CODE EXAMPLE FOR PYTHON

main code for bpsk scheme

import numpy as np
import matplotlib.pyplot as plt

from scipy.special import erfc
N=100000 # Number of symbols to transmi
EbN0dB=np.arange(-4,11,2)#EbN0 range in db for simulation
L=16 # oversampling factor ,L=Tb/Ts(Tb=bit period, Ts=sampling period )
# if a carrier is used use L=Fs/Fc where Fs>>2*fc
Fc=800
Fs=L*Fc
BER=np.zeros(len(EbN0dB))
ak=np.random.randint(2,size=N)# uniform random symbols from 0's and 1's
(s_bb,t)=bpsk_mod(ak,L)# BPSK modulation(waveform) - baseband
s=s_bb*np.cos(2*np.pi*Fc*t/Fs) # with carrier
# Waveforms at the transmitter
fig1, axs = plt.subplots(2, 2)
axs[0, 0].plot(t,s_bb) # baseband wfm zoomed to first 10 bits
axs[0, 0].set_xlabel('t(s)');axs[0, 1].set_ylabel(r'$s_{bb}(t)$-baseband')
axs[0, 1].plot(t,s) # transmitted wfm zoomed to first 10 bits
axs[0, 1].set_xlabel('t(s)');axs[0, 1].set_ylabel('s(t)-with carrier')
axs[0, 0].set_xlim(0,10*L);axs[0, 1].set_xlim(0,10*L)
#signal constellation at transmitter
axs[1, 0].plot(np.real(s_bb),np.imag(s_bb),'o')
axs[1, 0].set_xlim(-1.5,1.5);axs[1, 0].set_ylim(-1.5,1.5)
for i,EbN0 in enumerate(EbN0dB):
    # Compute and add AWGN noise
    r = awgn(s,EbN0,L)
    r_bb = r*np.cos(2*np.pi*Fc*t/Fs)# recovered baseband signal
    ak_hat = bpsk_dmod(r_bb,L)  # baseband correlation demodulator
    BER[i] = np.sum(ak !=ak_hat)/N # Bit Error Rate Computation
    axs[1, 1].plot(t,r) # received signal (with noise)
    axs[1, 1].set_xlabel('t(s)');axs[1, 1].set_ylabel('r(t)')
    axs[1, 1].set_xlim(0,10*L)
theoreticalBER = 0.5*erfc(np.sqrt(10**(EbN0dB/10))) 
fig2, ax1 = plt.subplots(nrows=1,ncols = 1)
ax1.semilogy(EbN0dB,BER,'k*',label='Simulated') # simulated BER
ax1.semilogy(EbN0dB,theoreticalBER,'r-',label='Theoretical')
ax1.set_xlabel(r'$E_b/N_0$ (dB)')
ax1.set_ylabel(r'Probability of Bit Error - $P_b$')
ax1.set_title(['Probability of Bit Error for BPSK modulation'])
ax1.legend();