couldn’t we use sinc function in time domain to get brick wall square pulse in frequency domain?

• Yes we can use sinc function shaped pulse and have nothing spilling out of the bandwidth.

Sinc function in time domain gives square pulse in frequency domain

One more wonderful part about using sinc function !

• Bandwidth required is half of the symbol rate.• Nyquist bandwidth.

Problem faced with sinc function

• In time domain, sinc function have infinite length with tails extending to infinity, so theoretically energy continues to add up even after signal has ended.

• The pulse that falls in adjacent symbols decay at the rate of 1/x so if there is error in timing, its not forgiving.

Solution ?

• Nyquist offered ways to build realizable pulses that had a good quality as sinc pulse and has less disadvantages.

• One class of pulse offered was raised cosine pulses.

• Sinc pulse has bandwidth, W= 1/2Ts, while raised cosine pulses have adjustable Bandwidth between W to 2W.

• Purpose is to achieve bandwidth as near to ideal Nyquist bandwidth as possible.

• The factor α called roll off factor relates ideal bandwidth to achieved bandwidth as

• Another way to indicate utilized bandwidth is

Raised cosine in time domain

Frequency response of raised cosine pulse