LPI waveforms for active sonar?

The idea of a low probability of intercept (LPI) waveform is that its form is chaotic. It can of course be recalled by the transmitter (platform), and matched to what is received; but to the target it appears only as noise, and consequently the robust target receiver can only detect a rise in energy. However, the platform pays a heavy two-way attenuation penalty: its signal to noise ratio (SNR) is far lower than that at the target. It is not immediately apparent that how these two factors trade off against one another, and that is the topic of this paper.