Digital Communication

Introduction

UNIT-1

DiscussionCommunication Systems.Digital Communication Systems.Functionality of Blocks.Medium Classification.Performance Measure.Mathematical Models of Communication

Channel.

Introduction Transmission of Information from one point

to another.Mode of Communication

Broadcasting e.g ? Point to point e.g.?

Primary Communication Resources Transmitted power Channel BW Classify communication channel as Band Limited

and Power limited. E.g.?

Data compression Encoder and Decoder

Lossless compression e.g Digital Text Lossy compression. E.g. reduce data size without

altering the quality of the image or audio signal.

Communication channelsTwo basic groups of communication channel

based on Guided propagation –Telephone channels , coaxial

cables and Optical Fibers Free propagation- Wireless broadcast channels ,

Mobile radio channels and satellite channels.

Types of Communication systems

Analog Communication system

Digital Communication System

Elements of Communication system

Introduction to Communication Systems

Basic Digital Communication TransformationsFormatting/Source Coding Source of information : speech, music, pictures and data.Transforms source information into digital symbols

(digitization) Selects compatible waveforms (matching function) Introduces redundancy which facilitates accurate

decoding despite errors It is essential for reliable communication

Modulation/Demodulation Modulation is the process of modifying the information

signal to facilitate transmission Demodulation reverses the process of modulation. It

involves the detection and retrieval of the information signal Types Coherent: Requires a reference info for detection Non coherent: Does not require reference phase

information

To combat noise in the communication channel, some redundancy is introduced in the message – This is done by channel encoder block.

The Primary purpose of the band pass modulator is to map the digital signal to high frequency analog signal waveforms.

To increase the spectral efficiency as much as possible.

ModulatorBaseband - Digital data can be transmitted

directly with out modulation of any carrier

Band pass- Binary data modulates some carrier and modulated carrier is transmitted over the channel.

Block Diagram of digital Communication system

Source coding theoremEfficient representation of data generated by a

source.

L – average no. bits per source symbol.

H(y)- Entropy of the source

Code words produced by encoder are in binary form.

Average code word length L of the encoder as

Efficiency of source encoder in terms of entropy

ProcedureMessages are arranged in non increasing

order.Message set is partitioned in to two most

equiprobable subsets.A ‘0’ is assigned to one subset and ‘1’ to

other subset.Same procedure is repeated for the subsets.Procedure is continued until each subset

contains only one message.

ProblemsGiven eight messages

m1,m2,m3,m4,m5,m6,m7,m8 with probability 0.5,0.15,0.15,0.08,0.08,0.02,0.01,0.01. Find the Shannon Fano code and evaluate the efficiency.

Communication channel ClassificationPhysical medium between the Tx and Rx.

Wired- Telephone, Ethernet.Wireless- Free space carrying EM Wave.

Advent of DC, how fast the signal can be transmitted by the channel.Bit transmission rateChannel supporting 20 KHz of analog speech.With the advent of PCM, supporting 64Kbps

speech transmission.ISDN -256 KbpsDSL- 52 Mbps

Repeaters- Keep the signal strength at the Rx sufficient for detection.

Performance Measures:Goal

Transports a message signal from a source across a noisy channel to a user at the other end of the channel.

ObjectiveMessage signal is delivered to the user both

efficiently and reliably, subject to certain design constraints Allowable transmit power Channel bandwidth

Reliability is expressed in terms of BER.Information Capacity

Maximum rate at which information can be transmitted across the channel with out error.

Frequency bandVLF- NavigationLF- Marine MF- RadioHF- Military VHF-TV,FMUHF- Cellular, GPSSHF- MicrowaveEHF- RADAR

Mathematical model of Communication channel

Mathematical model which reflects the most important characteristics of the transmission medium.

Mathematical model helps to connect the Tx and Rx mathematically.

Three popular are frequently used to characterize comm. Channel

Additive Noise Channel Linear Filter Channel----wireline Linear Time-Variant Filter Channel---

wireless

Additive Noise ChannelThe simplest mathematical model for a communication

channel is the additive noise channel, illustrated in Figure. In this model the transmitted signal s(t) is corrupted by an

additive random noise process n(t).Attenuation FactorThe model is called AWGN channel model – additive noise,

Uniform Spectral distribution and Gaussian Distribution.

The Linear Filter ChannelIn some physical channels such as wire line

telephone channels, filters are used to band limit the signals and prevent the interference.

Such channels are generally characterized mathematically as linear filter channels with additive noise, as illustrated in Figure .

In this Model , characteristics of the filter represent the channel does not change with time. Hence, if the channel input is the signal s(t).

Linear filter channel with additive noise.

Linear time-variant filter channel with additive noise

The Linear Time-Variant Filter ChannelChannels such as underwater acoustic

channels and Mobile cellular channels which result in time-variant filter channel.

Signal travel through various paths and arrives at receivers at different time- multipath propagation.

Such linear filters are characterized by time-variant channel impulse response h(t; d) where h(t; d) is the response of the channel at time t, due to an impulse applied at time t – t. d-delayed signal

Bandwidth Band Limited Channels which means no signal power is allowed

outside the defined band. Fourier analysis – Band limited signal are not realisable , because

signals imply with infinite duration.

Dimensionality Theorem A real waveform can be completely specified by N independent

pieces of information where N is given by N= 2B To N-Dimension of the waveform

B-Bandwidth To- Time

A digital signal is transmit over an interval of To second, Symbol Rate Rs

Rs=N/To, B=?

Bandwidth

Half power Bandwidth: This is the interval between frequencies at which Gx(f) has dropped to half-power or 3dB below the peak value. (In Fig. a)

Null to null Bandwidth: Width of the main spectral lobe, where most of the signal power is contained. (In Fig. C)

Absolute Bandwidth: Interval between frequencies. (In Fig. e)

Different Bandwidth Criteria

Channel CodingIncreases the resistance of digital

communication system.Inevitable presence of noise in channel

causes discrepancies (errors).Mapping the incoming data sequence in to

channel input sequence.’‘k’ message bits‘n’ encoder output Redundant bits = ?

Accurate reconstruction of the original source sequence at the destination requires low Prob. Of error.

Channel capacityMaximum rate at which information can be

transmitted over AWGN channel.SNR >>0 dB, then the channel is Band limited SNR <<0 dB, then the channel is power

limited For a noisy channel with capacity ‘c’

information transmitted at a rate “R’ bits/secR<C, coding tech./modulation tech.R>C, prob. Of error.

Channel capacity Suppose that the spectrum of a channel is

between 10 MHz and 12 MHz, and an intended capacity of 8 Mbps.(1) What should be the SNR in order to obtain this capacity?(2) What would be the capacity if the environment starts suffering lesser noise and the SNR goes up to 27 dB.

AnswerB=2 MHz=2*10^6, C=8 Mbps=8*10^6 bps

1. C=B*log2(1+SNR) <=> 2^(C/B)-1=SNR<=> SNR=15

2. SNR(dB)=10*log10(SNR)<=>SNR=10^2.7<=>SNR=501 (approximately),C=18Mbps=18*10^6 bps

Find the Nyquist rate and Nyquist interval for the following signals.