Continuous Learning
N. Metternich
3/10/2024
The crux of the modeling of BPSK is the use of the DigiCommPy\passband.py\bpsk_mod
function:
"""
Passband simulation models - modulation and demodulation techniques (Chapter 2)
@author: Mathuranathan Viswanathan
Created on Jul 17, 2019
"""
import numpy as np
import matplotlib.pyplot as plt
def bpsk_mod(ak,L):
"""
Function to modulate an incoming binary stream using BPSK (baseband)
Parameters:
ak : input binary data stream (0's and 1's) to modulate
L : oversampling factor (Tb/Ts)
Returns:
(s_bb,t) : tuple of following variables
s_bb: BPSK modulated signal(baseband) - s_bb(t)
t : generated time base for the modulated signal
"""
from scipy.signal import upfirdn
s_bb = upfirdn(h=[1]*L, x=2*ak-1, up = L) # NRZ encoder
t=np.arange(start = 0,stop = len(ak)*L) #discrete time base
return (s_bb,t)
def bpsk_demod(r_bb,L):
"""
Function to demodulate a BPSK (baseband) signal
Parameters:
r_bb : received signal at the receiver front end (baseband)
L : oversampling factor (Tsym/Ts)
Returns:
ak_hat : detected/estimated binary stream
"""
x = np.real(r_bb) # I arm
x = np.convolve(x,np.ones(L)) # integrate for Tb duration (L samples)
x = x[L-1:-1:L] # I arm - sample at every L
ak_hat = (x > 0).transpose() # threshold detector
return ak_hat
Continuous Learning
N. Metternich
3/10/2024
Not really sure what the scipy.signal\upfirdn function is doing; nor what the system transfer
function, h = “ones” of length L is about. Need to study this to see what happens when an MSK
signal is modeled: sure hope it is!
Edited the BPSK Performance example.
I think I started with Started with the “perf_bpsk_demo.py” under folder “Chapter 2”.
Also set the Path statement to the highlighted directory so VS Code would find the stuff under
“DIGICOMMPY”. I re-compiled all the files and deleted those .pcy starting with initial since I
don’t know how Python uses one file or another.
C:\Users\norbert.metternich\Documents\projects\python>tree DigiCommPy
Folder PATH listing
Volume serial number is EA30-38DC
C:\USERS\NORBERT.METTERNICH\DOCUMENTS\PROJECTS\PYTHON\DIGICOMMPY
├───.vscode
├───chapter_1
│
├───snippets
│
│
└───__pycache__
│
└───__pycache__
├───chapter_2
│
└───__pycache__
├───chapter_4
│
└───__pycache__
├───chapter_5
│
└───__pycache__
├───chapter_6
│
└───__pycache__
└───__pycache__
(1) reduced the plot size so it would finish in a timely manneradded a directive to use the axis
labels had some errors: don’t know how it ever worked for the author.
'''
File: nhm_student_chapter2_bpsk_performance_demo.py
@student: Norbert Metternich
Last edit on March 10, 2024
'''
"""
Performance of BPSK tx/rx chain (waveform simulation)
@author: Mathuranathan Viswanathan
Created on Jul 18, 2019
"""
Continuous Learning
N. Metternich
3/10/2024
#Use of exec is frowned upon.
#Execute in Python3: exec(open("chapter_2/bpsk.py").read())
# %%
# Import program components/initialize data
import numpy as np #for numerical computing
import matplotlib
matplotlib.use('TkAgg') # or any other backend that supports LaTeX
import matplotlib.pyplot as plt #for plotting functions
#plt.rcParams.update(plt.rcParamsDefault)
from passband_modulations import bpsk_mod, bpsk_demod
from channels import awgn
from nhm_user_control import prompt_to_continue
from scipy.special import erfc
from numpy import sum,isrealobj,sqrt
from numpy.random import standard_normal
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
# The author said plot the first 10 bis - so find the indexes for that:
fst10=np.arange(start=0,stop=L*10,step=1)
fig1, axs = plt.subplots(2, 2)
axs[0, 0].plot(t[fst10],s_bb[fst10]) # baseband wfm zoomed to first 10 bits
axs[0, 0].set_xlabel('t(s)')
axs[0, 0].set_ylabel(r'$s_{bb}(t)$-baseband')
axs[0, 1].plot(t[fst10],s[fst10]) # transmitted wfm zoomed to first 10 bits
Continuous Learning
N. Metternich
3/10/2024
axs[0, 1].set_xlabel('t(s)')
axs[0, 1].set_ylabel('s(t)-with carrier')
axs[0, 1].set_xlim(0,10*L)
axs[0, 1].set_xlim(0,10*L)
# The signals are not complex - so, the imaginary part is always zero!
#signal constellation at transmitter
axs[1, 0].plot(np.real(s_bb[fst10]),np.imag(s_bb[fst10]),'o')
axs[1, 0].set_xlim(-1.5,1.5)
axs[1, 0].set_ylim(-1.5,1.5)
axs[1, 0].set_xlabel(r'Re($s_{bb}$)')
axs[1, 0].set_ylabel(r'Im($s_{bb}$)')
plt.tight_layout()
fig1.show()
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[fst10],r[fst10]) # 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)
plt.tight_layout()
fig1.show()
#------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')
Continuous Learning
N. Metternich
3/10/2024
plt.tight_layout()
ax1.legend()
fig2.show()
# ChatGPT module
#if prompt_to_continue():
#
print("Continuing...")
#else:
#
print("Exiting...")
## %%
# %%
The Python file I was using appeared to have a problem pointing to the correct subplot; and
either I messed it all up or it was messed up from the start. Instead of having xlabel and
ylabel statements on the same line, I placed them underneath one another and cleaned up
the handles (which I may have broken to begin with).
Note: the “Constellation” in the bottom left shows that the BPSK is comprised of phases at 180 and +180-degrees. I have used +90 and +270 (anything that is orthogonal for BPSK -- I
think works – for Matlab auto-correlation and I am pretty sure that is OK to do. This
communications toolbox is true to either a signal at base-band (bb) or a signal up-converted
to a carrier (fC) frequency. I have a concern that that frequencies that result MSK should be
orthogonal to one another; that is the modulation that produces the hopefully the RF of one
symbol period or one half symbol period (if I have the nomenclature right) results in
orthogonal frequencies. This concern is based on a discussion on BFSK in “wirelesspiminimum-shift-keying-msk-a-tutorial.pdf” by Qasim Chaudhari which may or may not relate to
MSK.
Continuous Learning
N. Metternich
3/10/2024
Continuous Learning
N. Metternich
3/10/2024