Digital Design of Communication Systems - Digital Design of Signal Processing Systems: A Practical Approach - page 568

chan.StoreHistory = 1; % To plot the time varying channel

% Frequency selective multi-path fading channel
% Passing the signal through a multipath Rayleigh fading channel
% and adding other channel impurities
Received_Signal = filter(chan, ofdm_mod_out);

% Plot(chan)
Received_Signal = Received_Signal .*
exp(j*2*pi*(theta/N)*(0:length(Received_Signal)-1));
Received_Signal = awgn(Received_Signal, SNR, ' measured ' );
Received_Signal = [zeros(1,timing_offset) Received_Signal];

The coarse timing estimation is based on correlation of the training signal that consists of L parts
of M size sequence. The algorithm computes the peak of the timingmatrix given by the following set
of equations:

0
@

1
A

2

u e ðÞ¼ L

L 1 PðÞ

j j

EðÞ

L 2 M 1

PðÞ¼

0 bðÞ 0 r * d þkMþm

ð Þ rðd þ k þ 1 ð ÞMþmÞ

m¼

k¼

M 1 L 1

2

EðÞ¼

0 rdþ i þkM

ð Þj :

i¼ 0 k¼

The MATLAB code here implements these equations.

% RECEIVER
% Timing and frequency estimation
for k = 1:L-1
b(k) = Sign_Pattern(k)*Sign_Pattern(k+1);
end

% Timing estimation
for d=1:N
E(d)= sum(abs(Received_Signal(d:d+L*M-1)).^2);
P(d) = 0;
for k=0:L-2
index = d+k*M;
indexP1 = d+(k+1)*M;
P(d) = P(d) + (b(k+1) * Received_Signal(indexP1:
indexP1+M-1)*Received_Signal(index:index+M-1) ' );

end
Timing_Metric(d) = ((L/(L-1))*abs(P(d))/E(d))^2;

end

[x y] = max(Timing_Metric);
Coarse_Timing_Point = round(y);
d_max = Coarse_Timing_Point;