# Rayleigh fading channel Simulation Python code

This fading channel python code script simulates rayleigh channel coefficients with doppler frequency shift. The rayleigh python code output plots are also mentioned.

Introduction : The term fading refers to variation in the received signal strength due to various parameters between transmitter and receiver as well as their movements. These factors or parameters include path loss, multipaths, doppler spread, shadowing effect, mobility etc. The rayleigh channel model simulates only NLOS (Non Line of Sight) components between transmitter and receiver. In this channel model type, power is exponentially distributed and phase is uniformly distributed. Phase is independent from amplitude. Refer article on fading basics and fading types >>.

## Rayleigh Channel Python code

# This python script is used to generate rayleigh channel coefficients
import numpy as np
import matplotlib.pyplot as plt

# Sinusoidal waveform generation
t = np.linspace(1, 100, 750)
x_volts = 20*np.sin(t/(2*np.pi))
x_watts = x_volts ** 2
x_db = 10 * np.log10(x_watts)

# Parameters for simulation
v = 60 # velocity (meters per second)
center_freq = 100e6 # RF 100 MHz
Fs = 2e5 # sample rate 0.2 MHz
N = 1000 # Total numbers of sine waves
pi = 3.14
fd = v*center_freq/3e8 # Doppler frequency shift (maximum)
print("Doppler frequency shift (Max.):", fd)
t = np.arange(0, 1, 1/Fs) # time vector. (start, stop, step)
x = np.zeros(len(t))
y = np.zeros(len(t))
for i in range(N):
alpha = (np.random.rand() - 0.5) * 2 * pi
phi = (np.random.rand() - 0.5) * 2 * pi
x = x + np.random.randn() * np.cos(2 * pi * fd * t * np.cos(alpha) + phi)
y = y + np.random.randn() * np.sin(2 * pi * fd * t * np.cos(alpha) + phi)

z = (1/np.sqrt(N)) * (x + 1j*y) # This is channel response used to convolve with transmitted data or signal
z_mag = np.abs(z) # Used in plot
z_mag_dB = 10*np.log10(z_mag) # convert to dB

# Convolve sinusoidal waveform with Rayleigh Fading channel
y3 = np.convolve(z, x_volts)

# Plots
figure, axis = plt.subplots(2, 2)
axis[0, 0].plot(x_volts)
axis[0, 0].set_title("Pure sine wave signal")
axis[0, 1].plot(z)
axis[0, 1].set_title("Rayleigh Channel response")
axis[1, 0].plot(z_mag_dB)
axis[1, 0].set_title("Rayleigh Channel response (dB)")
axis[1, 1].plot(y3)
axis[1, 1].set_title("Convolved sine wave signal")
plt.tight_layout()
plt.show()

## Rayleigh fading channel output plots

Following are the plots of above Rayleigh fading channel python code.