MATLAB: Do I receive unexpected results if I use the BIN2GRAY function with the PSKMOD function in Communications Toolbox 3.1 (R14SP2)

bin2graycodingCommunications Toolboxgraypskdemodpskmod

I execute the following code using Communications Toolbox 3.1 (R14SP2):
pskdemod(pskmod(bin2gray(0:7,'psk',8),8),8,0,'gray')
I expect the result to be
 0 1 2 3 4 5 6 7
but instead I receive
 0 1 2 3 5 4 7 6

Best Answer

This enhancement has been incorporated in Release 2006a (R2006a). For previous product releases, read below for any possible workarounds:
The symbol order for the PSKMOD function must be set to 'gray' if you want to use a Gray constellation ordering. If the symbol order option is not set to 'gray', the input data is directly mapped to the natural binary-coded ordering using the following modulation formula:
theta = 2*pi*x/M; 
y = exp(j*(theta + ini_phase));
where, x is the input data and M is the modulation order.
If you wish to perform Gray encoding with the PSKMOD function, use the following syntax:
x = 0:7;
pskmod(x,8,0,'gray');
This will ensure that 'x' is first mapped to a Gray constellation before being modulated.
The following code further illustrates the correct method for using the PSKMOD function with symbol ordering set to 'gray':
y = [0:7];
xmap = pskmod(y,8,[]);
k=log2(8);
scatterplot(xmap);
h = get(gca,'Children');
hline = findobj(h,'type','line');
set(hline,'MarkerFaceColor','auto');
hold on;
   for jj=1:length(xmap)
          text(real(xmap(jj))-0.15,imag(xmap(jj))+0.15,dec2base(jj-1,2,3));
   end
set(gca,'yTick',(-(k+1)/4:(k+1)/4),'xTick',(-(k+1)/4:(k+1)/4),...
          'XLim',[-(k+1)/2 (k+1)/2],'YLim',[-(k+1)/2 (k+1)/2],'Box','on',...
          'YGrid','on', 'XGrid','on');
hold off;
title('Scatter plot 8-PSK input = [0,1,2,3,4,5,6,7]');
%%%INCORRECT RESULTS
y = bin2gray([0:7],'psk',8);
xmap = pskmod(y,8,[]);
k=log2(8);
scatterplot(xmap);
h = get(gca,'Children');
hline = findobj(h,'type','line');
set(hline,'MarkerFaceColor','auto');
hold on;
   for jj=1:length(xmap)
          text(real(xmap(jj))-0.15,imag(xmap(jj))+0.15,dec2base(jj-1,2,3));
   end
set(gca,'yTick',(-(k+1)/4:(k+1)/4),'xTick',(-(k+1)/4:(k+1)/4),...
          'XLim',[-(k+1)/2 (k+1)/2],'YLim',[-(k+1)/2 (k+1)/2],'Box','on',...
          'YGrid','on', 'XGrid','on');
hold off;
title({'Scatter plot 8-PSK pre Gray encoding','input = bin2gray([0:7],''psk'',8)=[0,1,3,2,6,7,5,4]'});
%%%CORRECT RESULTS
y = [0:7];
xmap = pskmod(y,8,[],'gray');
k=log2(8);
scatterplot(xmap);
h = get(gca,'Children');
hline = findobj(h,'type','line');
set(hline,'MarkerFaceColor','auto');
hold on;
   for jj=1:length(xmap)
          text(real(xmap(jj))-0.15,imag(xmap(jj))+0.15,dec2base(jj-1,2,3));
   end
set(gca,'yTick',(-(k+1)/4:(k+1)/4),'xTick',(-(k+1)/4:(k+1)/4),...
          'XLim',[-(k+1)/2 (k+1)/2],'YLim',[-(k+1)/2 (k+1)/2],'Box','on',...
          'YGrid','on', 'XGrid','on');
hold off;
title('Scatter plot 8-PSK Gray map input = [0,1,2,3,4,5,6,7]');
Figure 2 shows the incorrect results. As you can see, this is not a Gray encoded map, which is one where adjacent elements differ by more than one bit. This is a direct consequence of the input being used for calculations.
Figure 3 shows the correct results. As you can see, this is a Gray encoded map, as adjacent elements differ by only one bit.
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