Array Signal Processing

The Challenge

Why 3-D Sonar Imaging Is Hard

Reconstructing 3-D volumetric images of underwater targets requires a 2-D receiving array and computationally intensive beamforming. The cost scales with the square of the number of sensor elements.

Array Cost

A uniform planar array (UPA) for 1° angular resolution needs at least 100 × 100 elements with half-wavelength spacing. Manufacturing and cabling thousands of hydrophones is prohibitively expensive.

10,000+ ELEMENTS FOR CONVENTIONAL UPA

Computation Time

3-D delay-and-sum beamforming with a full planar array requires billions of real operations per beam slice. Processing a single 60 × 60 slice with DAS takes over 6 million operations.

6.2M OPERATIONS FOR ONE BEAM SLICE

Real-Time Demand

Autonomous underwater vehicles need obstacle avoidance in real time. The imaging system must reconstruct volumes quickly enough for navigation at speed, which conventional methods cannot deliver.

AUV NAVIGATION REQUIRES < 1 s IMAGING

Core Innovation

Orthogonal Linear Array Beamforming

An L-shaped arrangement of two perpendicular linear arrays replaces the full 2-D planar aperture. For a 24 × 24 UPA, element count drops from 576 to 47 hydrophones (92% reduction). Product beamforming combines the two beams, reconstructing the 3-D image in parallel across four quadrants.

Array Type L-shaped at edges of UPA (ELSA)
Elements 47 hydrophones (vs. 576 for full UPA)
MLW Improvement 2° narrower main lobe than DAS with UPA
Ambiguity Asymmetric PSF resolves multi-target ambiguity
Computation 97× fewer operations than conventional DAS
Frequency 500 kHz center, 200 kHz wideband operation

References

Orthogonal Linear Array-Based Product Beamforming for Real Time Underwater 3-D Acoustical Imaging Menakath, Panicker & Hareesh · IEEE J. Oceanic Eng., Vol. 51, No. 1, Jan 2026

Point spread function comparison across UPA, CSA, DCSA, CLSA, and ELSA array configurations

Point spread function comparison. Beam patterns for five array configurations at broadside (0°, 0°). The ELSA achieves the narrowest main lobe (2°) with only 47 elements.

Array Geometry	Elements	Method	Azimuth MLW	Elevation MLW	PSLL (dB)
UPA	576	DAS	4°	4°	−13
ELSA	47	DAS	4°	4°	−5
ELSA	47	Product	2°	2°	−7
CSA	47	Product	5°	5°	−6
CLSA	47	Product	2°	2°	−7
DCSA	95	Product	2°	2°	−7

Image quality analysis. The proposed ELSA with product beamforming achieves 2° main lobe width using only 47 elements, matching the resolution of the 576-element UPA while resolving multi-target ambiguity that the CSA cannot.

UPA vs ELSA 3-D sonar imaging comparison across XY, XZ, and YZ planes

3-D sonar imaging comparison. UPA (top) vs proposed ELSA (bottom) across XY, XZ, and YZ planes. The ELSA with 47 elements resolves the same target structure as the 576-element UPA.

Beamforming Methods

From Cross-Correlation to Nonlinear Product Beamforming

Cross-array spatial cross-correlation multiplies delay-compensated signals of horizontal and vertical arms for directional 3-D beams. The more advanced nonlinear product beamforming on the ELSA uses quadrant-based reconstruction, processing all four quadrants in parallel.

97× Faster Than DAS

12.72 SNR (dB)

1.35 CNR

94.6% Time Reduction

Cross-Array 22× faster than DAS for 120 × 120 beams (0.39 s vs 8.89 s)
Product BF 97× fewer operations, single-slice time 0.21 s vs 0.12 s (DAS), but with improved MLW
DMAS Compared against DMAS: 4 dB PSLL reduction, with 4.8× fewer operations
Platform Benchmarked on 11th Gen Intel Core i7-1165G7, 2.80 GHz, 8 GB RAM

References

An Efficient Cross Array Beamforming for Underwater Acoustical 3D Imaging Menakath, Panicker & Hareesh · OCEANS 2023, Limerick

12-panel cross-target 3-D imaging comparison across UPA, CSA, CLSA, and ELSA array configurations

Cross-target 3-D imaging. Four array configurations (UPA, CSA, CLSA, ELSA) imaged in XY, XZ, and YZ planes. The ELSA resolves the cross-shaped target without the ambiguity artifacts visible in the CSA result.

Sparse Arrays

Compressive Sensing for Wideband Sparse Array Synthesis

A multitask Bayesian compressive sensing (MTBCS) algorithm jointly optimizes sensor locations across all frequency bins. For ultra-wideband signals (150 to 450 kHz), MTBCS reduced a 10,000-element reference array to 917 elements while maintaining minimum mean-square error.

90.8% Max Element Savings

917 From 10,000 Elements

0.5 SSIM (Exp. Validation)

Algorithm Multitask Bayesian Compressive Sensing (MTBCS)
Signal Type Wideband (up to 100% relative bandwidth) and ultra-wideband
Patterns Frequency-dependent and frequency-invariant beam patterns
Steering Verified beam steering to (30°, 30°) with sparse array
Experiments Validated with 96-element uniform array data from NPOL, reduced to 29 elements

References

Toward Sparse Planar Array Underwater Acoustical Imaging Using Compressive Sensing Pattern Matching Technique Menakath, Panicker, Hareesh & Peter · IEEE Trans. Instrum. Meas., Vol. 74, 2025

3-D voxel reconstructions of cube and V-shape targets using orthogonal linear arrays

3-D voxel reconstructions. Cube and V-shape targets reconstructed with orthogonal linear array product beamforming. The volumetric rendering preserves target geometry with 92% fewer elements than the equivalent UPA.

Simulation & Validation

Underwater Target Modeling with k-Wave

The k-Wave acoustic toolbox solves the wave equation directly, capturing attenuation, reverberation, and speckle that analytical models miss. Two scaling approaches handle deep-water memory constraints while preserving angular resolution. Validated against experimental data from NPOL, Kochi, using a 96-element linear array at 725 kHz.

Toolbox k-Wave (open-source, MATLAB), time-domain wave equation solver
Shallow Water 0.4 m × 0.3 m × 0.3 m grid, 1 mm grid points, 725 kHz
Deep Water Scaled-down approach: factor 1/2.5 for practical memory usage
Targets Sphere, cube, cone, pyramid, meshed sphere, cross-shaped structures
Materials Mild steel: 3000 m/s acoustic speed, 7850 kg/m³ density
Validation Simulated vs experimental images at NPOL show matching target shapes

References

Experimental Validation of Underwater Target Modeling Using k-Wave Toolbox for Acoustical Imaging Menakath, Panicker, Hareesh, Madhusoodanan & Jose · IEEE Sensors Letters, Vol. 9, No. 7, Jul 2025 Modelling of Underwater Target for Sector Scan Sonar Imaging using K-Wave Toolbox Madhusoodanan, Panicker & Menakath · OCEANS 2024, Singapore

Six underwater target types with k-Wave 3-D renders and corresponding sector scan sonar images

Simulated target gallery. Six target geometries (sphere, cube, cone, pyramid, meshed sphere, cross) modeled in k-Wave with their corresponding sector scan sonar images. Simulated results validated against experimental data from NPOL.

Method	Operations	Time (s)	Speedup
DAS (UPA)	6,221,952	0.1210	1×
CZT	3.57 × 10¹¹	1.0630	0.11×
DM (Frequency)	1.99 × 10¹°	96.2032	0.001×
Proposed (ELSA)	864,000	0.0052	23×

Computation comparison for a 60 × 60 beam slice. The proposed orthogonal linear array product beamforming method is 23× faster than conventional DAS and 204× faster than CZT beamforming. Frequency-domain methods are not feasible for wideband signals.

Publications