Optimal Signal Design for a New Physically Motivated Clutter Model With Applications to Ultrasonic Testing

In this article, we will explore the optimal signal design problem for a new physically motivated clutter model. The reason to pursue the optimal signal design is that the model, even though it was simple, led to a robust detector that worked well on real ultrasonic data. Moreover, by using the model, an analytical solution for the optimal signal is obtained. In addition, the optimal waveform gives a new insight into the signal design problem that can be valuable for many applications. New proof has been provided for a finite data record that is lacking in the literature. We have found that the optimal signal is an impulse, and as a result, it has an impulsive autocorrelation sequence (ACS). Since an impulsive ACS signal is not realizable, in practice, a study for an alternative waveform is conducted. Waveforms from four different categories have been explored: linear frequency-modulated (LFM), nonlinear frequency-modulated (NLFM), phase-coded modulated (PCM) signals, and, finally, what we called other signals. Comparison analysis between these waveforms themselves and the most commonly used transmitted pulse in practice, which is the Gaussian amplitude-modulated sinusoid (GAMS) pulse, has been implemented. We show that the LFM pulse has a large advantage over the GAMS pulse in terms of detectability. In addition, a comparison between the LFM and the GAMS signals under a deviation from the single scatterer assumption, indicating a more complex target, using simulated noise is performed.