Implementation 16 QAM Base Band Implementation 16 QAM Base Band

Communication SystemCommunication System

22

What is QAMWhat is QAM

In QAM two DSB signals are transmitted using the In QAM two DSB signals are transmitted using the carrier of the same frequency but in Phase carrier of the same frequency but in Phase

Quadrature to each other.Quadrature to each other.

2/

m1(t)

m2(t)

Cos ωc t

Sin ωc t

Φ QAM(t)

Quadrature Modulator

33

MathematicallyMathematically

φ QAM(t) = m(t) cosωt + m(t) sinωt

44

Demodulator Demodulator

At the demodulator side the signal is coherently At the demodulator side the signal is coherently detected using to local carriers in phase detected using to local carriers in phase Quadrature as shown belowQuadrature as shown below

2/

2 Cos ωc t

2 Sin ωc t

X1 (t)

X 2 (t)

Low Pass Filter

Low Pass Filter

m1(t)

m2(t)

Φ QAM(t)

55

MathematicallyMathematically

x(t)x(t) == 22φφ cosω(t) cosω(t)

=2[m(t) cosωt + m(t) sinωt] cosωt=2[m(t) cosωt + m(t) sinωt] cosωt

= m(t)+ m(t) cos2ωt + m(t) sin2ωt= m(t)+ m(t) cos2ωt + m(t) sin2ωt

Matlab ImplementationMatlab Implementation

Part 2Part 2

77

Problem SolutionProblem Solution

Random signal generationRandom signal generation

Formation of symbols Formation of symbols

16-QAM modulation16-QAM modulation

AWGN channelAWGN channel

88

Problem Solution contd…Problem Solution contd…

DemodulationDemodulation

Computation of Prob. of Bit ErrorComputation of Prob. of Bit Error

Extraction of bits from the noisy symbols.Extraction of bits from the noisy symbols.

Computation of Prob. of Symbol ErrorComputation of Prob. of Symbol Error

99

AnalysisAnalysis

0 5 10 15 20 25 30 35 400

0.5

1(1st 40 out of 100,000) Message Bits

Bits-->

Bit

valu

e

1 2 3 4 5 6 7 8 9 100

5

10

15(1st 10 out of 25,000)Message Symbols

Symbols-->

Mag

nitu

de

data1

1010

-5 0 5-5

-4

-3

-2

-1

0

1

2

3

4

5

Qua

drat

ure

In-Phase

Received Signal Constellation

1111

Outputs (Command Prompt)Outputs (Command Prompt)

Total number of bits transmitted = 100000Total number of bits transmitted = 100000

Total_number_of_erroneous_bits_received = 3Total_number_of_erroneous_bits_received = 3

Probability_of_bit_error = 3.0000e-005Probability_of_bit_error = 3.0000e-005

Total_number_of_erroneous_symbols_received = 3Total_number_of_erroneous_symbols_received = 3

Probability_of_symbol_error = 1.2000e-004Probability_of_symbol_error = 1.2000e-004

1212

ApplicationsApplications

To multiplex the chrominance signals in To multiplex the chrominance signals in color televisioncolor television

POTSPOTS

1313

LimitationsLimitations

Source coding can be applied.Source coding can be applied.

Channel CodingChannel Coding

Random Voice Signal as InputRandom Voice Signal as Input

1414

ConclusionsConclusions

Transmission Symbol Rate Transmission Symbol Rate

Channel utility.Channel utility.

1515

Acknowledgements Acknowledgements

First of all we are thankful to all Mighty First of all we are thankful to all Mighty Allah. Allah. We really acknowledge Dr. Riaz Inayat for We really acknowledge Dr. Riaz Inayat for the knowledge that he conveyed to us.the knowledge that he conveyed to us.In the last but never the least, we are In the last but never the least, we are grateful to Mr. Raheel Satti and Usama grateful to Mr. Raheel Satti and Usama Bajwa for the support and help they gave Bajwa for the support and help they gave us when ever we required.us when ever we required.