# # 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 import modulation_utils2 from generic_mod_demod import generic_mod, generic_demod from utils.gray_code import gray_code from 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)