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In this paper, the task of model-based transmit signal design for optimizing detection is considered. Building on past work that designs the spectral magnitude for optimizing detection, two methods for synthesizing minimum duration signals with this spectral magnitude are developed. The methods are applied to the design of signals that are optimal for detecting elastic objects in the presence of additive noise and self-noise. Elastic objects are modeled as linear time-invariant systems with known impulse responses, while additive noise (e.g., ocean noise or receiver noise) and acoustic self-noise (e.g., reverberation or clutter) are modeled as stationary Gaussian random processes with known power spectral densities. The first approach finds the waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second approach yields a finite-length time-domain sequence by maximizing temporal energy concentration, subject to the constraint that the spectral magnitude is close (in a least-squares sense) to the optimal spectral magnitude. The two approaches are then connected analytically, showing the former is a limiting case of the latter. Simulation examples that illustrate the theory are accompanied by discussions that address practical applicability and how one might satisfy the need for target and environmental models in the real-world.

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.

Detection, classification, and localization of underwater objects is a primary function of active sonar systems. Detection involves making a decision on whether or not an object of interest is present. Once a positive detection has been made, further information may be needed to classify the object as one among a set of possible objects of interest. Previous efforts have been directed at designing transmit sonar waveforms to maximize detection performance. In this work, we extend the optimal sonar design approach to enhance classification after detection. In particular, we present an optimal signal design approach that is aimed at maximizing the probability of correctly classifying the true target from among a set of assumed candidates. The approach is evaluated theoretically and via simulations, by which it is shown that waveform design can yield improvements in classification performance. [Work supported by ONR.]

In undersea environments, particularly shallow water, the sonar backscatter from objects of interest can be subject to propagation effects such as dispersion, attenuation, and multi‐path, which can confound detection and classification. Detection and classification of buried objects are further complicated by dramatic changes in the backscatter due to the sediment layer. These propagation and environmental effects can induce time‐varying (or nonstationary) characteristics in the received sonar signal. In addition, the object itself can induce nonstationarities, such as the inherent dispersion characteristics of some elastic objects. The processing and analysis of such signals for detection and classification can be enhanced by applying time‐varying methods to the received signal, such as time‐frequency analysis and linear time‐varying filters. Detection can also be enhanced by designing a transmit waveform to optimize some metric, such as received signal‐to‐interference/noise power. In this talk, we explo...

Animals that navigate and hunt by echolocation, such as some bats and marine mammals, have been observed to change their sonar pulse depending on the environment, as well as during hunting. It has become of interest to incorporate these strategies into man‐made sonar waveform and receiver design. We examine the benefits of optimal waveform design versus transmitting a linear FM waveform for detecting elastic objects. Performance loss suffered by assuming a point target is also examined. Our approach utilizes a method recently proposed by Kay to design the optimal power spectrum of the transmit waveform. Because there is an unlimited number of waveforms with the same power spectrum, we further impose a time domain constraint, in terms of the signal duration, to obtain a unique optimal waveform. [Work supported by ONR 321US.]