From 02fd90029a1ec465f7c8da4a0d97dcdb8b3f438f Mon Sep 17 00:00:00 2001 From: Tom Rondeau <tom@trondeau.com> Date: Wed, 4 Sep 2013 15:44:20 -0400 Subject: digital: Python functions to support soft decision making and look-up table generation. --- gr-digital/python/digital/qam_constellations.py | 521 ++++++++++++++++++++++++ 1 file changed, 521 insertions(+) create mode 100755 gr-digital/python/digital/qam_constellations.py (limited to 'gr-digital/python/digital/qam_constellations.py') diff --git a/gr-digital/python/digital/qam_constellations.py b/gr-digital/python/digital/qam_constellations.py new file mode 100755 index 0000000000..4e8ee08a61 --- /dev/null +++ b/gr-digital/python/digital/qam_constellations.py @@ -0,0 +1,521 @@ +#!/usr/bin/env python +# +# Copyright 2013 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. +# + +import numpy +from constellation_map_generator import * + +''' +Note on the naming scheme. Each constellation is named using a prefix +for the type of constellation, the order of the constellation, and a +distinguishing feature, which comes in three modes: + +- No extra feature: the basic Gray-coded constellation map; others + will be derived from this type. +- A single number: an indexed number to uniquely identify different + constellation maps. +- 0xN_x0_x1..._xM: A permutation of the base constellation, explained + below. + +For rectangular constellations (BPSK, QPSK, QAM), we can define a +hyperspace and look for all symmetries. This is also known as the +automorphism group of the hypercube, aka the hyperoctahedral +group. What this means is that we can easily define all possible +rotations in terms of the first base mapping by creating the mapping: + + f(x) = k XOR pi(x) + +The x is the bit string for the symbol we are altering. Then k is a +bit string of n bits where n is the number of bits per symbol in the +constellation (e.g., 2 for QPSK or 6 for QAM64). The pi is a +permutation function specified as pi_0, pi_1..., pi_n-1. This permutes +the bits from the base constellation symbol to a new code, which is +then xor'd by k. + +The value of k is from 0 to 2^n-1 and pi is a list of all bit +positions. + +The permutation are given for b0_b1_b2_... for the total number of +bits. In the constellation diagrams shown in the comments, the bit +ordering is shown as [b3b2b1b0]. Bit values returned from the soft bit +LUTs are in the order [b3, b2, b1, b0]. + + +The total number of Gray coded modulations is (2^n)*(n!). + +We create aliases for all possible naming schemes for the +constellations. So if a hyperoctahedral group is defined, we also set +this function equal to a function name using a unique ID number, and +we always select one rotation as our basic rotation that the other +rotations are based off of. + +For 16QAM: + - n = 4 + - (2^n)*(n!) = 384 + - k \in [0x0, 0xF] + - pi = 0, 1, 2, 3 + 0, 1, 3, 2 + 0, 2, 1, 3 + 0, 2, 3, 1 + 0, 3, 1, 2 + 0, 3, 2, 1 + 1, 0, 2, 3 + 1, 0, 3, 2 + 1, 2, 0, 3 + 1, 2, 3, 0 + 1, 3, 0, 2 + 1, 3, 2, 0 + 2, 0, 1, 3 + 2, 0, 3, 1 + 2, 1, 0, 3 + 2, 1, 3, 0 + 2, 3, 0, 1 + 2, 3, 1, 0 + 3, 0, 1, 2 + 3, 0, 2, 1 + 3, 1, 0, 2 + 3, 1, 2, 0 + 3, 2, 0, 1 + 3, 2, 1, 0 +''' + +def qam_16_0x0_0_1_2_3(): + ''' + 0010 0110 | 1110 1010 + + 0011 0111 | 1111 1011 + ----------------------- + 0001 0101 | 1101 1001 + + 0000 0100 | 1100 1000 + ''' + const_points = [-3-3j, -1-3j, 1-3j, 3-3j, + -3-1j, -1-1j, 1-1j, 3-1j, + -3+1j, -1+1j, 1+1j, 3+1j, + -3+3j, -1+3j, 1+3j, 3+3j] + symbols = [0x0, 0x4, 0xC, 0x8, + 0x1, 0x5, 0xD, 0x9, + 0x3, 0x7, 0xF, 0xB, + 0x2, 0x6, 0xE, 0xA] + return (const_points, symbols) +qam_16 = qam_16_0x0_0_1_2_3 +qam_16_0 = qam_16 + +def qam_16_0x1_0_1_2_3(): + ''' + 0011 0111 | 1111 1011 + + 0010 0110 | 1110 1010 + ----------------------- + 0000 0100 | 1100 1000 + + 0001 0101 | 1101 1001 + ''' + k = 0x1 + pi = [0, 1, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_1 = qam_16_0x1_0_1_2_3 + +def qam_16_0x2_0_1_2_3(): + ''' + 0000 0100 | 1100 1000 + + 0001 0101 | 1101 1001 + ----------------------- + 0011 0111 | 1111 1011 + + 0010 0110 | 1110 1010 + ''' + k = 0x2 + pi = [0, 1, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_2 = qam_16_0x2_0_1_2_3 + +def qam_16_0x3_0_1_2_3(): + ''' + 0001 0101 | 1101 1001 + + 0000 0100 | 1100 1000 + ----------------------- + 0010 0110 | 1110 1010 + + 0011 0111 | 1111 1011 + ''' + k = 0x3 + pi = [0, 1, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_3 = qam_16_0x3_0_1_2_3 + + +def qam_16_0x0_1_0_2_3(): + ''' + 0001 0101 | 1101 1001 + + 0011 0111 | 1111 1011 + ----------------------- + 0010 0110 | 1110 1010 + + 0000 0100 | 1100 1000 + ''' + k = 0x0 + pi = [1, 0, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_4 = qam_16_0x0_1_0_2_3 + +def qam_16_0x1_1_0_2_3(): + ''' + 0000 0100 | 1100 1000 + + 0010 0110 | 1110 1010 + ----------------------- + 0011 0111 | 1111 1011 + + 0001 0101 | 1101 1001 + ''' + k = 0x1 + pi = [1, 0, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_5 = qam_16_0x1_1_0_2_3 + +def qam_16_0x2_1_0_2_3(): + ''' + 0011 0111 | 1111 1011 + + 0001 0101 | 1101 1001 + ----------------------- + 0000 0100 | 1100 1000 + + 0010 0110 | 1110 1010 + ''' + k = 0x2 + pi = [1, 0, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_6 = qam_16_0x2_1_0_2_3 + +def qam_16_0x3_1_0_2_3(): + ''' + 0010 0110 | 1110 1010 + + 0000 0100 | 1100 1000 + ----------------------- + 0001 0101 | 1101 1001 + + 0011 0111 | 1111 1011 + ''' + k = 0x3 + pi = [1, 0, 2, 3] + return constellation_map_generator(qam_16, k, pi) +qam_16_7 = qam_16_0x3_1_0_2_3 + + +# Soft bit LUT generators + +def sd_qam_16_0x0_0_1_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0010 0110 | 1110 1010 + + 0011 0111 | 1111 1011 + ----------------------- + 0001 0101 | 1101 1001 + + 0000 0100 | 1100 1000 + ''' + + dist = Es*numpy.sqrt(2) + boundary = dist/3.0 + dist0 = dist/6.0 +# print "Sample: ", x +# print "Es: ", Es +# print "Distance: ", dist +# print "Boundary: ", boundary +# print "1st Bound: ", dist0 + + x_re = x.real + x_im = x.imag + + if x_re < -boundary: + b3 = boundary*(x_re + dist0) + elif x_re < boundary: + b3 = x_re + else: + b3 = boundary*(x_re - dist0) + + if x_im < -boundary: + b1 = boundary*(x_im + dist0) + elif x_im < boundary: + b1 = x_im + else: + b1 = boundary*(x_im - dist0) + + b2 = -abs(x_re) + boundary + b0 = -abs(x_im) + boundary + + return [(Es/2)*b3, (Es/2)*b2, (Es/2)*b1, (Es/2)*b0] +sd_qam_16 = sd_qam_16_0x0_0_1_2_3 +sd_qam_16_0 = sd_qam_16 + +def sd_qam_16_0x1_0_1_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0011 0111 | 1111 1011 + + 0010 0110 | 1110 1010 + ----------------------- + 0000 0100 | 1100 1000 + + 0001 0101 | 1101 1001 + ''' + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b1 = 2*(x_im + 1) + elif x_im < 2: + b1 = x_im + else: + b1 = 2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b0 = +abs(x_im) - 2 + + return [b3, b2, b1, b0] +sd_qam_16_1 = sd_qam_16_0x1_0_1_2_3 + +def sd_qam_16_0x2_0_1_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0000 0100 | 1100 1000 + + 0001 0101 | 1101 1001 + ----------------------- + 0011 0111 | 1111 1011 + + 0010 0110 | 1110 1010 + ''' + + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b1 = -2*(x_im + 1) + elif x_im < 2: + b1 = -x_im + else: + b1 = -2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b0 = -abs(x_im) + 2 + + return [b3, b2, b1, b0] +sd_qam_16_2 = sd_qam_16_0x2_0_1_2_3 + +def sd_qam_16_0x3_0_1_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0001 0101 | 1101 1001 + + 0000 0100 | 1100 1000 + ----------------------- + 0010 0110 | 1110 1010 + + 0011 0111 | 1111 1011 + ''' + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b1 = -2*(x_im + 1) + elif x_im < 2: + b1 = -x_im + else: + b1 = -2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b0 = +abs(x_im) - 2 + + return [b3, b2, b1, b0] +sd_qam_16_3 = sd_qam_16_0x3_0_1_2_3 + +def sd_qam_16_0x0_1_0_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0001 0101 | 1101 1001 + + 0011 0111 | 1111 1011 + ----------------------- + 0010 0110 | 1110 1010 + + 0000 0100 | 1100 1000 + ''' + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b0 = 2*(x_im + 1) + elif x_im < 2: + b0 = x_im + else: + b0 = 2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b1 = -abs(x_im) + 2 + + return [b3, b2, b1, b0] +sd_qam_16_4 = sd_qam_16_0x0_1_0_2_3 + +def sd_qam_16_0x1_1_0_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0000 0100 | 1100 1000 + + 0010 0110 | 1110 1010 + ----------------------- + 0011 0111 | 1111 1011 + + 0001 0101 | 1101 1001 + ''' + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b0 = -2*(x_im + 1) + elif x_im < 2: + b0 = -x_im + else: + b0 = -2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b1 = -abs(x_im) + 2 + + return [b3, b2, b1, b0] +sd_qam_16_5 = sd_qam_16_0x1_1_0_2_3 + +def sd_qam_16_0x2_1_0_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0011 0111 | 1111 1011 + + 0001 0101 | 1101 1001 + ----------------------- + 0000 0100 | 1100 1000 + + 0010 0110 | 1110 1010 + ''' + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b0 = 2*(x_im + 1) + elif x_im < 2: + b0 = x_im + else: + b0 = 2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b1 = +abs(x_im) - 2 + + return [b3, b2, b1, b0] +sd_qam_16_6 = sd_qam_16_0x2_1_0_2_3 + +def sd_qam_16_0x3_1_0_2_3(x, Es=1): + ''' + Soft bit LUT generator for constellation: + + 0010 0110 | 1110 1010 + + 0000 0100 | 1100 1000 + ----------------------- + 0001 0101 | 1101 1001 + + 0011 0111 | 1111 1011 + ''' + x_re = 3*x.real + x_im = 3*x.imag + + if x_re < -2: + b3 = 2*(x_re + 1) + elif x_re < 2: + b3 = x_re + else: + b3 = 2*(x_re - 1) + + if x_im < -2: + b0 = -2*(x_im + 1) + elif x_im < 2: + b0 = -x_im + else: + b0 = -2*(x_im - 1) + + b2 = -abs(x_re) + 2 + b1 = +abs(x_im) - 2 + + return [b3, b2, b1, b0] +sd_qam_16_7 = sd_qam_16_0x3_1_0_2_3 -- cgit v1.2.3