octave-communications-common 1.2.0-2 / usr / share / octave / packages / communications-1.2.0 / qaskenco.m

## Copyright (C) 2003 David Bateman
##
## This program 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 of the License, or (at your option) any later
## version.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {Function File} {} qaskenco (@var{m})
## @deftypefnx {Function File} {} qaskenco (@var{msg}, @var{m})
## @deftypefnx {Function File} {@var{y} =} qaskenco (@dots{})
## @deftypefnx {Function File} {[@var{inphase}, @var{quadr}] =} qaskenco (@dots{})
##
## Map a digital signal using a square QASK constellation. The argument
## @var{m} must be a positive integer power of 2. With two input arguments
## the variable @var{msg} represents the message to be encoded. The values
## of @var{msg} must be between 0 and @code{@var{m}-1}. In all cases
## @code{qaskenco (@var{M})} is equivalent to @code{qaskenco (1:@var{m}, @var{m})}
##
## Three types of outputs can be created depending on the number of output
## arguments. That is
##
## @table @asis
## @item No output arguments
## In this case @code{qaskenco} plots the constellation. Only the
## points in @var{msg} are plotted, which in the case of a single input
## argument is all constellation points.
## @item A single output argument
## The returned variable is a complex variable representing the in-phase
## and quadrature components of the mapped message @var{msg}. With, a
## single input argument this effectively gives the mapping from symbols
## to constellation points
## @item Two output arguments
## This is the same as one output argument, expect that the in-phase
## and quadrature components are returned explicitly. That is
##
## @example
## c = qaskenco (msg, m);
## [a, b] = qaskenco (msg, m);
## all (c == a + 1i*b)
##     @result{} 1
## @end example
## @end table
##
## If @code{sqrt (@var{m})} is an integer, then @code{qaskenco} uses a Gray
## mapping. Otherwise, an attempt is made to create a nearly square mapping
## with a minimum Hamming distance between adjacent constellation points.
## @seealso{qaskdeco}
## @end deftypefn

function [a, b] = qaskenco (msg, M)

  if (nargin == 1)
    M = msg;
  elseif (nargin == 2)
    if (min (msg(:)) < 0 || max (msg(:)) > M-1)
      error ("qaskenco: all elements of MSG must be in the range [0:M-1]");
    endif
  else
    print_usage ();
  endif

  if (!isscalar (M) || M != ceil (M) || M < 2)
    error ("qaskenco: M must be a positive integer greater than 2");
  endif

  if (log2 (M) != ceil (log2 (M)))
    error ("qaskenco: M must be a power of 2");
  endif

  if (M == 2)
    inphase = [-1,  1];
    quadr =   [ 0,  0];
  elseif (M == 4)
    inphase = [-1, -1,  1,  1];
    quadr =   [-1,  1, -1,  1];
  elseif (M == 8)
    inphase = [-1, -1,  1,  1, -3, -3,  3,  3];
    quadr =   [-1,  1, -1,  1, -1,  1, -1,  1];
  else
    NC = 2^floor (log2 (sqrt (M)));
    MM = NC * NC;
    Gray = [0, 1];
    for i = 2:ceil (log2 (NC))
      Gray = [Gray 2^(i-1) + fliplr(Gray)];
    endfor
    Gray = fliplr (de2bi (shift (Gray, length (Gray)/2 - 1)));
    Gray2 = zeros (MM, log2 (MM));
    Gray2(:,1:2:log2 (MM)) = repmat (Gray, NC, 1);
    for i = 1:NC
      Gray2(i:NC:MM,2:2:log2 (MM)) = Gray;
    endfor
    layout = reshape (bi2de (fliplr (Gray2)), NC, NC);

    if (MM != M)
      ## Not sure this is the best that can be done for these mappings. If
      ## anyone wants to improve this, go ahead, but do it in qaskdeco too.
      OFF = sqrt (M/32);
      NR = NC + 2*OFF;
      layout2 = NaN * ones (NR);
      layout2(1+OFF:OFF+NC,1+OFF:OFF+NC) = layout;

      layout2(1:OFF,1+OFF:OFF+NC) = MM + layout(OFF:-1:1,:);
      layout2(NR-OFF+1:NR,1+OFF:OFF+NC) = MM + layout(NC:-1:NC-OFF+1,:);

      layout2(1+2*OFF:NC,1:OFF) = MM + layout(OFF+1:NC-OFF,OFF:-1:1);
      layout2(1+2*OFF:NC,NR-OFF+1:NR) = MM + ...
                                        layout(OFF+1:NC-OFF,NC:-1:NC-OFF+1);

      layout2(1+OFF:2*OFF,1:OFF) = MM + ...
                                   layout(NC/2:-1:NC/2-OFF+1,NC/2:-1:OFF+1);
      layout2(NC+1:OFF+NC,1:OFF) = MM + ...
                                   layout(NC-OFF:-1:NC/2+1,NC/2:-1:OFF+1);

      layout2(1+OFF:2*OFF,NR-OFF+1:NR) = MM + ...
                                         layout(NC/2:-1:NC/2-OFF+1,NC-OFF:-1:NC/2+1);
      layout2(NC+1:OFF+NC,NR-OFF+1:NR) = MM + ...
                                         layout(NC-OFF:-1:NC/2+1,NC-OFF:-1:NC/2+1);
      NC = NR;
      layout = layout2;
    endif

    inphase = repmat ([0:NC-1]*2 - NC + 1, 1, NC);
    for i = 1:NC
      quadr(i:NC:NC*NC) = [0:NC-1]*2 - NC + 1;
    endfor
    [dummy, indx] = sort (layout(:));
    indx = indx(1:M);                   ## Get rid of remaining NaN's
    inphase = inphase(indx);
    quadr = quadr(indx);
  endif

  if (nargin == 2)
    inphase = inphase(msg+1);
    quadr = quadr(msg+1);
    ## Fix up indexing if using column vector
    if (size (msg, 2) == 1)
      inphase = inphase';
      quadr = quadr';
    endif
  endif

  if (nargout == 0)
    inphase = inphase(:);
    quadr = quadr(:);
    plot (inphase, quadr, "r+");
    title ("QASK Constellation");
    xlabel ("In-phase");
    ylabel ("Quadrature");
    axis ([min(inphase) - 1, max(inphase) + 1, min(quadr) - 1, max(quadr) + 1]);
    xd = 0.02 * max (inphase);
    if (nargin == 2)
      msg = msg(:);
      for i = 1:length (inphase)
        text (inphase(i) + xd, quadr(i), num2str (msg(i)));
      endfor
    else
      for i = 1:length (inphase)
        text (inphase(i) + xd, quadr(i), num2str (i-1));
      endfor
    endif
  elseif (nargout == 1)
    a = inphase + 1i * quadr;
  else
    a = inphase;
    b = quadr;
  endif

endfunction

%% Test input validation
%!error qaskenco ()
%!error qaskenco (1, 2, 3)
%!error qaskenco (0:7, 3)