64-QAM Communications System Design and

CharacterizationProject #1

EE283

daeik.kim@duke.edu

What you need to do (red)• Assignments:• 1. Data Source (0)• Propose a data source that you will use for your communication system. Discuss the randomness of data.• 2. 64-QAM Memoryless Channel Coder (25)• Design a channel coder with a code rate 1. The designed data source feeds the channel coder. The coder outputs are

64-QAM in-phase and quadrature-phase data. For example, with 6-bits taken from data source, an in-phase and a quadrature-phase amplitudes are produced.

• 3. QAM Base Band Modulation (25)• Design a QAM modulator. Modulator inputs are the output of 64-QAM channel coder and the modulation

frequency, etc. The output is a modulated QAM waveform. Show unit in-phase, unit quadrature-phase, and random data waveforms in a fine time resolution (for readability).

• 4. Channel Modeling (0)• Design a channel module that adds Gaussian noise to the modulated data with a given noise intensity. Show a 64-

QAM eye diagram.• 5. QAM Base Band Demodulation (25)• Design a QAM demodulator. Assume that full phase information is given and the phase is locked. The demodulator

outputs are in-phase and quadrature-phase amplitudes. Show a demodulated 64-QAM constellation with noise.• 6. 64-QAM Channel Decoder (25)• Design a QAM decoder that performs the inverse of the designed 64-QAM channel coder. • 7. BER Measurements (0)• Design a module calculates bit-error-rate with the original data source and the decoded data stream. Discuss how

many measurements are required to get 95% or 99% confidence. Make a plot of BER vs SNR. All the numbers, such as signal power and noise power, must be obtained from simulation.

• 8. Bandwidth Efficiency (0)• Calculate the bandwidth efficiency with a given BER. All the numbers, such as bandwidth must be obtained from

simulation. Discuss the definition of bandwidth of your baseband waveform.

Outline

• 64-QAM communications system

• Testing and measurements

• Tools, grading, etc.

64-QAM Communications System Design

• Signal source and source coding

• Channel coding• Baseband modulation• Channel modeling• Baseband demodulation• Channel decoding• Source decoding and

signal sinkSimplified 64-QAM communications system

Signal source and source coding

• Ideal source coded data– “Random”– Memoryless source– Equiprobable– Spectrum and autocorrelation

• A randomly generated data

• What if the data is not random?

64-QAM Channel Coding• 2^6=64• Use rate 1 code• Map a sequence of 6-bits

to 64 symbols• Symbol error• Bit error

An example of 16-QAM mapping

Baseband Modulation (1)

In-phase Quadrature-phase

Baseband Modulation (2)

(-1,-1)(+1,-1)

(-1,+1)(+1,+1)

Baseband Modulation (3)

64-QAM waveform with random data

Baseband Modulation (4)• Sampling of waveform

– Minimum samples per symbol

• Number of waves per symbol

• Orthogonal signals– [1 1] vs. [1 -1]

– [1 0 -1 0] vs. [0 1 0 -1]

Channel Modeling• Noise

– Additive

– White

– Gaussian

Contaminated baseband signal

Eye Diagram

Baseband Demodulation• Correlative receiver• Matched filter receiver

64-QAM Demodulated Data

Clock Recovery and Phase Locking• Clock recovery from

baseband signal• Phase locking • Maintain constant clock

and locked phase• Clock synchronization

pilot signal• Assume perfect clock

recovery and phase locking

64-QAM Demodulated with perfect phase and 2.5% phase lag

Channel Decoding and Signal Sink

• Channel Decoding– Inverse of channel coding– Simple hard decision

• Signal Sink– Compare received and decoded data with signal source

Testing and Measurements

• Obtain– 64-QAM waveform– Eye diagram– Bit error rate– Bandwidth efficiency

Signal Power and SNR

X () E[X(t)X(t )]

X ( f ) X ( )

e j 2fd

Power X ( f )

df X (0) E[X(t)X(t)]

X () X ( f )

e j2fdf

RX (,T) 1

2Tx(t )x(t)

T

T dt

limTRX (,T) RX ()

limT

var[RX (,T)] 0

SNRPowersignalPowernoise

SNRdB 10 logPowersignalPowernoise

Symbol / Bit Error Rate• S/BER=Symbol or Bit

Error / Tx-Rx Bits• How many symbols/bits

to test for a given BER• How many measurements

for a given BER• 95% or 99% confidence

interval• t-test

An example of 64-QAM BER plotSNR(dB)

BE

R

Channel Bandwidth• 3-dB bandwidth• Or your definition and

justification

Modulated 64-QAM spectrum

Theory vs. Practice• Given BER plot vs.

experimented BER plot• Given bandwidth

efficiency vs. experimented bandwidth efficiency

Tools

• Any tools supported by ECE

• MATLAB recommended

• C, C++, Java, Visual Basic, Perl, PHP…

• Simulink ?

MATLAB (1)>> A=[0 1 2; 3 4 5]A = 0 1 2 3 4 5>> A=(0:0.2:1)'A = 0 0.2000 0.4000 0.6000 0.8000 1.0000>> plot(A,cos(2*pi*A))

>> ta=1:-0.01:0;>> tb=(0:.01:1)';>> ta+tb';>> ta'.*tb;>> ta.^2;>> ta(1:10)=tb(11:20)’;>> help>> help elfun>> lookfor signal>> demo

MATLAB (2)• Flow control

for N=1:10, ---; endif <true/false>, ---;

else, ---;

endswitch <var>case <cond1>

---;case <cond2>

---;otherwise

---;end

• Function callfunction [Y,Z]=Name(X)%Name.m%Usage%function Y=Name(X)<Commands>Y=1;Z=2;return;

>> Y=Name(1);>> [Y,Z]=Name(2);

Matlab (3)• Useful functions

– mean– sum– size– length– zeros– ones– rand– randn– figure– plot– xlabel– ylabel– title

– semilogx– semilogy– loglog– log10– log– i– j– pi– round– ceil– floor– sgn– fft– spectrum

MATLAB (4)

• Vector operation vs. scalar operation>> A=1:1e4; MeanSquare=mean(A.^2);>> A=1:1e8;

• Vector preparation before usage>> A=zeros(1,100); for k=1:100, A(k)=k+1; end

>> for k=1:100, A(k)=k+1; end>> A=[]; for k=1:100, A=[A k+1]; end

Things to submit

• Documentation– An electronic copy in PDF of PS format– IEEE journal format– Scripts execution methods

• Scripts– “tar”ed and compressed scripts– “lastname_firstname.tar.gz” or “.tar.Z”– All scripts should be in “lastname_firstname” directory– Script execution must be one-step, i.e.

‘filename’+’enter’

Deadline

• Submit to dkim@ee.duke.edu

• 9/24 (Fri) 11:00pm

• Time marked by the recipient server (ee.duke.edu)

• Penalty for late submission without permission (-20% per a day)

• No virus (frown per a virus)