As I understand matched filter is optimal linear filter for maximizing the Signal to noise ratio (SNR) in presence of additive stochastic noise. Consider a radar/sonar system with narrow-band transmit signal and I guess generally people use matched filter for detection, specifically for range resolution. As per my understanding, under this condition we cannot resolve if there are multiple target within the signal, my first question: is it correct? We can detect multiple target within the signal if we use linear chirp with reasonable bandwidth. Multiple target within the signal refers to point targets within transmission time, (the return comes from more than one target).
My second question (sorry not a technical question) : Is anyone in the community is interested to resolve targets within transmission time with narrow-band transmit signal in the expense of high (O(N)=$N^3$, $N$ is number of samples) computational cost?