one_bit_freq_offset.py

import numpy as np
import matplotlib.pyplot as plt

# We always send +1
delta_omega = 0.01 * np.pi
n = np.arange(100)
received_symbols = np.exp(1j * delta_omega * n) # AWGN here
#plt.scatter(np.real(received_symbols), np.imag(received_symbols))
#plt.show()
quantized_points = np.array([1, -1, 1j, -1j])
indices = np.argmin(np.abs(
    np.outer(received_symbols, [1, 1, 1, 1]) - \
    np.outer(np.ones(100),
             np.array(quantized_points))), axis=1)
quantized_received_symbols = quantized_points[indices]
# Sanity check of quantization
plt.plot(np.real(received_symbols))
plt.plot(np.real(quantized_received_symbols))
plt.show()