Acoustic Array Steering

• Acoustic array steering is the electronic manipulation of transducer arrays using phase shifts and time delays to dynamically steer beam patterns.
• It employs methods such as delay-and-sum, differential beamforming, and modal matching to achieve broadband, frequency-invariant performance with controlled sidelobes.
• Advanced architectures like hyperuniform, topological, and virtual element arrays enhance multi-beam operation and nonreciprocal transmission in complex environments.

Acoustic array steering refers to the electronic control of the directional response of an array of transducers—microphones or loudspeakers—by dynamically selecting or synthesizing spatial beampatterns through weighted combinations of their signals. This core technology supports applications ranging from ultrasonic imaging and parametric audio to speech capture, sonar, and novel topological acoustic devices. Contemporary advances enable precise, frequency-invariant, broadband, multi-beam, nonreciprocal, and topologically protected beam steering using algorithmic, physical, and device-architected methods.

1. Fundamental Principles of Array Steering

The principle of array steering is to manipulate the radiation (or reception) pattern of an array by applying element-wise phase shifts or time delays, effectively steering the collective beam in a desired direction. For a generic array of $N$ elements at positions $\{\mathbf{r}_j\}$, the far-field pressure pattern at angle $(\theta,\phi)$ is governed by the array factor,

$$A(\theta,\phi) = \frac{1}{N} \sum_{j=1}^N e^{i\mathbf{k}\cdot\mathbf{r}_j} \qquad \mathbf{k} = \frac{2\pi}{\lambda} (\sin\theta\cos\phi,\,\sin\theta\sin\phi)$$

Steering is implemented by multiplying each element's excitation with a phase factor $w_j = \exp[-i\mathbf{k}_s\cdot\mathbf{r}_j]$, where $\mathbf{k}_s$ corresponds to the “look” direction $(\theta_s,\phi_s)$. For far-field plane wave reception, the same formalism governs the spatial filtering of incident signals.

Periodic arrays with pitch $d$ exhibit grating lobes at angles where $\sin\theta = \sin\theta_0 + n\lambda/d$ for $|n|\geq1$ if $\{\mathbf{r}_j\}$0. This can be mitigated or eliminated via aperiodic, disordered, or hyperuniform arrangements (Tang et al., 2023).

2. Broadband, Frequency-Invariant, and Optimal Design

Conventional delay-and-sum (DAS) steering is frequency-dependent due to wavelength scaling. Differential beamforming (DBF) leverages pressure differences between closely spaced elements, approximating spatial derivatives, and thus produces frequency-invariant beampatterns (Miotello et al., 17 Aug 2025, Xiong et al., 26 Feb 2026). For arbitrary planar arrays of first-order elements, DBF with modal matching solves for frequency-dependent weight vectors using a truncated circular-harmonic expansion and accommodates real (non-omnidirectional) transducer responses. The design process includes:

• Selecting a target pattern: $\{\mathbf{r}_j\}$1 (e.g., supercardioid, hypercardioid).
• Expressing element directivity: $\{\mathbf{r}_j\}$2.
• Modal matching: Encoding response constraints in a linear system per frequency and solving via least-squares or regularized minimization.

For uniform circular arrays, directional-derivative-constrained frameworks enforce unit gain and prescribed derivatives at the look direction, enabling robust continuous steering and sidelobe control (Xiong et al., 26 Feb 2026). Key performance metrics include mainlobe width, directivity index (DI), white-noise gain (WNG), and maximum sidelobe level.

3. Nontraditional Array Geometries and Advanced Architectures

Array steering theory extends beyond simple linear or uniform circular arrays. Key developments include:

• Hyperuniform disordered (HUD) arrays (Tang et al., 2023): Suppress grating lobes over wide angles by designing spatial distributions with vanishing structure factor $\{\mathbf{r}_j\}$3 for $\{\mathbf{r}_j\}$4. HUD arrays maintain mainbeam sharpness and can be tiled indefinitely for large apertures.
• Topological acoustic metamaterials (Sirota et al., 2020): Active feedback-based transducer lattices dynamically pattern local acoustic impedance to realize topologically protected edge states, supporting robust steering of tightly confined curved sound beams immune to defects or backscatter.
• Arrays with virtual elements (Zhao et al., 2024): Physics-informed neural networks (PINN) infer soundfield values at virtual microphone positions from physical sensor data, augmenting array aperture and mitigating beampattern nulls at Bessel zeros without increased hardware complexity.
• Spherical arrays and harmonics-based steering (Rafaely et al., 2023): Spherical arrays decomposed by spherical harmonics enable closed-form, physically optimal steering in 3D, with side- and mainlobe control and directivity akin to the best model-based microphone arrays.

4. Practical Implementations, Adaptive and Multi-Beam Steering

Practical array steering systems must contend with wideband signals, device nonidealities, environmental perturbations, and real-time operation:

• Broadband MEMS arrays: The ConamArray (32-element MEMS, staggered geometry) achieves sub-5° beamwidth and low sidelobes over 20–100 kHz, but physical spacing and geometry determine onset of grating lobes and steering range (Laurijssen et al., 1 Sep 2025).
• IMU-stabilized 3D sonar arrays: Dynamic steering matrices compensate for platform tilt by integrating real-time IMU measurements into the DAS beamforming pipeline, enhancing spatial consistency and temporal stability for navigation (Jansen et al., 2024).
• Optical/Acousto-optic arrays: Multi-channel integrated acousto-optic beam steering employs digitally synthesized multi-tone microwaves to generate hundreds of independent optical beams via Bragg diffraction on a chip, supporting parallel communication and imaging (Lin et al., 2024).

5. Nonreciprocal, Multi-Channel, and Topological Steering

Space–time–periodic modulation of array phase enables nonreciprocal transmission and reception patterns, breaking acoustic reciprocity. Controlled modulation generates frequency-shifted sidebands and decouples transmit and receive beampatterns, supporting frequency-selective, asymmetric, and multi-directional operation from the same hardware (Adlakha et al., 2020). Topologically inspired feedback laws further allow unidirectional, reflection-immune propagation for robust beam steering along arbitrarily shaped paths (Sirota et al., 2020).

6. Algorithmic Beamforming, Steering Vector Subspace Methods, and Multipath Processing

Algorithmic innovations in steering leverage sample covariance and subspace decomposition (e.g., MUSIC) to estimate arrival angles of multiple sources or echoes. The SubAoA method iteratively nulls previously estimated directions, enabling successive AoA extraction in strongly multipath environments and extending to RF and other array modalities (Wei et al., 2021). This approach is computationally tractable and robust in high correlation or noise.

7. Performance, Scalability, and Applications

The choice of element spacing, layout topology, and steering law governs trade-offs among beamwidth, onset of grating lobes, white-noise gain, bandwidth, and spatial aliasing. Innovations such as HUD layouts, virtual microphones, and topological constraints permit scaling to arbitrarily large or compact arrays, high-resolution beamforming, and enhanced robustness with moderate hardware overhead (Tang et al., 2023, Zhao et al., 2024, Rafaely et al., 2023).

Notable application domains include ultrasonic imaging, parametric audio, speech enhancement, SONAR, free-space optical communication, quantum qubit addressing, and bio-inspired robotics. Adaptive and model-based steering strategies provide resilience to environmental variability, hardware imperfections, and operational constraints across these contexts.