1. MATLAB: In this part, you will modulate the given bit stream, s, with the following modulation schemes.
s = f1; 0; 1; 1; 1; 1; 0; 0g,
(a) BPSK,
(b) QPSK,
(c) 4-PAM,
(d) 16-QAM,
(e) Binary FSK.
For each modulation scheme, give the following:
The constellation diagram of the modulation scheme,
Sinusoidal waveforms to represent the symbols in the constellation diagram (one waveform per symbol),
The modulated pulse stream that represents the given bit stream.
Note:
Use MATLAB for coding and plotting.
For all symbols, use sinusoidal waveforms with the frequency of 5 Hz and the period for each symbol (symbolling period) as 1 s. Therefore you need to repeat the waveform to produce a symbol.
Normalize the waveforms so that the average symbol energy for each constellation is unity.
You may need multiple bits per waveform for some of the modulation schemes given above. Notice that you are given a stream of binary symbols (bits) and you can convert them to M-ary symbols easily.
2. (a) Find an orthonormal basis, i, for the set of the following vectors. Then express sj , in terms of i’s. (i; j 2 f1; : : : ; 4g).
s1 = (2; 1; 1; 1);
s2 = ( 2; 1; 1; 0);
s3 = (1; 1; 1; 1);
s4 = (1; 2; 2; 2):
(b) Now, nd an orthonormal basis, i, for sj ’s by the Gram-Schmidt orthonormalization method.
Then express sj , in terms of i’s.
Report and Submission:
MATLAB: The MATLAB part of your report should include the plots - all axes have to be labelled and all plots have to be captioned. Avoid huge blank spaces in your report (use subplots in MATLAB if necessary). Explain every gure you have in your report. This part does not need to exceed two pages. Also, you must upload the m- le that includes the code -with necessary comments- that executes this part.
Part 2: You can prepare your answer for this part either handwritten or on computer. Handwritten reports have to be scanned for upload. Make sure your scans are readable.
ALL SUBMISSIONS ARE ON MOODLE. Late submission is penalized with 10% per day.
