Problem 6: 6. OFDM Simulation [25 points] In this problem you will simulate a communication system using OFDM. Start with the simula- tion sim1.m (on Canvas). (a) Generate two data waveforms, si(t) and s2(t) with different data streams. (b) Combine the two streams mixed onto two different carriers at frequency fa = 8 Hz and fb = 12 Hz. s(t) = $1(t)√2 cos(2π fat) + s2 (1)√2 cos(27 fit). (c) Add noise n(t) with signal-to-noise ratio Eb/No = 30 dB. (d) Before filtering the received signal, mix down to baseband by multiplying by √2 cos(2n fat) and √2 cos(27 fit). (e) Filter each of the two signals after mixing down with a matched filter (a filter with the same impulse response) as used in generate the waveforms, namely a filter with impulse response pr(t) where T = 1 second./nTurn in the following: (a) Your Matlab code (b) A figure showing the data signal si(t) in the time domain and S₁(f) in the frequency domain. (c) A figure showing the signal s(t) in the time and frequency domain. (d) A figure showing the noise signal in the time and frequency domain. (e) A figure showing the received signal in the time and frequency domain. (f) A figure showing the output of the receiver filter (time domain and frequency domain) for the first data stream. Overlay the time domain plot with the original data signal (si(t)). (g) A figure showing the output of the receiver filter (time domain and frequency domain) for the second data stream. Overlay the time domain plot with the original data signal (s2(t)).

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