Digital Modulation

Est. read time: 1 minute | Last updated: July 13, 2025 by John Gentile

Contents

Phase Shift-Keying (PSK)
- Binary Phase-Shift Keying (BPSK)
- Quadrature Phase-Shift Keying (QPSK)
Direct Sequence Spread Spectrum (DSSS) / Code Division Multiple Access (CDMA)
OFDM
References

import numpy as np
import matplotlib.pyplot as plt
from scipy import signal
from rfproto import filter, modulation, plot, sig_gen

Phase Shift-Keying (PSK)

Phase-shift keying- Wikipedia

Binary Phase-Shift Keying (BPSK)

Quadrature Phase-Shift Keying (QPSK)

Direct Sequence Spread Spectrum (DSSS) / Code Division Multiple Access (CDMA)

data_bits = np.array([1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]) # 11-bit barker code
bpsk_symbols = 2 * data_bits - 1
print(f"BPSK symbols: {bpsk_symbols}")

BPSK symbols: [ 1 -1 1 1 -1 1 1 1 -1 -1 -1]

tx = np.concatenate([bpsk_symbols, bpsk_symbols, bpsk_symbols, bpsk_symbols, bpsk_symbols, bpsk_symbols])
# sliding correlation of the transmitted sequence with the reference code:
result = np.correlate(tx,bpsk_symbols, mode='full')

plt.plot(result)
plt.show()
print(max(result))

png

tx = np.zeros(100)
tx[21:21+len(bpsk_symbols)] = bpsk_symbols
tx += np.random.normal(-0.5, 0.5, 100)
plt.plot(tx)
plt.show()

png

result = np.correlate(tx,bpsk_symbols, mode='full')
plt.plot(result)
plt.show()
print(f"Max correlation of {max(result)} at {list(result).index(max(result))}")

png

Max correlation of 8.722090712649463 at 31

OFDM

from IPython.display import YouTubeVideo

YouTubeVideo('1rpoUqx0360')

YouTubeVideo('UCRildDdrX4')

References

The History of Orthogonal Frequency-Division Multiplexing (OFDM) - IEEE