delay sine wave and correlation

1. Simulate in Matlab/Python a damped sine wave as the emitted signal (x(n). The damped signal can be obtained by multiplying a sine wave by a decreased exponential.

1. Simulate the received signal y(n) according to the following model.

y(n=ax(n-k)+b(n)

Where a is the attenuation coefficient and k is a delay.

Is it correct if I do as below.

1. In this simulation, consider a=1. Choose any value of the delay.

Using the cross-correlation function between the emitted signal and the received signal, it is asked to estimate the delay k for different SNR (Signal-Noise-Ratio) in dB. Represent the curve delay vs. SNR.

How can I estimate the delay k for different SNR and represent the curve delay with SNR.

[Adam Danz]

[r,lags] = xcorr(___)