Module DigiCommPy.scripts.chapter_2.bpsk

"""
Performance of BPSK tx/rx chain (waveform simulation)

@author: Mathuranathan Viswanathan
Created on Jul 18, 2019
"""
#Execute in Python3: exec(open("chapter_2/bpsk.py").read())
import numpy as np #for numerical computing
import matplotlib.pyplot as plt #for plotting functions
from passband_modulations import bpsk_mod, bpsk_demod
from channels import awgn
from scipy.special import erfc

N=100000 # Number of symbols to transmit
EbN0dB = np.arange(start=-4,stop = 11,step = 2) # Eb/N0 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 >> 2xFc
Fc=800 # carrier frequency
Fs=L*Fc # sampling frequency
BER = np.zeros(len(EbN0dB)) # for BER values for each Eb/N0
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) # refer Chapter section 4.1
    
    r_bb = r*np.cos(2*np.pi*Fc*t/Fs) # recovered baseband signal
    ak_hat = bpsk_demod(r_bb,L) # baseband correlation demodulator
    BER[i] = np.sum(ak !=ak_hat)/N # Bit Error Rate Computation
    
    # Received signal waveform zoomed to first 10 bits
    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)
#------Theoretical Bit/Symbol Error Rates-------------
theoreticalBER = 0.5*erfc(np.sqrt(10**(EbN0dB/10))) # Theoretical bit error rate
#-------------Plots---------------------------
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();fig1.show();fig2.show()