Elements of a Digital Communication SystemBlock diagram of a communication system:

Y-Axis

Information source and input transducer

Channel decoder

Output transducer

Channel

Digital modulator

Channel encoder

Source encoder

Source decoder

Digital demodulator

Mathematical Models for Communication ChannelsAdditive Noise Channel:In presence of attenuation:

+

S(t)

r(t) = s(t) + n(t)

n(t)

channel

Mathematical Models for Communication ChannelsThe Linear filter channel:

Linear filter c(t)

+

channel

s(t)

n(t)

r(t) = s(t)*c(t)+n(t)

Mathematical Models for Communication ChannelsLinear Time-Variant Filter Channel:Are charachterized by a time-variant channel impulse response

Linear time_variant filter

+

channel

s(t)

n(t)

r(t)

Representation of Band-Pass Signals and SystemsRepresentation of Band-Pass Signals:

Energy of the signal:

Representation of Linear Band-Pass Systems:Response of a Band-Pass System to a Band-Pass Signal:

Orthogonal Expansion of SignalsWe can express M orthonormal signals as a Linear combination of basis functions and hence can be defined as

Linear digitally modulated signals can be expanded in terms of two orthonormal basis functions given by:

and

Representation of Digitally Modulated SignalsPulse-amplitude-modulated Signals (PAM):

Phase-modulated signals (PSK):

Quadrature amplitude modulation (QAM):

m=1,2,M m=1,2,..,M,

Representation of Digitally Modulated SignalsOrthogonal multidimensional signals:

Biorthogonal signals:Simplex signals: m=1, 2,, M..

Signal waveforms from binary codes:

Optimum Receivers Corrupted by additive White Gaussian Noise- IGeneral Receiver:

Receiver is subdivided into:1. Demodulator.(a) Correlation Demodulator.(b) Matched Filter Demodulator.2. Detector.

+

Sm(t)

r(t) = sm(t) + n(t)

n(t)

channel

Optimum Receivers Corrupted by additive White Gaussian Noise- IICorrelation Demodulator:Decomposes the received signal and noise into a series of linearly weighted orthonormal basis functions.

Equations for correlation demodulator:

Optimum Receivers Corrupted by additive White Gaussian Noise- IIIMatched Filter Demodulator:Equation of a matched filter:

Output of the matched filter is given by:

k=1,2, N

Optimum Receivers Corrupted by additive White Gaussian Noise- IVOptimum Detector:The optimum detector should make a decision on the transmitted signal in each signal interval based on the observed vector.

Optimum detector is defined by:

m=1,2, M

or

OFDMIt is a block modulation scheme where data symbols are transmitted in parallel by employing a large number of orthogonal sub-carriers.Equation of complex envelope of the OFDM signal:

where

General FFT based OFDM system-IBlock diagram of FFT based OFDM transmitter :

Equations at the transmmitter end:

X0

XN-1

XN-2

...

X1

X0

IFFT

XN-1

XN-2

...

X1

Insert Cyclic prefix

D/A

D/A

General FFT based OFDM system-IIBlock diagram of FFT based OFDM receiver:

At the demodulator:

R0

ZN-1

ZN-2

...

Z1

Z0

FFT

RN-1

RN-2

...

R1

Serial metric computer

Remove cyclic prefix

A/D

A/D

General FFT based OFDM system-IIMerits of OFDM:

1. the modulation and the demodulation can be achieved in the frequency-domain by using a DFT.

2. the effects of ISI can be eliminated with the introduction of the guard interval.

IMPLEMENTATION OF OFDM SYSTEM-IBasic implementation of OFDM system:

Serial To Parallel Converter

BPSK

Detector

BPSK

BPSK

+

+

+

Bits

R0

R127

R1

...

...

...

...

...

...

...

...

...

...

X0

X1

X127

n0

n1

n127

SIMULATION RESULTS.Perfomance charachteristics were obtained for the simulated OFDM system.

Conclusion.1. OFDM communication system exhibits better Pe Vs SNR curves in case of Non-Fading channel as compared to the Fading channel.

2. As the value of the SNR is increased the value of Pe gradually decreases.

3. Perfomance charachteristics of simulated OFDM communication system are consistent with the performance charachteristics of the general OFDM communication system.