64-QAM Communications System Design and Characterization Project #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 sink Simplified 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?

An example of 16-QAM mapping 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 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

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 BER SNR(dB) An example of 64-QAM BER plot

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 0 1 2 3 4 5 >> A=(0:0.2:1)' 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) Function call Flow control for N=1:10, ---; end if <true/false>, else, switch <var> case <cond1> case <cond2> otherwise Function call function [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 semilogx sum semilogy size loglog 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 Scripts 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)