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qam_modulator.py
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qam_modulator.py
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# -*- coding:utf-8 -*-
# @Time: 2023/5/28 15:49
import math
import numpy as np
from matplotlib import pyplot as plt
from scipy.ndimage.filters import gaussian_filter1d
def qam_mod(M):
"""
Generate M-QAM mapping table and demapping table.
Parameters
----------
M: int. Modulation order, must be a positive integer power of 2 and a perfect square number, or one of 8 and 32.
Returns
-------
map_table: dict. M-QAM mapping table.
demap_table: dict.M-QAM demapping table
"""
sqrtM = int(math.sqrt(M))
assert (sqrtM ** 2 == M and M & (M-1) == 0) or (M == 32) or (M == 8),\
"M must be a positive integer power of 2 and a perfect square number, or one of 8 and 32."
if M == 8:
graycode = np.array([0, 1, 3, 7, 5, 4, 6, 2])
constellation = [(-2-2j), (-2+0j), (-2+2j), (0+2j), (2+2j), (2+0j), (2-2j), (0-2j)]
elif M == 32:
temp1 = np.bitwise_xor(np.arange(8), np.right_shift(np.arange(8), 1))
temp2 = np.bitwise_xor(np.arange(4), np.right_shift(np.arange(4), 1))
graycode = np.zeros(M, dtype=int)
num = 0
for i in temp1:
for j in temp2:
graycode[num] = 4 * i + j
num += 1
constellation = [(-7 - 3j) + 2 * (x + y * 1j) for x, y in np.ndindex(8, 4)]
else:
temp = np.bitwise_xor(np.arange(sqrtM), np.right_shift(np.arange(sqrtM), 1))
graycode = np.zeros(M, dtype=int)
num = 0
for i in temp:
for j in temp:
graycode[num] = sqrtM * i + j
num += 1
constellation = [-(sqrtM-1)*(1+1j) + 2*(x+y*1j) for x, y in np.ndindex(sqrtM, sqrtM)]
map_table = dict(zip(graycode, constellation))
demap_table = {v: k for k, v in map_table.items()}
return map_table, demap_table
def qam_mapper(bits, map_table):
"""
Map coded bits into symbols using M-QAM technique.
Parameters
----------
bits: array(num_bit, ). Coded bits to be modulated.
map_table: dict. M-QAM mapping table.
Returns
-------
syms: array(num_symbol, ). Modulated symbols to be transmitted.
"""
M = len(map_table)
bits = np.reshape(bits, (-1, ))
nbits = int(math.log2(M))
if len(bits) % nbits != 0:
bits = np.pad(bits, (0, nbits - len(bits) % nbits), constant_values=(0, 0))
bit_blocks = np.reshape(bits, (-1, nbits)) # divide bits into bit blocks
blocks_bin = [''.join(str(_) for _ in block) for block in bit_blocks]
blocks_dec = [int(block, 2) for block in blocks_bin] # binary to decimal
syms = np.array([map_table[block] for block in blocks_dec])
return syms
def qam_demapper(syms, demap_table):
"""
Demap received symbols into digital bits according to M-QAM mapping table.
Parameters
----------
syms: array(num_bits, ). Received symbols with channel noise.
demap_table: dict. M-QAM demapping table.
Returns
-------
bits: array(num_bit, ). Demodulated bits.
"""
M = len(demap_table)
nbits = int(math.log2(M))
constellation = np.array([x for x in demap_table.keys()])
dists = np.abs(syms.reshape(-1, 1) - constellation.reshape(1, -1))
const_index = dists.argmin(axis=1)
hardDecision = constellation[const_index]
bit_blocks = [bin(demap_table[C])[2:].rjust(nbits, '0') for C in hardDecision]
bits_str = ''.join(block for block in bit_blocks)
bits = np.array([int(_) for _ in bits_str])
return bits
def channel_Awgn(tx_signal, snr, output_power=False):
"""
AWGN channel model.
Parameters
----------
tx_signal: array(num_symbols, ). Signal to be transmitted.
snr: int. SNR at the receiver side.
output_power: bool, default False. Whether to print signal power and noise power.
Returns
-------
bits: array(num_bit, ). Demodulated bits.
"""
signal_power = np.mean(abs(tx_signal ** 2))
n_var = signal_power * 10 ** (- snr / 10) # calculate noise power based on signal power and SNR
if output_power:
print(f"RX Signal power: {signal_power: .4f}. Noise power: {n_var: .4f}")
# Generate complex noise
noise = math.sqrt(n_var/2) * (np.random.randn(*tx_signal.shape)+1j*np.random.randn(*tx_signal.shape))
return tx_signal + noise
def channel_Rayleigh(tx_signal, snr, output_power=False):
"""
Rayleigh channel model.
Parameters
----------
tx_signal: array(num_symbols, ). Signal to be transmitted.
snr: int. SNR at the receiver side.
output_power: bool, default False. Whether to print signal power and noise power.
Returns
-------
bits: array(num_bit, ). Demodulated bits.
"""
shape = tx_signal.shape
sigma = math.sqrt(1 / 2)
H = np.random.normal(0.0, sigma, size=shape) + 1j * np.random.normal(0.0, sigma, size=shape)
Tx_sig = tx_signal * H
Rx_sig = channel_Awgn(Tx_sig, snr, output_power=output_power)
# Channel estimation
Rx_sig = Rx_sig / H
return Rx_sig
def channel_Rician(tx_signal, snr, output_power=False, K=1):
"""
Rician channel model.
Parameters
----------
tx_signal: array(num_symbols, ). Signal to be transmitted.
snr: int. SNR at the receiver side.
output_power: bool, default False. Whether to print signal power and noise power.
Returns
-------
bits: array(num_bit, ). Demodulated bits.
"""
shape = tx_signal.shape
mean = math.sqrt(K / (K + 1))
std = math.sqrt(1 / (K + 1))
H = np.random.normal(mean, std, size=shape) + 1j * np.random.normal(mean, std, size=shape)
Tx_sig = tx_signal * H
Rx_sig = channel_Awgn(Tx_sig, snr, output_power=output_power)
# Channel estimation
Rx_sig = Rx_sig / H
return Rx_sig
def bit_error_rate(tx_bits, rx_bits):
return np.sum(abs(tx_bits - rx_bits)) / len(tx_bits)
def q_func(x):
Qx = 0.5*math.erfc(x/math.sqrt(2))
return Qx
def draw_mod_constellation(map_table):
"""
Draw constellation of M-QAM.
Parameters
----------
map_table: int. dict. M-QAM mapping table.
"""
M = len(map_table)
nbits = int(math.log2(M))
for i in range(M):
Q = map_table[i]
plt.title(f"{M}-QAM Mapping Table")
plt.plot(Q.real, Q.imag, 'bo')
plt.text(Q.real, Q.imag + 0.1, bin(i)[2:].rjust(nbits, '0'), ha='center')
plt.show()
def draw_trx_constellation(syms, tx=True, snr=None, channel=None):
"""
Draw constellation of transmitted or received signal.
Parameters
----------
syms: array(num_symbol, ). Modulated symbols to be transmitted or received symbols.
tx: bool, default True. 1: Draw constellation of transmitted signal. 2: Draw constellation of received signal.
snr: int. SNR at the receiver side.
channel: str. Type of wireless channel.
"""
if tx:
plt.title(f"Constellation of Transmitted Signal")
else:
assert snr is not None, "SNR is required."
assert channel, "Channel type is required."
plt.title(f"Constellation of Received Signal ({channel.upper()}, SNR={snr}dB)")
for sym in syms:
plt.plot(sym.real, sym.imag, 'bo')
plt.show()
def draw_ber_curve(tx_bits, M, snr_range, channel='all'):
"""
Draw BER versus SNR curves over different channel types.
Parameters
----------
tx_bits: array(num_bit, ). Coded bits to be modulated.
M: int. Modulation order.
snr_range: array(*, ). Test SNR range.
channel: str. Type of wireless channel, "all" for all types.
"""
mapping_table, demapping_table = qam_mod(M)
tx_symbols = qam_mapper(tx_bits, mapping_table)
ber_awgn = []
ber_awgn_the = []
ber_rayleigh = []
ber_rician = []
for snr in snr_range:
if channel == 'awgn' or channel == 'all':
rx_awgn = qam_demapper(channel_Awgn(tx_symbols, snr=snr), demapping_table)
ber_awgn.append(bit_error_rate(tx_bits, rx_awgn))
ber_awgn_the.append(4*(1-1./math.sqrt(M))*q_func(math.sqrt(3*(10**(snr/10.))/(M-1)))/math.log2(M))
if channel == 'rayleigh' or channel == 'all':
rx_rayleigh = qam_demapper(channel_Rayleigh(tx_symbols, snr=snr), demapping_table)
ber_rayleigh.append(bit_error_rate(tx_bits, rx_rayleigh))
if channel == 'rician' or channel == 'all':
rx_rician = qam_demapper(channel_Rician(tx_symbols, snr=snr), demapping_table)
ber_rician.append(bit_error_rate(tx_bits, rx_rician))
if channel == 'awgn' or channel == 'all':
plt.plot(snr_range, ber_awgn, label='AWGN')
plt.plot(snr_range, ber_awgn_the, label='AWGN Theory')
if channel == 'rayleigh' or channel == 'all':
plt.plot(snr_range, ber_rayleigh, label='Rayleigh')
if channel == 'rician' or channel == 'all':
plt.plot(snr_range, ber_rician, label='Rician')
plt.title("BER versus SNR")
plt.xlabel("SNR(E0/N0)")
plt.ylabel("Bit error rate (BER)")
plt.yscale('log')
plt.legend(loc='best')
plt.grid(True)
plt.show()
def draw_ber_curve_smooth(tx_bits, M, snr_range, channel='all'):
"""
Draw BER versus SNR curves over different channel types.
Parameters
----------
tx_bits: array(num_bit, ). Coded bits to be modulated.
M: int. Modulation order.
snr_range: array(*, ). Test SNR range.
channel: str. Type of wireless channel, "all" for all types.
"""
mapping_table, demapping_table = qam_mod(M)
tx_symbols = qam_mapper(tx_bits, mapping_table)
ber_awgn = []
ber_awgn_the = []
ber_rayleigh = []
ber_rician = []
for snr in snr_range:
if channel == 'awgn' or channel == 'all':
rx_awgn = qam_demapper(channel_Awgn(tx_symbols, snr=snr), demapping_table)
ber_awgn.append(bit_error_rate(tx_bits, rx_awgn))
ber_awgn_the.append(4*(1-1./math.sqrt(M))*q_func(math.sqrt(3*(10**(snr/10.))/(M-1)))/math.log2(M))
if channel == 'rayleigh' or channel == 'all':
rx_rayleigh = qam_demapper(channel_Rayleigh(tx_symbols, snr=snr), demapping_table)
ber_rayleigh.append(bit_error_rate(tx_bits, rx_rayleigh))
if channel == 'rician' or channel == 'all':
rx_rician = qam_demapper(channel_Rician(tx_symbols, snr=snr), demapping_table)
ber_rician.append(bit_error_rate(tx_bits, rx_rician))
if channel == 'awgn' or channel == 'all':
ber_awgn = gaussian_filter1d(ber_awgn, sigma=15)
ber_awgn_the = gaussian_filter1d(ber_awgn_the, sigma=15)
plt.plot(snr_range, ber_awgn, label='AWGN')
plt.plot(snr_range, ber_awgn_the, label='AWGN Theory')
if channel == 'rayleigh' or channel == 'all':
ber_rayleigh = gaussian_filter1d(ber_rayleigh, sigma=15)
plt.plot(snr_range, ber_rayleigh, label='Rayleigh')
if channel == 'rician' or channel == 'all':
ber_rician = gaussian_filter1d(ber_rician, sigma=15)
plt.plot(snr_range, ber_rician, label='Rician')
plt.title("BER versus SNR")
plt.xlabel("SNR(E0/N0)")
plt.ylabel("Bit error rate (BER)")
plt.yscale('log')
plt.legend(loc='best')
plt.grid(True)
plt.show()