In the situation where the unwanted scatterers are uniformly distributed in range and have a Doppler distribution that is independent of range, the reverberation power spectrum is completely determined by the energy spectrum of the signal transmitted. The optimum detector of an echo in noise plus reverberation is the colored‐noise type of matched filter the output signal‐to‐noise ratio of which depends only upon the energy spectrum of the echo and the power spectra of the noise plus reverberation. It is significant that this output does not depend upon the phase spectrum of the signal and hence upon its waveform. This limitation of signal design to energy spectral design does not take into account the possible effects of the angular distribution of the unwanted scatterers. The optimal energy spectrum design of signals is discussed for low and high Doppler targets, indicating the limiting values of the output of the colored‐noise filter as a function of available bandwidth. The special cases of the Urkowitz filter and MTI signals and processing are discussed.