64-QAM Communications System Design and Characterization

1. 64-QAM Communications System Design and Characterization Project #1 EE283 daeik.kim@duke.edu

2. 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.

3. Outline • 64-QAM communications system • Testing and measurements • Tools, grading, etc.

4. 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

5. 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?

6. 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

7. Baseband Modulation (1) In-phase Quadrature-phase

8. Baseband Modulation (2) (-1,-1) (-1,+1) (+1,-1) (+1,+1)

9. Baseband Modulation (3) 64-QAM waveform with random data

10. 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]

11. Channel Modeling • Noise • Additive • White • Gaussian Contaminated baseband signal

12. Eye Diagram

13. Baseband Demodulation • Correlative receiver • Matched filter receiver 64-QAM Demodulated Data

14. 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

15. Channel Decoding and Signal Sink • Channel Decoding • Inverse of channel coding • Simple hard decision • Signal Sink • Compare received and decoded data with signal source

16. Testing and Measurements • Obtain • 64-QAM waveform • Eye diagram • Bit error rate • Bandwidth efficiency

17. Signal Power and SNR

18. 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

19. Channel Bandwidth • 3-dB bandwidth • Or your definition and justification Modulated 64-QAM spectrum

20. Theory vs. Practice • Given BER plot vs. experimented BER plot • Given bandwidth efficiency vs. experimented bandwidth efficiency

21. Tools • Any tools supported by ECE • MATLAB recommended • C, C++, Java, Visual Basic, Perl, PHP… • Simulink ?

22. >> 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 (1)

23. Flow control for N=1:10, ---; end if <true/false>, ---; else, ---; end switch <var> case <cond1> ---; case <cond2> ---; otherwise ---; end 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 (2)

24. 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 (3)

25. 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

26. 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’

27. 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)