Concentric Circular Microphone Array (CCMA)

• Concentric Circular Microphone Array (CCMA) is a planar sensor array featuring multiple coplanar circular rings with uniformly distributed omnidirectional microphones for dual-axis beamforming.
• It leverages circular harmonic formulations and gradient-based optimization to achieve broadband, frequency-invariant performance with controlled beamwidth in both azimuth and elevation.
• Practical implementations in databases and real-time DSP systems validate CCMA’s superior capabilities in sound source localization, room acoustic measurement, and spatial audio capture.

A concentric circular microphone array (CCMA) is a planar acoustic sensor arrangement comprising two or more coplanar circular rings, each populated with uniformly distributed omnidirectional microphones at distinct radii from a shared origin. This geometry affords key advantages in broadband beamforming, dual-axis steering (azimuth and elevation), and spatial aliasing control. CCMAs are foundational in advanced sound source localization, spatial audio capture, and room acoustic measurement, enabling highly robust, frequency-invariant and fine-resolution localization capabilities in challenging acoustical environments.

1. Array Geometries and Sensors

A CCMA is specified by the set of ring radii $\{\rho_r\}$ and, for each ring $r$, the number of microphones $M_r$ and their angular positions $\phi_{r,m}$. Prototypical configurations include:

• Two-ring configurations: A UCCA with rings at $r_1=6\,\mathrm{cm}$ (9 microphones) and $r_2=4\,\mathrm{cm}$ (7 microphones), totaling 16 capsules on a rigid plane (Zhang et al., 2019).
• Database arrays (MYRiAD): Inner ring: $r_1=0.10\,\mathrm{m}$, $M_1=4$ (DPA 4060). Outer ring: $r_2=0.20\,\mathrm{m}$, $M_2=8$ (AKG CK32), yielding 12 channels, with microphone coordinates precisely measured and housed at $r$0 (Dietzen et al., 2023).
• Multi-ring research arrays: $r$1 rings at radii $r$2, populated via a spatial aliasing constraint $r$3 with $r$4 (Ortigoso-Narro et al., 24 Nov 2025).

Uniform angular spacing within each ring, flush mounting, and capsule selection (for sensitivity and noise floor) determine the effective aperture, maximum usable frequency, and beamforming fidelity. Inner and outer rings are often populated with distinct microphone models for experimental control of frequency response and SNR.

2. Theoretical Foundations: Steering Vector and Harmonic Domain Formulations

For a planar CCMA, the frequency-domain steering vector for a plane wave from azimuth $r$5 and elevation $r$6 is

$r$7

where $r$8 is the speed of sound and $r$9 locates the $M_r$0th sensor on ring $M_r$1 (Ortigoso-Narro et al., 24 Nov 2025). For purely planar tasks ($M_r$2), this simplifies to classic 2D circular geometry.

Circular harmonic (Fourier) decomposition provides a frequency-invariant basis. The pressure at angle $M_r$3 on the $M_r$4th ring is expanded as

$M_r$5

with corresponding $M_r$6th-order modal coefficients $M_r$7, where $M_r$8 is the $M_r$9th Bessel function (Zhang et al., 2019).

Frequency-invariant beamforming is obtained by compensating the radial and order dependence via ring-wise modal weights $\phi_{r,m}$0: $\phi_{r,m}$1 These filters eliminate the Bessel-induced frequency variations that plague single-ring arrays, enabling robust wideband directivity.

3. Beamforming, Optimization, and Frequency Invariance

Classical approaches include delay-and-sum and modal (harmonic domain) beamforming. With CCMAs, broadband frequency-invariant performance is optimized by (1) regularizing against Bessel zero-crossings (via multiple rings), and (2) solving least-squares problems per modal order (Zhang et al., 2019).

Recent work formulates CCMA beamformer design as a differentiable optimization subject to beamwidth constraints in both azimuth and elevation: $\phi_{r,m}$2 where $\phi_{r,m}$3 includes penalties for deviation from target beamwidths and irregularities in directivity factor (DF) and white noise gain (WNG) across frequency (Ortigoso-Narro et al., 24 Nov 2025). The beamformer is parameterized over ring-level weights $\phi_{r,m}$4 and intra-ring Gaussian tapers $\phi_{r,m}$5. Automatic differentiation (autograd, typically via PyTorch RProp) enables end-to-end joint optimization of all beamforming parameters, resulting in mainlobes and sidelobes that remain virtually constant across frequency and both axes.

Table 1. Summary of Key CCMA Beamforming Performance (Ortigoso-Narro et al., 24 Nov 2025, Zhang et al., 2019)

Metric	Typical Value/Range	Notes
$\phi_{r,m}$6 Elev./Az. Beamwidth	$\phi_{r,m}$7	Across $\phi_{r,m}$8 kHz
Directivity Factor (DF)	$\phi_{r,m}$9–$r_1=6\,\mathrm{cm}$0 (mid-band)	Slight roll-off at band edges
White Noise Gain (WNG)	$r_1=6\,\mathrm{cm}$1	Robustness to sensor noise
Mainlobe error (SRP)	$r_1=6\,\mathrm{cm}$2 (UCCA); $r_1=6\,\mathrm{cm}$3–$r_1=6\,\mathrm{cm}$4 (UCA)	$r_1=6\,\mathrm{cm}$5–$r_1=6\,\mathrm{cm}$6, real-time (Zhang et al., 2019)
Real-time latency	$r_1=6\,\mathrm{cm}$7	DSP implementation; 512 samples

4. Experimental Protocols and Multi-Microphone Data

CCMAs have been realized in laboratory and field measurement environments:

• MYRiAD database: CCMAs (two rings, 12 microphones) deployed at calibrated positions in the AIL, with all coordinates available in reference CSV files and code loaders in MATLAB/Python (Dietzen et al., 2023).
  • Microphones synchronously sampled at $r_1=6\,\mathrm{cm}$8/24 bit.
  • Room impulse responses and cocktail party scenarios spanned over $r_1=6\,\mathrm{cm}$9 RIRs, speech, noise, and music playback.
• Real-time DSP implementation: A 2-ring UCCA ($r_2=4\,\mathrm{cm}$0, $r_2=4\,\mathrm{cm}$1) realized on TI TMS320C6678 (16-channel ADC, 16 kHz per channel), with frame-based beamforming for azimuth estimation in $r_2=4\,\mathrm{cm}$2 angular bins (Zhang et al., 2019).
  • Frame size $r_2=4\,\mathrm{cm}$3 ($r_2=4\,\mathrm{cm}$4), Blackman window; $r_2=4\,\mathrm{cm}$5 modal order achieved, operating optimally over $r_2=4\,\mathrm{cm}$6–$r_2=4\,\mathrm{cm}$7.
  • Real-time accuracy: UCCA attained $r_2=4\,\mathrm{cm}$8 mean error, outperforming single-ring UCAs by $r_2=4\,\mathrm{cm}$9 in both angular error and standard deviation, even in reverberant room conditions.

5. Applications and Performance Benchmarks

The dual-axis, frequency-invariant control offered by CCMA beamformers is essential in spatial audio recording, teleconferencing, robust sound source localization (SSL), and acoustic scene analysis:

• Sound source localization: UCCA achieved $r_1=0.10\,\mathrm{m}$0 success (within $r_1=0.10\,\mathrm{m}$1 accuracy) in azimuth estimation for nearby targets and $r_1=0.10\,\mathrm{m}$2 at $r_1=0.10\,\mathrm{m}$3 range—far surpassing single-ring UCAs (which drop below $r_1=0.10\,\mathrm{m}$4 for farfield under speech and noise) (Zhang et al., 2019).
• Room impulse response (RIR) capture: CCMAs in MYRiAD enable high-resolution capture of spatial room transfer functions, supporting evaluation and benchmarking of enhancement systems (Dietzen et al., 2023).
• Broadband spatial beamforming: Multi-ring design suppresses the deleterious effects of Bessel zero-crossings, maintaining mainlobe width and directivity without inflection-induced nulls across the targeted operational frequency range (Zhang et al., 2019, Ortigoso-Narro et al., 24 Nov 2025).
• Elevation and azimuth control: Recent autograd-optimized CCMA beamformers achieve explicit, tunable beamwidth targets (e.g., $r_1=0.10\,\mathrm{m}$5 bandwidth adherence across $r_1=0.10\,\mathrm{m}$6–$r_1=0.10\,\mathrm{m}$7) along both angular dimensions, outperforming delay-and-sum and classical modal approaches, especially at low frequencies (Ortigoso-Narro et al., 24 Nov 2025).

6. Design Principles, Limitations, and Research Directions

Designing a CCMA involves strategic choices for ring radii and microphone counts to match modal order constraints ($r_1=0.10\,\mathrm{m}$8), spatial aliasing limits, and to avoid Bessel function zero-crossings within the operational band. The multi-radius architecture, with tailored ring-level weights and intra-ring tapers, allows for both frequency invariance and sidelobe suppression otherwise unattainable with single-ring topologies (Zhang et al., 2019, Ortigoso-Narro et al., 24 Nov 2025).

A plausible implication is that the flexibility in CCMA weight design—exploited via gradient-based optimization—permits trade-offs between directivity, robustness (WNG), and symmetry of the beampattern as application needs dictate.

Limitations include increased hardware complexity (additional capsules, channels), the requirement for precise geometric calibration (especially in databases such as MYRiAD), and computational expense for end-to-end autograd design (currently off-line optimized) (Ortigoso-Narro et al., 24 Nov 2025). Sensitivity to sensor misplacement and spectral colorations above $r_1=0.10\,\mathrm{m}$9 require further engineering or compensation.

Emerging research is extending these frameworks to support real-time autograd implementations, robust adaptation to mechanical tolerances, and exploitation of higher-order differential CCMA modalities. Future CCMA systems are anticipated to underpin both ubiquitous spatial audio applications and fundamental studies in room acoustics and array processing.

7. Database Resources and Practical Implementation

Publicly available datasets, such as MYRiAD, provide not only synchronized CCMA capture of speech, music, noise, and RIRs, but also precise 3D microphone and source coordinates in room referential frames (Dietzen et al., 2023). Scripts enable direct integration into MATLAB and Python spatial audio pipelines.

In implementation, the coordinate and array-manifold information uniformly supports both classical frequency-domain beamforming and modern modal/optimization-based approaches, facilitating reproducible benchmarking and algorithm development.

CCMA-enabled systems, combining robust array design, calibrated data, and end-to-end optimization pipelines, represent a central platform for pushing the boundaries of spatial audio science and practical acoustic signal processing.