MTI RADAR, DSP algorithm question
The second way is how it is done.
In the fast-time (or range-bin dimension) you are right to perform the matched filter.
However, Doppler information is gathered from sampling pulse-to-pulse. The MTI filter essentially subtracts pulses so that if they have similar phase, or the phase is not changing at all, then there is little to no Doppler being generated and thus the target is not moving.
In other words, the three-pulse canceller applies a filter across the Doppler dimension for each range bin, as the second pulse matrix suggests.