Speech and Audio Signal Processing Utilising the Co-prime Microphone Array

This paper proposes a semi-adaptive beamforming (SAB) algorithm for the co-prime circular microphone array (CPCMA), which takes advantage of subarray-based adaptive beamforming to achieve an optimised overall beampattern. The SAB approach calculates the bearings of grating lobes or the largest side lobes in the first sub-array before setting nulls at these directions in the beampattern of the second sub-array, aiming at removing the largest amplifications of undesired sources in the first beampattern. Compared with state-of-the-art co-prime array adaptive beamforming methods, the SAB considers the beamformer weights for each sub-array separately before combining them and generating the overall microphone array output, which fully utilises the co-prime property. Simulations indicate that the SAB improves the beampattern and array gain (AG) at low frequencies, which are dominant components of the speech energy, whilst maintaining equivalent results to the conventional CPCMA at high frequencies, leading to overall better performances in terms of beampattern and AG.

This paper evaluates the performance of semi-coprime microphone arrays (SCPMAs) for speech source direction of arrival (DOA) estimation based on the steered response power-phase transform (SRP-PHAT) algorithm. The SCPMA is an extension of the coprime microphone array (CPMA), which combines the outputs of three sub-arrays to reduce the impact of spatial aliasing and achieves performance comparable to that obtained from arrays using much larger numbers of microphones. The proposed approach considers two different processors to calculate the outputs from the sub-arrays and adapts the SRP-PHAT approach to these arrays. Simulations are conducted under anechoic and reverberant scenarios in a noisy room. Beam pattern and array gain results indicate that the SCPMA works better than the conventional CPMA at reducing the peak side lobe (PSL) level and total side lobe area while increasing the capability of amplifying the desired target signal and restraining noise from all other directions for typical frequencies of speeches. DOA Estimation results also show that the SCPMA achieves accurate DOA estimates in anechoic and low reverberant conditions, which is comparable to the equivalent full ULA, while the large side lobes in the beam pattern of the SCPMA lead to less accurate results in the highly reverberant environment.

This paper evaluates the performance of semi-coprime microphone arrays (SCPMAs) for speech source direction of arrival (DOA) estimation based on the steered response power-phase transform (SRP-PHAT) algorithm. The SCPMA is an extension of the coprime microphone array (CPMA), which combines the outputs of three sub-arrays to reduce the impact of spatial aliasing and achieves performance comparable to that obtained from arrays using much larger numbers of microphones. The proposed approach considers two different processors to calculate the outputs from the sub-arrays and adapts the SRP-PHAT approach to these arrays. Simulations are conducted under anechoic and reverberant scenarios in a noisy room. Beam pattern and array gain results indicate that the SCPMA works better than the conventional CPMA at reducing the peak side lobe (PSL) level and total side lobe area while increasing the capability of amplifying the desired target signal and restraining noise from all other directions for typical frequencies of speeches. DOA Estimation results also show that the SCPMA achieves accurate DOA estimates in anechoic and low reverberant conditions, which is comparable to the equivalent full ULA, while the large side lobes in the beam pattern of the SCPMA lead to less accurate results in the highly reverberant environment.

This paper proposes the co-prime circular microphone array (CPCMA), which applies co-prime array theory to circular microphone arrays. Compared with a conventional uniform circular array (UCA) with the same number of microphones and radius, the CPCMA achieves beampatterns with a narrower main lobe and fewer side lobes, whilst also avoiding spatial aliasing, thus having no grating lobes above the Nyquist frequency of the UCA. Array gain (AG) results indicate that the CPCMA is better than the UCA at amplifying the desired target signal while suppressing noise from other directions for typical speech signal frequencies. Compared with a UCA with similar performance and the same spatial Nyquist frequency, the CPCMA significantly reduces the required number of microphones. Simulations also indicate advantages of the CPCMA in speech source DOA estimation under high noise and low reverberation, especially when there are simultaneous multiple sources.

This paper investigates the application of the steered response power-phase transform (SRP-PHAT) method to co-prime microphone array (CPMA) recordings to estimate the direction of arrival (DOA) of speech sources. While existing CPMA approaches for acoustics applications are limited, especially under reverberant conditions, the proposed algorithm utilises SRP-PHAT to estimate the DOA of speech sources and then employs a histogram-based stochastic algorithm using steered response power (SRP) adjustment and kernel density evaluation (KDE) to improve the DOA estimation accuracy. Experiments are conducted for up to three simultaneous speech sources in the far field considering both anechoic and reverberant scenarios. Results suggest that the proposed approach achieves more accurate DOA estimates than a uniform linear array (ULA) with the same number of microphones under both anechoic and low reverberant conditions, and it significantly decreases the number of microphones of another equivalent ULA while maintaining similar performances. Moreover, the operating frequency of the microphone array is largely increased without changing the number of microphones, making it possible to accurately record higher-frequency components of source signals.