#
# 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 itertools import islice
from gnuradio import gr, gru, modulation_utils
from gnuradio.blks2impl.generic_mod_demod import generic_mod, generic_demod
# default values (used in __init__ and add_options)
_def_samples_per_symbol = 2
_def_excess_bw = 0.35
_def_verbose = False
_def_log = False
# Frequency correction
_def_freq_alpha = 0.010
# Symbol timing recovery
_def_timing_alpha = 0.100
_def_timing_beta = 0.010
_def_timing_max_dev = 1.5
# Fine frequency / Phase correction
_def_costas_alpha = 0.1
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 gray_codes():
""" Generates gray codes."""
gcs = [0, 1]
yield 0
yield 1
# The last power of two passed through.
lp2 = 2
# The next power of two that will be passed through.
np2 = 4
i = 2
while True:
if i == lp2:
# if i is a power of two then gray number is of form 1100000...
result = i + i/2
else:
# if not we take advantage of the symmetry of all but the last bit
# around a power of two.
result = gcs[2*lp2-1-i] + lp2
gcs.append(result)
yield result
i += 1
if i == np2:
lp2 = i
np2 = i*2
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 = list(islice(gray_codes(), 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 modulator
# /////////////////////////////////////////////////////////////////////////////
class qam_mod(generic_mod):
def __init__(self, m,
samples_per_symbol=_def_samples_per_symbol,
excess_bw=_def_excess_bw,
verbose=_def_verbose,
log=_def_log):
"""
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.
@param m: Number of constellation points. Must be a power of four.
@type m: integer
@param samples_per_symbol: samples per baud >= 2
@type samples_per_symbol: integer
@param excess_bw: Root-raised cosine filter excess bandwidth
@type excess_bw: float
@param verbose: Print information about modulator?
@type verbose: bool
@param log: Log modulation data to files?
@type log: bool
"""
if not isinstance(m, int) or not is_power_of_four(m):
raise ValueError("m must be a power of two integer greater than or equal to 4.")
points = make_constellation(m)
constellation = gr.gr_constellation(points)
super(qam_mod, self).__init__(constellation, samples_per_symbol,
excess_bw, verbose, log)
# /////////////////////////////////////////////////////////////////////////////
# QAM demodulator
#
# /////////////////////////////////////////////////////////////////////////////
class qam_demod(generic_demod):
def __init__(self, m,
samples_per_symbol=_def_samples_per_symbol,
excess_bw=_def_excess_bw,
freq_alpha=_def_freq_alpha,
timing_alpha=_def_timing_alpha,
timing_max_dev=_def_timing_max_dev,
costas_alpha=_def_costas_alpha,
verbose=_def_verbose,
log=_def_log):
"""
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.
@param m: Number of constellation points. Must be a power of four.
@type m: integer
@param samples_per_symbol: samples per symbol >= 2
@type samples_per_symbol: float
@param excess_bw: Root-raised cosine filter excess bandwidth
@type excess_bw: float
@param freq_alpha: loop filter gain for frequency recovery
@type freq_alpha: float
@param timing_alpha: loop alpha gain for timing recovery
@type timing_alpha: float
@param timing_max_dev: timing loop maximum rate deviations
@type timing_max_dev: float
@param costas_alpha: loop filter gain in costas loop
@type costas_alphas: float
@param verbose: Print information about modulator?
@type verbose: bool
@param debug: Print modualtion data to files?
@type debug: bool
"""
points = make_constellation(m)
constellation = gr.gr_constellation(points)
super(qam_demod, self).__init__(constellation, samples_per_symbol,
excess_bw, freq_alpha, timing_alpha,
timing_max_dev, costas_alpha, verbose,
log)
#
# Add these to the mod/demod registry
#
# NOT READY TO BE USED YET -- ENABLE AT YOUR OWN RISK
#modulation_utils.add_type_1_mod('qam16', qam16_mod)
#modulation_utils.add_type_1_demod('qam16', qam16_demod)