Citation: Rixon Fuchs, L.; Maki, A.;
Gällström, A. Optimization Method
for Wide Beam Sonar Transmit
Beamforming. Sensors 2022, 22, 7526.
https://doi.org/10.3390/s22197526
Academic Editor: Andrzej
Stateczny
Received: 26 August 2022
Accepted: 30 September 2022
Published: 4 October 2022
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Article
Optimization Method for Wide Beam Sonar
Transmit Beamforming
Louise Rixon Fuchs
1,2,
* , Atsuto Maki
1
and Andreas Gällström
2
1
Division of Robotics, Perception and Learning, KTH Royal Institute of Technology,
SE-100 44 Stockholm, Sweden
2
Saab Dynamics, SE-581 88 Linköping, Sweden
* Correspondence: rixon@kth.se
Abstract:
Imaging and mapping sonars such as forward-looking sonars (FLS) and side-scan sonars
(SSS) are sensors frequently used onboard autonomous underwater vehicles. To acquire information
from around the vehicle, it is desirable for these sonar systems to insonify a large area; thus, the
sonar transmit beampattern should have a wide field of view. In this work, we study the problem of
the optimization of wide transmission beampatterns. We consider the conventional phased-array
beampattern design problem where all array elements transmit an identical waveform. The complex
weight vector is adjusted to create the desired beampattern shape. In our experiments, we consider
wide transmission beampatterns (
≥
20
◦
) with uniform output power. In this paper, we introduce a new
iterative-convex optimization method for narrowband linear phased arrays and compare it to existing
approaches for convex and concave–convex optimization. In the iterative-convex method, the phase
of the weight parameters is allowed to be complex as in disciplined convex–concave programming
(DCCP). Comparing the iterative-convex optimization method and DCCP to the standard convex
optimization, we see that the former methods archive optimized beampatterns closer to the desired
beampatterns. Furthermore, for the same number of iterations, the proposed iterative-convex method
achieves optimized beampatterns, which are closer to the desired beampattern than the beampatterns
achieved by optimization with DCCP.
Keywords:
autonomous underwater vehicles; sonar; phased antenna arrays; transmit beamforming;
convex optimization; beampattern; side-scan sonar; forward-looking sonar; seabed mapping
1. Introduction
Sonar systems are remote sensing systems used for determining the presence of objects
or geometrical structures in the sea. Autonomous underwater vehicles (AUVs) are often
equipped with sonar systems for tasks such as obstacle avoidance and seabed mapping.
Active sonar involves the transmission of an acoustic sound beam, where the reflections
on underwater targets are then received and processed [
1
]. The sonar produces the trans-
mission beam through the spatial filtering technique beamforming [
2
]. Beamforming is
essential in several fields such as radar, sonar, communications, imaging, biomedical, geo-
physical exploration, and astrophysical exploration [
3
]. A recent review [
4
] covers the
progress of array synthesis for phased antenna arrays in the wireless communication and
remote sensing domain.
Beamforming aims to design a beampattern suitable for the desired application. For
conventional sonar systems, it is desirable to send out a wide transmission beampattern
(
>
20
◦
). Aide transmission beampattern is of importance for sonar in several different
applications. Some of these applications are Forward-Looking sonars (FLS) for obstacle
avoidance [
5
], seabed mapping with side-scan sonars (SSS) [
6
], Synthetic Aperture sonar
Systems (SAS) [
7
], and acoustic navigation aid using Compact Correlation Velocity Logs
(CVLs) [
8
]. In its simplest form (delay-and-sum), the beamformer linearly combines
Sensors 2022, 22, 7526. https://doi.org/10.3390/s22197526 https://www.mdpi.com/journal/sensors
