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#
# Copyright 2005,2006,2011 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, modulation_utils2
from gnuradio.digital.generic_mod_demod import generic_mod, generic_demod
from gnuradio.digital.utils.gray_code import gray_code
from gnuradio.digital.utils import mod_codes
# Default number of points in constellation.
_def_constellation_points = 16
# Whether the quadrant bits are coded differentially.
_def_differential = True
# Whether gray coding is used. If differential is True then gray
# coding is used within but not between each quadrant.
_def_mod_code = mod_codes.NO_CODE
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_differential_constellation(m, gray_coded):
"""
Create a constellation with m possible symbols where m must be
a power of 4.
Points are laid out in a square grid.
Bits referring to the quadrant are differentilly encoded,
remaining bits are gray coded.
"""
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)
if gray_coded:
# 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)])
else:
i_gcs = dict([(i, i) for i in range(0, side)])
# 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
def make_not_differential_constellation(m, gray_coded):
side = int(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))
if gray_coded:
# Number rows and columns using gray codes.
gcs = gray_code(side)
# Get inverse gray codes.
i_gcs = mod_codes.invert_code(gcs)
else:
i_gcs = range(0, side)
# The distance between points is found.
step = 2.0/(side-1)
gc_to_x = [-1 + i_gcs[gc]*step for gc in range(0, side)]
# First k/2 bits determine x position.
# Following k/2 bits determine y position.
const_map = []
for i in range(m):
y = gc_to_x[get_bits(i, 0, k/2)]
x = gc_to_x[get_bits(i, k/2, k/2)]
const_map.append(complex(x,y))
return const_map
# /////////////////////////////////////////////////////////////////////////////
# QAM constellation
# /////////////////////////////////////////////////////////////////////////////
def qam_constellation(constellation_points=_def_constellation_points,
differential=_def_differential,
mod_code=_def_mod_code):
"""
Creates a QAM constellation object.
"""
if mod_code == mod_codes.GRAY_CODE:
gray_coded = True
elif mod_code == mod_codes.NO_CODE:
gray_coded = False
else:
raise ValueError("Mod code is not implemented for QAM")
if differential:
points = make_differential_constellation(constellation_points, gray_coded)
else:
points = make_not_differential_constellation(constellation_points, gray_coded)
side = int(sqrt(constellation_points))
width = 2.0/(side-1)
# No pre-diff code
# Should add one so that we can gray-code the quadrant bits too.
pre_diff_code = []
constellation = gr.constellation_rect(points, pre_diff_code, 4, side, side, width, width)
return constellation
# /////////////////////////////////////////////////////////////////////////////
# QAM modulator
# /////////////////////////////////////////////////////////////////////////////
class qam_mod(generic_mod):
def __init__(self, constellation_points=_def_constellation_points,
differential=_def_differential,
mod_code=_def_mod_code,
*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.
"""
constellation = qam_constellation(constellation_points, differential, mod_code)
# We take care of the gray coding in the constellation generation so it doesn't
# need to be done in the block.
super(qam_mod, self).__init__(constellation, differential=differential,
*args, **kwargs)
# /////////////////////////////////////////////////////////////////////////////
# QAM demodulator
#
# /////////////////////////////////////////////////////////////////////////////
class qam_demod(generic_demod):
def __init__(self, constellation_points=_def_constellation_points,
differential=_def_differential,
mod_code=_def_mod_code,
*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, differential, mod_code)
# We take care of the gray coding in the constellation generation so it doesn't
# need to be done in the block.
super(qam_demod, self).__init__(constellation, differential=differential,
*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)
modulation_utils2.add_type_1_constellation('qam', qam_constellation)
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