BPSK_mod_example.py

#!/usr/bin/python
# BPSK digital modulation example
# by Ivo Maljevic

from numpy import *
from scipy.special import erfc
import matplotlib.pyplot as plt

SNR_MIN     = 0
SNR_MAX     = 9
Eb_No_dB    = arange(SNR_MIN,SNR_MAX+1)
SNR         = 10**(Eb_No_dB/10.0)  # linear SNR

Pe          = empty(shape(SNR))
BER         = empty(shape(SNR))

loop = 0
for snr in SNR:      # SNR loop
 Pe[loop] = 0.5*erfc(sqrt(snr))
 VEC_SIZE = ceil(100/Pe[loop])  # vector length is a function of Pe

 # signal vector, new vector for each SNR value
 s = 2*random.randint(0,high=2,size=VEC_SIZE)-1

 # linear power of the noise; average signal power = 1
 No = 1.0/snr

 # noise
 n = sqrt(No/2)*random.randn(VEC_SIZE)

 # signal + noise
 x = s + n

 # decode received signal + noise
 y = sign(x)

 # find erroneous symbols
 err = where(y != s)
 error_sum = float(len(err[0]))
 BER[loop] = error_sum/VEC_SIZE
 print 'Eb_No_dB=%4.2f, BER=%10.4e, Pe=%10.4e' % \
        (Eb_No_dB[loop], BER[loop], Pe[loop])
 loop += 1

#plt.semilogy(Eb_No_dB, Pe,'r',Eb_No_dB, BER,'s')
plt.semilogy(Eb_No_dB, Pe,'r',linewidth=2)
plt.semilogy(Eb_No_dB, BER,'-s')
plt.grid(True)
plt.legend(('analytical','simulation'))
plt.xlabel('Eb/No (dB)')
plt.ylabel('BER')
plt.show()