#part 1
- Generate a binary stream for 20 symbols for 4-PAM modulation
- Bit rate of 20Mbps
- sps 8 (Sample per symbol)
- Plot the transmit waveform for square pulse
- Plot the transmit waveform for RRC pulse with beta=0.25
- Plot the spectrum of the transmitted signal using FFT function of matlab/Python
Hint for plotting spectrum: R=20 Mbps, which implies 1010^6 symbols per second (2 bits per symbol for 4-PAM). Samples per symbol (sps) is 8. Thus the sampling rate is Fs=81010^6. Thus to plot FFT assume Fs=80MHz. Let vector xm is the samples of modulated signal, ie, 820=160 samples.
X=fftshift(fft(yc,800)); f_axis=(0:800-1)Fs/800-Fs/2; plot(f_axis/1e6,20log10(abs(X))) title('Spectrum of modulated signal') xlabel('f in MHz') ylabel('PSD in dB') grid on
- Choose the appropriate matched filter for 5 and 6
- Assume perfect synchronization at the receiver and plot the constellation diagram for both 5&6 with matched filter mentioned in 8.
#part 2
This is simple extension of part 1 of baseband communication
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Generate a sine wave of frequency fc=Fs/4, where Fs is the sampling frequency in the previous assignment.
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Multiply the carrier signal with the modulated signal at the transmitter after the pulse shaping filter. x_pb(n)=x_bb(n).cos(2pifcn/Fs) x_pb means passband signal, and x_bb is the baseband signal generated in previous assignment
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Multiply the transmitted signal again with the carrier signal x_rx(n)=x_pb(n).cos(2pifcn/Fs)
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Then pass it through a LPF with cut-off frequency f_BW (bandwidth of x_mod) Hint: use the spectrum to find the bandwidth of the modulated signal from previous assignment. from scipy import signal
numtaps = 25 f = f_BW/Fs h=signal.firwin(numtaps, f) yc=filter(x_rx,h)
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Continue with the baseband receiver processing as in previous assignment.