Optimal time and frequency domain waveform design for target detection

Abstract

Some marine mammals as well as bats are known to emit sophisticated waveforms while searching for objects or hunting prey. Some dolphins have been observed to change their sonar pulse depending on the environment. Incorporating these strategies into sonar waveform and receiver design has become an active area of research. In this paper, we explore the application of an optimal waveform design scheme recently given by Kay, to the detection of elastic objects. We examine the benefits of optimal waveform design versus transmitting a linear FM waveform, as well as performance loss suffered by assuming a point target. The optimization approach designs the magnitude spectrum of the transmit waveform and, accordingly, there is an unlimited number of "optimal" transmit waveforms with the same magnitude spectrum. We propose a time domain optimization criterion to obtain the transmit waveform with the optimal magnitude spectrum and the smallest possible duration, as well as the waveform with the optimal magnitude spectrum and the longest possible duration. The former waveform allows for higher ping rates, but necessarily has higher time domain peak power, while the latter waveform has lower time domain peak power and lower ping rates. A method to obtain waveforms that are a blend of these two extremes is also presented, allowing a smooth trade-off between ping rate and peak power.