Optimal transmit signal design for active sonar/radar

This work is concerned with the optimization of an active sonar or radar transmit signal, to maximize the probability of detecting a nonmoving point target in the presence of signal-dependent reverberation and colored ambient noise whose power spectral densities are known. An analytical solution first reported by Kooij is corrected and extended. A simple example for the white ambient noise case is included to provide insight into the transmit signal optimization. This example shows that the effect of the solution is to “pre-emphasize” the transmit signal, which results in the whitening of the signal-dependent reverberation power spectral density.