examp_ofdm.m

linear time－frequency toolbox

%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.
%
%     - The channel should be modelled by a pseudo-differential operator
%       that causes time and frequency shifts / dispersion in the signal.
%       This example just uses white noise.
%
%
%   FIGURE 1 Received coefficients.
%
%     This figure shows the distribution in the complex plane of the 
%     received coefficients.
%

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

% Number of channels to use
M=8;

% Time-distance between succesive transmission. This must be
% larger than M, otherwise the symbols will interfere.
a=10;

% Order of QAM
qamorder=4;

% Noiselevel for the channel.
noiselevel=0.1;

% Choose a long transmission to even out statistical fluctuations.
L=4000;

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

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

% Create a random stream of bits.
inputdata=round(rand(L*log2(qamorder),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 ----------

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

% --- reconsruction 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:');
disp(sum(abs(receivedbits-inputdata)))