N. P. Krasnenko1, I. A. Rybakov2
1, 2 Institute of Monitoring of Climatic and Ecological Systems of the Siberian Branch of the Russian Academy of Sciences (Tomsk, Russia)

1 krasnenko@imces.ru, 2 vaniarybakov98@gmail.com

This paper addresses the critical problem of insufficient noise immunity in atmospheric acoustic sounding systems (sodars) operating under intense and non-stationary noise conditions typical for urban, industrial, and airport environments. Direct shielding methods and conventional software-based filtering often fail to suppress wideband acoustic interference, which frequently exceeds the useful signal by several orders of magnitude.

The objective of this work is to develop and evaluate an adaptive spatial filtering technique based on a subband minimum variance distortionless response (MVDR) beamformer applied to an acoustic antenna array.

The study considers an 8-element linear equidistant array of horn piezoelectric transducers with an inter-element spacing of half the wavelength (7.5 cm at 2 kHz). Classical narrowband MVDR beamforming minimizes output interference power while maintaining unity gain in the desired signal direction. However, its direct application to wideband sodar signals is limited because array steering vectors are frequency-dependent, causing null positions to shift across the frequency band and reducing suppression effectiveness. To overcome this, the subband MVDR method is employed: the wideband spectrum is split into narrow subbands using a Hamming window and a 64-point fast Fourier transform (FFT), resulting in subbands of approximately 156 Hz width (sampling rate 10 kHz). For each subband, an independent spatial covariance matrix is estimated, and optimal complex weights are computed. The resulting partial beam patterns are then averaged to produce the final pattern. The adaptation is performed during passive intervals between sodar pulses, where only background noise and interference are received, thus avoiding distortion of the desired signal.

Numerical simulations have been conducted in MATLAB using real-world recordings of aircraft engine noise and bird flock sounds as interference sources. The desired signal was a 2 kHz harmonic tone. Two scenarios have been investigated: two interference sources (−15° and −30°; −10° and 25°) and a more challenging case with five sources (−40°, −25°, −15°, 20°, 35°) at interference-to-noise ratios (INR) ranging from 10 to 30 dB. The signal-to-noise ratio was fixed at −10 dB, reflecting realistic weak echo conditions.

Results demonstrate that the subband MVDR method achieves interference suppression levels between −21.6 dB and −34.6 dB, depending on source power and angular separation. The directivity factor of the main lobe decreases by no more than 1.05 dB (from ~10 dB to ~8.9–9.3 dB), which is an acceptable trade-off for significant noise suppression. Higher INR values improve suppression accuracy due to better covariance matrix estimation. The five‑interference case confirms that an 8‑element array can form up to N–1 nulls (here 5 nulls) while maintaining main-beam integrity.

Practical significance lies in the feasibility of implementing the algorithm during passive sodar listening intervals without affecting the sounding process. The proposed approach substantially enhances sodar performance in high-noise environments, expanding its applicability in urban, industrial, and airport zones.

Krasnenko N.P., Rybakov I.A. Adaptive antenna array for atmospheric acoustic sounding systems // Antennas. 2026. № 4. P. 42–55. DOI: https://doi.org/10.18127/j03209601-202604-05

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