I'm currently simulating radar target detection using Linear Frequency Modulation (LFM) signals, and I have a few questions regarding the detection process in the presence of a stochastically modulated echo.
In my setup, the detection is based on the modulus of the received signal after passing it through a matched filter. The noise is modeled as a complex Gaussian distribution, specifically $\mathcal C \mathcal N (0,\sigma^2_n)$. Consequently, the detection threshold can be calculated using the formula:
$V_T=\sqrt{\varepsilon\sigma^2_n\ln{1/P_{fa}}}$,
where $\varepsilon$ is the energy of transmitted signal.
Questions:
- In the case where there is a target at the $n th$ range gate, the amplitude of the echo signal is influenced by the target's characteristics (e.g., a Reconfigurable Intelligent Surface (RIS)). This implies that the energy of the echo $\varepsilon$ is stochastic in nature. How should I go about determining the detection threshold in this scenario?
- Should I first calculate the expected energy of the echo $\varepsilon$, and then derive $\sigma^2_n$ based on the provided Signal-to-Noise Ratio (SNR) before calculating the detection threshold using the aforementioned formula?
- Lastly, what constitutes effective detection in this context? Is it sufficient for the peak of the signal after the matched filter to exceed the threshold, or must the value at the specific $n th$ range gate also surpass the threshold?
