examp_ofdm.m

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%EXAMP_OFDM  Example of Gabor systems used for OFDM
%
%   This example shows how to use a Gabor Riesz basis for OFDM.
%   The example is simple, and assumes that all the whole spectrum
%   is available for transmission.
%
%   Some further simplifications used to make this example simple:
%
%     - The window and its dual have full length support. This is not
%       practical, because all data would have to be processed at once.
%       Instead, a filter bank approach should be used, with both the
%       window and its dual having a short length. 
%
%     - The window is periodic. The data at the very end interferes with
%       the data at the very beginning. A simple way to solve this is to
%       transmit zeros at the beginning and at the end, to flush the system
%       properly.
%
%   FIGURE 1 Received coefficients.
%
%     This figure shows the distribution in the complex plane of the 
%     received coefficients.
%

% 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/>.

disp('Type "help examp_ofdm" to see a description of how this example works.');
% ----------- setup ------------------------

% Number of channels to use
M=16;

% Time-distance between succesive transmission. This must be
% larger than M, otherwise the symbols will interfere.
a=32;

% Order of QAM
qamorder=4;

% Number of bits to transmit, must be divisable by log2(qamorder)*M
nbits=16000;

% Noiselevel for the channel.
noiselevel=0.1;

% Maximum spread in time, must be even for simplicity
tspread=2;

% Maximum spread in frequency
fspread=2;

% Length (in samples) of transmitted signal.
L=nbits/(log2(qamorder)*M)*a;

% We choose an orthonormal window.
g=cantight(a,M,L);

% ------------ preparation of input data -------------------

% Create a random stream of bits.
inputdata=round(rand(nbits,1));

% QAM modulate it
transmitdata=qam(inputdata,qamorder);

% Create the signal to be tranmitted
f=idgt(reshape(transmitdata,M,[]),g,a);

% --- transmission of signal - influence of the channel ----------

% Construct the symbol of the underspread operator.
symbol=sparse(L,L);

%symbol(1:fspread/2,[L-tspread/2+1:L,1:tspread/2])=randn(fspread/2,tspread);
symbol(1,2)=1;

% Make the symbol conserve real signals.
symbol=(symbol+involute(symbol))/2;

% Apply the underspread operator.
f=spreadop(f,symbol);

% add white noise.
%f=f+noiselevel*((randn(size(f))-.5)+i*(randn(size(f))-.5));

% --- reconstruction of received signal.

receivedcoefficients = dgt(f,g,a,M);

% Plot the coefficients in the complex plane.
figure(1);
if isoctave
  plot(receivedcoefficients(:),'.;;');
else
  plot(receivedcoefficients(:),'.');
end;

receivedbits=iqam(receivedcoefficients(:),qamorder);

% Test for errors.

disp(' ');
disp('Number of faulty bits:');
faulty=sum(abs(receivedbits-inputdata))

disp(' ');
disp('Error rate:');
faulty/nbits