PSK.m

%% Phase Shift Keying
%% Signal formula
% $s_m(t) = \sqrt{\frac{2\epsilon_s}{T}}\cos\left(2\pi f_ct + \frac{2\pi
% m}{M}\right)g_T(t)$
%% Return value
% This function returns the _vector representation_ of the PSK
% constellation.
%%
% $\underline{\underline{PSK_M}}(\epsilon_s) = \pmatrix{
% \sqrt{\epsilon_s} & 0\cr
% \sqrt{\epsilon_s}\cos\left(\frac{2\pi}{M}\right) &
% \sqrt{\epsilon_s}\sin\left(\frac{2\pi}{M}\right)\cr
% ... & ...\cr
% \sqrt{\epsilon_s}\cos\left(\frac{2\pi m}{M}\right) &
% \sqrt{\epsilon_s}\sin\left(\frac{2\pi m}{M}\right)
% }$
%
%% Implementation and example
% The code below represents the implementation of the function, while the
% result is obtained computing:
%%
% $\underline{\underline{PSK_8}}(4)$
function s = PSK(M, Es)
    s = [1:M; 1:M];
    
    s(1,:) = sqrt(Es)*cos(2*s(1,:)*pi/M);
    s(2,:) = sqrt(Es)*sin(2*s(2,:)*pi/M);
    
    s = s';
end

%% License
% Copyright (C) 2019 helllayde
%%
% Redistribution and use in source and binary forms, with or without 
% modification, are permitted provided that the following conditions are 
% met:
%%
% 1. Redistributions of source code must retain the above copyright notice, 
% this list of conditions and the following disclaimer.
%%
% 2. Redistributions in binary form must reproduce the above copyright 
% notice, this list of conditions and the following disclaimer in the 
% documentation and/or other materials provided with the distribution.
%% 
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
% "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 
% TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 
% PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR 
% CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 
% EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
% PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
% LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 
% NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
% SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.