BPSK, QPSK, 16QAM, and 64QAM Modulation in Python

This document provides Python code for BPSK, QPSK, 16QAM, and 64QAM modulation schemes.

Introduction:

Digital modulation techniques, such as QPSK, 16QAM, and 64QAM, enhance bandwidth efficiency by mapping multiple bits onto a single carrier. BPSK is known for its robustness and is often employed in long-distance communication and pilot subcarrier mapping.

Python Script for Data Mapping/Modulation

The following Python code can map digital binary data according to different modulation constellation points like BPSK, QPSK, 16QAM, and 64QAM.

# Binary data generator (1's and 0's as per user defined length)
import random
import numpy as np
import numpy
import matplotlib.pyplot as plt

# Python code to generate binary stream of data
input_data = ""
len1 = 1000  # length of input data
for i in range(len1):
    temp1 = str(random.randint(0, 1))
    input_data += temp1
print(input_data)

input_data1 = [int(i) for i in input_data]  # convert string to list
print(input_data1)

# Setting up parameters such as modulation type, number of bits per carrier (nc) and norm_factor
modulation_type = int(input("Enter modulation type (0: BPSK, 1: QPSK, 2:16QAM, 3: 64QAM: "))
print(modulation_type)

norm_factor = [1.0, 0.7071, 0.3162, 0.1543]
nc = [1, 2, 4, 6]

k = norm_factor[modulation_type]
print(k)

mode = nc[modulation_type]
print(mode)

M0 = []
match mode:
    case 1:
        M0 = np.array([1, -1])
        i = len(M0)
        b = np.zeros(i)
        for i in M0:
            M0 = numpy.multiply(M0, k)
        plt.plot(M0.real, M0.imag, "g*")
        plt.title("Figure-1 : BPSK constellation")
        plt.show()
    case 2:
        M0 = np.array([1. + 1.j, -1. + 1.j, 1. - 1.j, -1. - 1.j])
        i = len(M0)
        b = np.zeros(i)
        for i in M0:
            N0 = numpy.multiply(M0, k)
        plt.plot(M0.real, M0.imag, "g*")
        plt.title("Figure-2 : QPSK constellation")
        plt.show()
    case 4:
        M0 = np.array([1. + 1.j, 1. + 3.j, 1. - 1.j, 1. - 3.j, 3. + 1.j, 3. + 3.j, 3. - 1.j, 3. - 3.j, -1. + 1.j, -1. + 3.j, -1. - 1.j, -1. - 3.j, -3. + 1.j, -3. + 3.j, -3. - 1.j, -3. - 3.j])
        i = len(M0)
        b = np.zeros(i)
        for i in M0:
            M0 = numpy.multiply(M0, k)
        plt.plot(M0.real, M0.imag, "g*")
        plt.title("Figure-3 : 16QAM constellation")
        plt.show()
    case 6:
        M0 = np.array([3 + 3j, 3 + 1j, 3 + 5j, 3 + 7j, 3 - 3j, 3 - 1j, 3 - 5j, 3 - 7j, 1 + 3j, 1 + 1j, 1 + 5j, 1 + 7j, 1 - 3j, 1 - 1j, 1 - 5j, 1 - 7j, 5 + 3j, 5 + 1j, 5 + 5j, 5 + 7j, 5 - 3j, 5 - 1j, 5 - 5j, 5 - 7j, 7 + 3j, 7 + 1j, 7 + 5j, 7 + 7j, 7 - 3j, 7 - 1j, 7 - 5j, 7 - 7j, -3 + 3j, 3 + 1j, -3 + 5j, -3 + 7j, -3 - 3j, -3 - 1j, -3 - 5j, -3 - 7j, -1 + 3j, -1 + 1j, -1 + 5j, -1 + 7j, -1 - 3j, -1 - 1j, -1 - 5j, -1 - 7j, -5 + 3j, -5 + 1j, -5 + 5j, -5 + 7j, -5 - 3j, -5 - 1j, -5 - 5j, -5 - 7j, -7 + 3j, -7 + 1j, -7 + 5j, -7 + 7j, -7 - 3j, -7 - 1j, -7 - 5j, -7 - 7j])
        i = len(M0)
        b = np.zeros(i)
        for i in M0:
            M0 = numpy.multiply(M0, k)
        plt.plot(M0.real, M0.imag, "g*")
        plt.title("Figure-4 : 64QAM constellation")
        plt.show()

# checking length of data to add padding zero at the end if required
remainder = len1 % mode
print(remainder)

if remainder != 0:
    remainder = mode-remainder
    input_data1 = np.pad(input_data1, (0, remainder))
    len1 = len(input_data1)

len2 = int(len1/mode)
input_data_r = np.reshape(input_data1, (len2, mode))
print(input_data_r)

s1 = input_data
s2 = []
chunks = [s1[i:i+mode] for i in range(0, len(s1), mode)]

for piece in chunks:
    temp = int(piece, 2)
    print(temp, piece)
    s2.append(temp)

map_out = []
for value in s2:
    map_out.append(M0[value])
print(M0[value])

Input (User Interface)

The script prompts the user to select the modulation type:

Enter modulation type (0: BPSK, 1: QPSK, 2:16QAM, 3: 64QAM:)

Output Plots

The following are output plots for various modulation types based on the input provided in the Python command prompt.

BPSK Constellation Plot

QPSK Constellation Plot

16QAM Constellation Plot

64QAM Constellation Plot