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function [S, mapping] = CreateConstellation( mod_type, varargin )
% CreateConstellation creates a K-dimensional signal constellation with M points.
%
% The calling syntax is:
% S = CreateConstellation( mod_type, M, label_type, h )
%
% S = the K by M complex signal constellation.
% K is dimensionality, and M is number of symbols
%
% mod_type = the modulation type, as a string
% must be 'BPSK', 'QPSK', 'PSK', 'QAM', 'APSK', 'HEX', 'HSDPA', or 'FSK'
% [M] = the number of points in the constellation
% must be a power of 2
% not needed for 'BPSK' (M=2), 'QPSK' (M=4), or 'HEX' (M=16). Default for 'FSK' is M=2.
% [label_type] = the labelling type, may be a string or a vector.
% strings must be 'gray', 'Antigray', 'SP', 'SSP', 'MSEW',
% 'huangITNr1', 'huangITNr2', 'huangLetterNr1', or 'huangLetterNr2'
% not needed for BPSK, QPSK, HSDPA, HEX, APSK, or orthogonal FSK (h=1).
% [h] = modulation index. Used only for FSK modulation. Default h=1.
%
% Copyright (C) 2005-2007, Matthew C. Valenti and Shi Cheng
%
% Last updated on Dec. 27, 2007
%
% Function CreateConstellation is part of the Iterative Solutions Coded Modulation
% Library (ISCML).
%
% The Iterative Solutions Coded Modulation Library is free software;
% you can redistribute it and/or modify it under the terms of
% the GNU Lesser General Public License as published by the
% Free Software Foundation; either version 2.1 of the License,
% or (at your option) any later version.
%
% This library 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
% Lesser General Public License for more details.
%
% You should have received a copy of the GNU Lesser General Public
% License along with this library; if not, write to the Free Software
% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
% Optional argument: M
if (length(varargin)>=1)
M = varargin{1};
% make sure that M is a power of 2.
if ( nargin > 1 )
m = log(M)/log(2);
if ( rem(m,1) )
error( 'M must be a power of 2' );
end
end
else
% default value
M = 2;
end
% Optional argument: Label Type
if (length(varargin)>=2)
label_type = varargin{2};
if ~ischar( label_type )
if (length( label_type ) ~= M )
error( 'Length of label_type must be M' );
elseif (sum( sort( label_type ) ~= [0:M-1] ) > 0)
% revised 2-22-07
error( 'Label_type must contain integers 0 through M-1' );
else
mapping = label_type;
end
end
else
% default value
mapping = 0:M-1;
label_type = mapping;
end
% Optional argument: h
if (length(varargin)>=3)
h = varargin{3};
else
% default value
h = 1;
end
% HSDPA modulation
if ( strcmpi( mod_type, 'HSDPA' ) )
if (M==4) % QPSK
temp = [1 1
1 -1
-1 1
-1 -1]';
S = (temp(1,:) + sqrt(-1)*temp(2,:))/sqrt(2);
mapping = [0:3];
elseif (M==16) % 16-QAM
for point=0:15
temp = point;
for i=4:-1:1
bit_vector(4-i+1) = fix( temp/(2^(i-1)) );
temp = temp - bit_vector(4-i+1)*2^(i-1);
end
iq = (-1).^bit_vector;
% S(1,point+1) = (iq(1)*(2-iq(3)) + sqrt(-1)*iq(2)*(2-iq(4)) )/sqrt(5);
S(1,point+1) = (iq(1)*(2-iq(3)) + sqrt(-1)*iq(2)*(2-iq(4)) )/sqrt(10);
end
else
error( 'Modulation order must be 4 or 16 for HSDPA' );
end
elseif ( strcmpi( mod_type, 'BPSK' ) )
S = [1 -1]; % BPSK
mapping = 0:1;
elseif ( strcmpi( mod_type, 'QPSK' ) )
S = [1 +j -j -1]; % QPSK
mapping = 0:3;
elseif ( strcmpi( mod_type, 'PSK' ) )
% PSK modulation
temps = exp( j*2*pi * [0:M-1]/M);
if isstr( label_type )
switch label_type
case 'gray'
mapping = [0,1];
for m = 2:log2(M)
mapping = [mapping, 2^(m-1) + fliplr( mapping )];
end
case 'SP'
if (M == 8)
mapping = [ 0,1,2,3,4,5,6,7];
elseif (M == 4)
mapping = [0,1,2,3];
else
error( 'SP coded PSK only supported for M=4 or 8' );
end
case 'SSP'
if M == 8
mapping = [ 0, 5, 2, 7 , 4, 1, 6, 3];
else
error( 'SSP coded PSK only supported for M=8' );
end
case 'MSEW'
if M == 8
mapping = [ 0,3,5,6,1,2,4,7];
else
error( 'MSEW coded PSK only supported for M=8' );
end
otherwise
error('labeling or symbol set size not supported for PSK');
end
end
S( mapping + 1) = temps; % corrected on 7-25-06
elseif ( strcmpi( mod_type, 'HEX' ) ) % HEX modulation
% only 16-HEX is supported
if ( nargin > 1 )
if (M ~= 16)
error( 'Only 16-HEX supported' )
end
end
% fixed mapping
S = transpose( [0
-2
2
4
(-1 +j*sqrt(3) )
(-3 +j*sqrt(3) )
( 1 +j*sqrt(3) )
( 3 +j*sqrt(3) )
( 1 -j*sqrt(3) )
(-1 -j*sqrt(3) )
( 3 -j*sqrt(3) )
(-3 -j*sqrt(3) )
(-2 +j*2*sqrt(3) )
( -j*2*sqrt(3) )
( +j*2*sqrt(3) )
(-2 -j*2*sqrt(3) ) ] );
% normalize
temps = S/sqrt( mean( abs(S).^2 ) );;
% fix mapping
S(mapping+1) = temps;
elseif ( strcmpi(mod_type, 'APSK' ) )% APSK modulation
% inner ring is QPSK
temps = [+1 +j -1 -j];
% mapping is fixed
if (M==16)
rho = 2.85; % this could be varied
% outer ring is 12-PSK w/ radius rho
temps(5:16) = rho*exp( j*2*pi*[0:11]'/12);
% mapping = [3 11 9 1 6 2 10 14 15 13 12 8 0 4 5 7];
elseif (M==32)
rho1 = 2.84; % these could be varied
rho2 = 5.27
% middle and outer rings
temps(5:16) = rho1*exp( j*2*pi*[0:11]'/12);
temps(17:32) = rho2*exp( j*2*pi*[0:15]'/16 );
mapping = [24 8 0 16 29 28 12 13 9 1 5 4 20 21 17 25 ...
26 30 14 10 15 11 3 7 2 6 22 18 23 19 27 31];
else
error( 'APSK requires M=16 or 32' );
end
% mapping is fixed
S(mapping+1) = temps;
% normalize
S = S/sqrt( mean( abs(S).^2 ) );
elseif ( strcmpi( mod_type, 'QAM') )% QAM modulation
if ( M == 32)
% the mapping is not right here (just CM capacity)
S(1:4) = [ ((-3:2:3)'+j*5) ];
S(5:10) = [ ((-5:2:5)'+j*3) ];
S(11:16) = [ ((-5:2:5)'+j*1) ];
S(17:32) = conj(S(1:16));
% normalize
temps = S/sqrt( mean( abs(S).^2 ) );
% mapping is fixed (added on 12-27-07)
S(mapping+1) = temps;
return;
end
t = (- sqrt(M) +1) :2: (sqrt(M) - 1);
temps = ones( sqrt(M), 1) * t;
temps = temps - j*temps';
temps = reshape( temps.', 1, M);
% fprintf( 'Energy = %f\n', mean( abs(temps/2).^2 ) );
if (isstr( label_type )&(nargin>=3) )
switch label_type
case 'gray'
if M == 16
mapping = [ 15, 11, 3, 7, 14, 10, 2, 6, 12, 8, 0, 4, 13, 9, 1, 5 ];
S( mapping + 1) = temps;
elseif M == 64
submapping = [0, 1, 3, 2, 6, 7, 5, 4];
tempmapping = ones(sqrt(M), 1) *submapping;
tempmapping = sqrt(M)*tempmapping + flipud( tempmapping.');
mapping = reshape( tempmapping.', 1, M);
S( mapping + 1) = temps;
elseif M == 256
submapping = [ [0, 1, 3, 2, 6, 7, 5, 4] , 8+[0, 1, 3, 2, 6, 7, 5, 4]];
tempmapping = ones(sqrt(M), 1) *submapping;
tempmapping = sqrt(M)*tempmapping + flipud( tempmapping.');
mapping = reshape( tempmapping.', 1, M);
S( mapping + 1) = temps;
else
error( 'Gray mapping for QAM only supported for M=16,64, or 256' );
end
case 'SP'
if M == 16
mapping = [ 8, 13, 12, 9, 15, 10, 11, 14, 4, 1, 0, 5, 3, 6, 7, 2];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'MSP'
if M == 16
mapping = [ 8, 11, 12, 15, 1, 2, 5, 6, 4, 7, 0, 3, 13, 14, 9, 10];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'MSEW'
if M == 16
mapping = [ 2, 1, 7, 4, 8, 11, 13, 14, 5, 6, 0, 3, 15, 12, 10, 9];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'Antigray'
if M == 16
mapping = [ 2, 14, 6, 10, 1, 13, 5, 9, 3, 15, 7, 11, 0, 12, 4, 8];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'huangITNr1'
if M == 16
mapping = [ 7, 14, 1, 11, 13, 4, 8, 2, 10, 3, 15, 5, 0, 9, 6, 12];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'huangITNr2'
if M == 16
mapping = [ 12, 10, 5, 6, 15, 9, 3, 0, 2, 4, 14, 13, 1, 7, 8, 11];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'huangLetterNr1'
if M == 16
mapping = [ 13, 7, 1, 11, 14, 4, 2, 8, 3, 9, 15, 5, 0, 10, 12, 6];
S( mapping + 1) = temps;
else
error( 'Modulation not supported' );
end
case 'huangLetterNr2'
if M == 16
mapping = [ 12, 15, 10, 9, 5, 6, 3, 0, 11, 8, 13, 14, 2, 1, 4, 7];
else
error( 'Modulation not supported' );
end
otherwise
error('labeling or symbol set size not supported for QAM');
end
end
S( mapping + 1) = temps;
% normalize
S = S/sqrt( mean( abs(S).^2 ) );
elseif ( strcmpi( mod_type, 'FSK' ) )
if (h==1)
% orthogonal FSK
temps = eye( M );
else
% nonorthogonal FSK
for m = 1:M
for n = 1:M
temps(n,m) = sinc((m-n)*h)* exp(-j*pi*(m-n)*h);
end
end
end
if isstr( label_type )
if ( strcmpi( label_type, 'gray' ) )
mapping = [0,1];
for m = 2:log2(M)
mapping = [mapping, 2^(m-1) + fliplr( mapping )];
end
elseif ( strcmpi( label_type, 'mv' ) )
if ( M == 8 )
mapping = [6 1 0 3 2 5 4 7];
elseif ( M == 16 )
mapping = [0 2 14 12 11 9 5 7 6 4 8 10 13 15 3 1];
else
error( 'dt mapping only supported for M=8 and M=16' );
end
elseif ( strcmpi( label_type, 'dt' ) )
if ( M == 8 )
% mapping = [6 1 0 3 2 5 4 7];
mapping = [2 1 4 3 6 5 0 7];
elseif ( M == 16 )
% mapping = [0 2 14 12 11 9 5 7 6 4 8 10 13 15 3 1];
mapping = [0 15 1 14 9 6 8 7 10 5 11 4 3 12 2 13];
else
error( 'dt mapping only supported for M=8 and M=16' );
end
elseif ( strcmpi( label_type, 'gray2' ) )
if ( M ~= 8 )
error( 'gray2 mapping only supported for M=8' );
else
mapping = [0 1 5 7 3 2 6 4];
end
elseif ( strcmpi( label_type, 'gray3' ) )
if ( M ~= 8 )
error( 'gray3 mapping only supported for M=8' );
else
mapping = [0 1 5 4 6 7 3 2];
end
elseif ( strcmpi( label_type, 'gray4' ) )
if ( M ~= 8 )
error( 'gray4 mapping only supported for M=8' );
else
mapping = [0 1 5 4 6 2 3 7];
end
elseif ( strcmpi( label_type, 'gray5' ) )
if ( M ~= 8 )
error( 'gray5 mapping only supported for M=8' );
else
mapping = [0 1 3 7 5 4 6 2];
end
elseif ( strcmpi( label_type, 'gray6' ) )
if ( M ~= 8 )
error( 'gray6 mapping only supported for M=8' );
else
mapping = [0 1 3 2 6 4 5 7];
end
elseif (strcmpi( label_type, 'reversegray' ) )
if (M==8)
mapping = [0 1 3 2 7 6 4 5];
elseif (M==16)
mapping = [0 1 3 2 7 6 4 5 15 14 12 13 8 9 11 10]
else
error( 'reversegray mapping only supported for M=8 or 16' );
end
else
% natural mapping
mapping = 0:M-1;
end
end
% mapping: rearrange rows
S( :, mapping + 1 ) = temps;
else
error('Modulation and/or labeling not supported');
end
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