Calculating Standard Deviation and Unit Vector (x, y) from Delay in S_fg Spectrum

I am trying to calculate the unit vector and standard deviation of the signal. I hope everyone can give me ideas.

Here is my scenario:

I have 2 rx channels: - f is channel 1 with the length 1x256 complex, then FFT. - g is channel 2 with the length 1x256 complex, then FFT. - from f and g, I can calculate the spectrum density S_fg = f * conj(g), with the length 1x256 complex


S_fg = f * conj(g)
t_0 = 1 / f_0;
r_0 = t_0 / (2 * pi);
delay = angle(S_fg) * r_0 * 1e12; % in pico second
d = median(delay);


since I have those parameters, How can i calculate the unit vector (x,y), and standard deviation?

The unit vector maybe calculated by the equation:

x = 1*cos(delay); % 1x256

y = 1*sin(delay); % 1x256

but I do not know how to get the standard deviation?

Hope anyone can help?

This might help , https://www.mathworks.com/help/matlab/ref/std.html?s_tid=gn_loc_drop