Exploring the Interdependencies Between Transmit Waveform Ambiguity Function Shape and Off-Axis Bearing Estimation

TL;DR

This paper examines how the shape of the ambiguity function of various sonar waveforms affects off-axis bearing estimation, highlighting the influence of spectral filtering and waveform type on Fisher Information.

Contribution

It provides new insights into the relationship between transmit waveform spectral characteristics and off-axis bearing estimation performance in active sonar systems.

Findings

High Q waveforms perform similarly to LFM in off-axis estimation.

Spectral filtering perturbs the ambiguity function shape.

Waveform spectral characteristics influence Fisher Information for bearing estimation.

Abstract

The frequency dependent beampatterns of an active sonar projector filters the acoustic signal that is transmitted into the medium, also known as the transmit waveform. This filtering encodes information about the target's bearing relative to the main response axis. For any given projector and transmit waveform spectrum, there exists an optimal angle of operation which maximizes the Fisher Information (FI) of the target bearing estimate. Previous investigations into this phenomena show that for narrowband (i.e, high $Q$) Linear Frequency Modulated (LFM) waveforms, the angle of maximum FI is solely determined by its center frequency $f_c$. Steering the region of maximum bearing estimation precision is then achieved by appropriate selection of the LFM waveform's center frequency $f_c$. This fine bearing estimation is accomplished without steering the projector's main response axis. In addition to LFM waveforms, a wide variety of other active sonar waveform types exist that possess distinct spectral characteristics. These other waveforms possess different Ambiguity Function (AF) shapes from the LFM and are typically utilized to suite the range-Doppler resolution requirements of the active sonar system. This paper investigates the transmit waveform impact on off-axis bearing estimation performance and the spectral filtering impact on the waveform's AF shape. High $Q$ waveforms perform similarly to the LFM for off-axis bearing estimation while the transducer's spectral filtering perturbs the waveform's AF shape.