ofdm_example.py

import numpy as np

NFFT = 16
NCP = 4
# Generate QPSK symbols

symbols = np.sign(np.random.randn(NFFT)) + 1j * np.sign(np.random.randn(NFFT))

# LTI channel
# Generate h according to a power delay profile
# h = [h_0, h_1, h_2]
# h_0 = sqrt(var0) * (randn + 1j * randn / 2)
# h_1 = sqrt(var1) * (randn + 1j * randn / 2)
# Power delay profile = [1, 0.5, 0.25]
h = [0.4 + 0.3j, 0.2 - 0.1j, 0.1 + 0.05j]

# Take IDFT
x = np.fft.ifft(symbols)

# Add cyclic prefix
x_cp = np.concatenate([x[-NCP:], x])

# Perform linear convolution
y_recv = np.convolve(h, x_cp)
y = y_recv[NCP:NFFT+NCP]

# Take FFT
Y = np.fft.fft(y)

# Recover symbols by zero forcing
x_hat = Y / np.fft.fft(h, NFFT)
print(np.max(np.abs(x_hat - symbols)))