MATLAB - Signal Noise Ratio

I have a damped sine wave which is a emitted signal as below:

x = x = A*exp(-t).*sin(2*pi*f*t);

And I define a received signal, so that

y(n)=ax(n-k)+b(n), where a is the attenuation coefficient and k is a delay.

Then I calculate the cross-correlation between them

[xc,lags] = xcorr(y,x);

1. How can I estimate the delay k for different SNR (Signal-Noise-Ratio) in dB
2. How to represent the curve delay vs. SNR.