How do I design a matched filter receiver for pulse radar applications?

Designing a matched filter receiver for pulse radar applications maximizes the output signal-to-noise ratio for detecting radar echoes by processing the received signal with a filter whose frequency response is the conjugate of the transmitted waveform's spectrum. The matched filter provides the maximum achievable output SNR of 2E/N0 (where E is the received pulse energy and N0 is the noise power spectral density) regardless of the transmitted pulse shape. For simple pulse radar (unmodulated rectangular pulse): the matched filter is a bandpass filter with bandwidth B approximately 1/tau (where tau is the pulse width); the matched filter compresses the received pulse to a peak with width approximately 1/B and height proportional to the pulse energy. For chirp (linear FM) pulse radar: the transmitted pulse has bandwidth B over duration tau (time-bandwidth product = B x tau); the matched filter is a dispersive filter with the opposite frequency-versus-time slope; it compresses the long chirp pulse into a short pulse of width approximately 1/B; the pulse compression ratio is B x tau (typically 100-10000 for modern radars); this provides the detection sensitivity of a long pulse (high energy E = P_peak x tau) with the range resolution of a short pulse (delta_R = c/(2B)). Implementation: surface acoustic wave (SAW) filters (analog matched filters for chirp waveforms; the SAW device provides the dispersive delay required for pulse compression; used in: legacy radars and some commercial applications), digital pulse compression (the received signal is digitized and the matched filter is implemented in an FPGA or DSP using: time-domain correlation (multiply and accumulate with the reference waveform) or frequency-domain correlation (FFT of the received signal × conjugate FFT of the reference, then IFFT); modern radars use digital pulse compression exclusively due to its flexibility and accuracy).