1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
|
#
# Copyright 2005,2006 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# GNU Radio is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3, or (at your option)
# any later version.
#
# GNU Radio is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with GNU Radio; see the file COPYING. If not, write to
# the Free Software Foundation, Inc., 51 Franklin Street,
# Boston, MA 02110-1301, USA.
#
"""
QAM modulation and demodulation.
"""
from math import pi, sqrt, log
from gnuradio import gr, gru, modulation_utils2
from gnuradio.blks2impl.generic_mod_demod import generic_mod, generic_demod
from gnuradio.utils.gray_code import gray_code
# Default number of points in constellation.
_def_constellation_points = 16
def is_power_of_four(x):
v = log(x)/log(4)
return int(v) == v
def get_bit(x, n):
""" Get the n'th bit of integer x (from little end)."""
return (x&(0x01 << n)) >> n
def get_bits(x, n, k):
""" Get the k bits of integer x starting at bit n(from little end)."""
# Remove the n smallest bits
v = x >> n
# Remove all bits bigger than n+k-1
return v % pow(2, k)
def make_constellation(m):
"""
Create a constellation with m possible symbols where m must be
a power of 4.
Points are laid out in a square grid.
"""
sqrtm = pow(m, 0.5)
if (not isinstance(m, int) or m < 4 or not is_power_of_four(m)):
raise ValueError("m must be a power of 4 integer.")
# Each symbol holds k bits.
k = int(log(m) / log(2.0))
# First create a constellation for one quadrant containing m/4 points.
# The quadrant has 'side' points along each side of a quadrant.
side = int(sqrtm/2)
# Number rows and columns using gray codes.
gcs = gray_code(side)
# Get inverse gray codes.
i_gcs = dict([(v, key) for key, v in enumerate(gcs)])
# The distance between points is found.
step = 1/(side-0.5)
gc_to_x = [(i_gcs[gc]+0.5)*step for gc in range(0, side)]
# Takes the (x, y) location of the point with the quadrant along
# with the quadrant number. (x, y) are integers referring to which
# point within the quadrant it is.
# A complex number representing this location of this point is returned.
def get_c(gc_x, gc_y, quad):
if quad == 0:
return complex(gc_to_x[gc_x], gc_to_x[gc_y])
if quad == 1:
return complex(-gc_to_x[gc_y], gc_to_x[gc_x])
if quad == 2:
return complex(-gc_to_x[gc_x], -gc_to_x[gc_y])
if quad == 3:
return complex(gc_to_x[gc_y], -gc_to_x[gc_x])
raise StandardError("Impossible!")
# First two bits determine quadrant.
# Next (k-2)/2 bits determine x position.
# Following (k-2)/2 bits determine y position.
# How x and y relate to real and imag depends on quadrant (see get_c function).
const_map = []
for i in range(m):
y = get_bits(i, 0, (k-2)/2)
x = get_bits(i, (k-2)/2, (k-2)/2)
quad = get_bits(i, k-2, 2)
const_map.append(get_c(x, y, quad))
return const_map
# /////////////////////////////////////////////////////////////////////////////
# QAM constellation
# /////////////////////////////////////////////////////////////////////////////
def qam_constellation(constellation_points=_def_constellation_points):
"""
Creates a QAM constellation object.
"""
points = make_constellation(constellation_points)
side = int(sqrt(constellation_points))
width = 2.0/(side-1)
constellation = gr.constellation_sector(points, side, side, width, width)
return constellation
# /////////////////////////////////////////////////////////////////////////////
# QAM modulator
# /////////////////////////////////////////////////////////////////////////////
class qam_mod(generic_mod):
def __init__(self, constellation_points=_def_constellation_points, *args, **kwargs):
"""
Hierarchical block for RRC-filtered QAM modulation.
The input is a byte stream (unsigned char) and the
output is the complex modulated signal at baseband.
See generic_mod block for list of parameters.
"""
if not isinstance(constellation_points, int) or not is_power_of_four(constellation_points):
raise ValueError("number of constellation points must be a power of four.")
constellation = qam_constellation(constellation_points)
super(qam_mod, self).__init__(constellation, *args, **kwargs)
# /////////////////////////////////////////////////////////////////////////////
# QAM demodulator
#
# /////////////////////////////////////////////////////////////////////////////
class qam_demod(generic_demod):
def __init__(self, constellation_points=_def_constellation_points, *args, **kwargs):
"""
Hierarchical block for RRC-filtered QAM modulation.
The input is a byte stream (unsigned char) and the
output is the complex modulated signal at baseband.
See generic_demod block for list of parameters.
"""
constellation = qam_constellation(constellation_points)
super(qam_demod, self).__init__(constellation, *args, **kwargs)
#
# Add these to the mod/demod registry
#
modulation_utils2.add_type_1_mod('qam', qam_mod)
modulation_utils2.add_type_1_demod('qam', qam_demod)
|
