No collaboration or help is allowed on this take-home exam, it must be your own work!
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The Problems:
(1 [10 pts]) Problem 4.12
Comment: Equivalence of correlates and matched filters.
(2 [10 pts]) Problem 4.13
Comment: Equivalence of correlates and matched filters at time T, but significant differences elsewhere.
(3 [10 pts]) Problem 4.16
Comment: Suboptimal filter. Note: based on the filter structure, there would still be a signal output at 2T, 3T, etc. This must be considered the intersymbol interference.
(4 [10 pts]) Problem 4.18
Additional work: After deriving the new probability of error formula, use Matlab to plot this curves and the orthogonal FSK bit error rate curves together to observe the differences. On one more curve, plot the orthogonal FSK, the “minimum FSK” and the antipodal curves on the same plot. Note we are most interest in bit-error rates from 10^-1 to 110^-6.
(5 [10 pts]) Problem 4.28
Comment: Many communications systems estimate the received SNR. If they have a continuously high SNR they negotiate with the transmitter to increase the complexity of the symbols being set in order to increase the data transfer rate up to some maximum acceptable
BER.
MATLAB Simulations
(6 [40 pts]) Generate a Matlab simulation to verify the bit error rate performance of Coherently
Detected Multilevel Phase Shift Keyed (MPSK) communication based on Dr. Bazuin’s
MPSK_FilterTest.m provided MATLAB code.
(a) Find the tx_filter = and rx_filter = statements. First use the rect_filter as the applied transmit and receive filters. I would like to see valid symbol-error and bit-error plots that extend to 10^-4 SER. You will need to increase the number of symbols (Hint: Nsyms on the order of
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EXAM #1
10^5 needed. 2^16 to 2^17 ) . Use a smaller number of symbols to get familiar with the program.
In addition, you should collect data files for at least M=4, 16, and 64.
(b) Find the tx_filter = and rx_filter = statements. Next use the hsqnyq_firrcos filter and repeat your tests. Compare these results to the results in part (a) … plotting the SERvsEs/No and
BERvs.Eb/No curves from the stored data.
(c) Repeat the code for M=4 using the tri2_filter and sinc_filter provided. These filters produce intersymbol interference. By observing the convolved filters at sample offsets of the expand value you can see how much of previous (and future) signals are being combined prior to signal detection. Plot the SERvsEs/No and BERvs.Eb/No curves for all 4 test filters together on one plot to see the difference in performance.
(d) Can you generate either identical transmit and receive filters or separate transmit and receive filters that perform as well as the rectangular filter or the square root Nyquist (square root raised cosine) filter? Try and see. For your filter, is the transmitted waveform continuous, what is the receive filters equivalent noise bandwidth (less than or greater than 0.5?). Compare your performance for M=4 to other filter performances.
(7 [40 pts]) Generate a Matlab simulation to verify the bit error rate performance of Coherently
Detected QAM communication based on Dr. Bazuin’s QAM_FilterTest.m provided MATLAB code.
Repeat parts (a), (b), (c) and (d) for the QAM_FilterTest simulation.
(8 [10 pts]) Provide SERvsEs/No and BERvs.Eb/No curves that compare MPSK and QAM for M=4, 15, and 64. Table 4.3-1 described the SNR advantage of M-art QAM over M-ary PSK.
Do your results validate the information in the table?
For your solutions:
(a) Design, simulate and document in a written report the solution and results including all required code to justify your results.
(b) Provide equations, figures, and plots that demonstrate that all elements of the problems have been completed.
(c) Provide a printout of the Matlab *.m file code you used to generate your solutions.
(d) E-mail the Matlab *.m file code to me. The files must be received AND execute without modification in order to receive credit. It is likely that I will execute your code to verify the results that you submit. Therefore, if non-standard functions or sub-circuits are used, send them as well.
(e) Provide references for all textbooks, articles or other references that you use.
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