Abstract: In this paper optimum signals with an energy constraint are studied for active sonar detection. It is proved that the optimum signal is the solution of a homogeneous nonlinear integral equation and the optimum reference function of the correlation receiver is the same as this signal, if the target and the medium scattering functions and the reverberation distribution are symmetric. For the channel of which scattering function is symmetric and independent of delay, it is further shown that only the frequency-dependent magnitude function of optimum signal is required to consider and we have a free choice of its frequency-dependent phase function.