I would like to evaluate the Maximum Likelihood Estimator for the SNR of a given signal:
$ x(t) = as(t-\tau) + n(t) $
Under the following assumptions (This is the model of Radar Signal):
- The input signal is the sum of the attenuated and delayed reference signal and AWGN. This is the model of a Radar signal.
- The signal $ s(t) $ is known. The signal has finite Support and Energy s.t. $ \int_{0}^{T}{s(t)}^{2}dt = p < \infty $.
- The attenuation factor, $ a $, is unknown.
- The noise, $ n(t) $ is Additive White Gaussian Noise with $ E[n(t)] = 0 $ and $ E[{n(t)}^{2}] = \delta(t){\sigma}^{2} $ where $ {\sigma}^{2} $ is unknown.
How would you estimate the SNR of the given signal $ x(t) $? How would you change the answer given $ a $, $ {\sigma}^{2} $ or both?
Thanks.