communication

#part 1

1. Generate a binary stream for 20 symbols for 4-PAM modulation
2. Bit rate of 20Mbps
3. sps 8 (Sample per symbol)
4. Plot the transmit waveform for square pulse
5. Plot the transmit waveform for RRC pulse with beta=0.25
6. 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

7. Choose the appropriate matched filter for 5 and 6
8. 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

1. Generate a sine wave of frequency fc=Fs/4, where Fs is the sampling frequency in the previous assignment.

2. 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

3. Multiply the transmitted signal again with the carrier signal x_rx(n)=x_pb(n).cos(2pifcn/Fs)

4. 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)

5. Continue with the baseband receiver processing as in previous assignment.