discrete signals - GCC-PHAT (Generalized cross correlation MATLAB)

I've been trying to implement generalized cross correlation with a PHAT weighting function for a while now, and cannot get it to work. I have tried correlating using MATLAB's xcorr.m file, and it works for getting a correct delay tau (on simulated sinusoidal signals).

The code for the signals are thus:

Fs = 8000;
dt = 1/Fs;%0.125e-3
f1 = 100;
tdelay = 0.625e-03;%try different values
t3 = (0:dt:(1)-dt)';
x3 = cos(2*pi*f1*t3);
x4 = cos(2*pi*f1*(t3-tdelay));

As can be seen in part of the source code for xcorr.m, the cross correlation is implemented thus:

%Transform both vectors

X = fft(x,2^nextpow2(2*M-1));
Y = fft(y,2^nextpow2(2*M-1));

% Compute cross-correlation

c = ifft(X.*conj(Y));

According to definitions of GCC-PHAT, the only addition I needed to make was to divide the product by its own magnitude, before taking the ifft. Here is my version with this change.

%Transform both vectors
X = fft(x,2^nextpow2(2*M-1));
Y = fft(y,2^nextpow2(2*M-1));

% Compute cross-correlation

R = X.*conj(Y);
c = ifft(R./abs(R));

However I always end up with a tau of zero with the PHAT weighting! On closer examination of the array produced as a result of this division, it seems as if the first value of R is a real value (with no imaginary component), and so when divided by its magnitude it becomes 1. All the other values in array R are complex, so do not end up as 1 when divided by their own magnitude and so end up with a value of <1.

This can be seen below, for the 1st 10 values of R.

    K>> R(1:10,1)

ans =

  0.000000000000000 + 0.000000000000000i
 -0.494299608718696 - 0.003002230689022i
 -0.002678647083223 - 0.000032538742345i
 -0.488954228290329 - 0.008909374553649i
 -0.010656518992354 - 0.000258902698589i

 -0.478379290671260 - 0.014528074329782i
 -0.023760667475633 - 0.000865926459320i
 -0.462803929640386 - 0.019677623220519i
 -0.041707017319469 - 0.002026674993917i
 -0.442565618721743 - 0.024194329448597i

K>> abs(R(1:10,1))

ans =


   0.000000000000000
   0.494308725968464
   0.002678844707371
   0.489035391682370
   0.010659663580139
   0.478599844010494
   0.023776441018801
   0.463222070011989
   0.041756229537848
   0.443226457301486


K>> R(1:10,1)./abs(R(1:10,1))

ans =

  1.000000000000000 + 0.000000000000000i
 -0.999981555555690 - 0.006073594357736i
 -0.999926227844417 - 0.012146557900713i
 -0.999834033705084 - 0.018218261306199i
 -0.999705001216859 - 0.024288074069393i

 -0.999539169638280 - 0.030355367874845i
 -0.999336589392997 - 0.036419515378054i
 -0.999097322000240 - 0.042479891383435i
 -0.998821440083941 - 0.048535871565711i
 -0.998509027227826 - 0.054586834901284i

As can be seen above, the largest value ends up being at the 1st index, when we divide R by its own magnitude. So once the ifft is taken, the highest value is ALWAYS at the beginning of the array, which gives a lag and timediff of zero...even when I set the delay between the 2 identical signals at the beginning to a nonzero value (e.g. delay = 0.75e-03).

What am I doing wrong?? Any help appreciated.

Rory

P.S. if anyone is wondering why I'm bothering with the PHAT weighting, its because it should give far better results (in theory) in a real life scenario, for TDOA.