Optimally phase-fluctuation and doppler tolerant waveforms for a system using correlation : Dolphin and bat signals.

Abstract

This paper attempts to find optimally phase-fluctuation and doppler tolerant waveforms, i. e. , signals such that magnitude of correlator output is relatively insensitive for phase-fluctuation and doppler. So, theoretical consideration is made to derive the signal maximizing the wide band ambiguity function, in which both phase-fluctuation and doppler effects are included. An analysis is made by using techniques of variational calculus, with appropriate constraint conditions for making physically realizable waveforms. The derived signals are approximately the liner period modulated ones and found to be very similar to some of the waveforms used by dolphins and bats for echolocation. It is also shown that these waveforms are obtained by changing only the coefficient of the same differential equation derived under the same assumptions (the correlation process for detection and the constraints). This makes us expect the similarity of their signal generating mechanism and signal processing system.