Investigating statistical and spatial loss functions for geometry-aware unsupervised virtual microphone estimation in multi-source environments

Purpose Small-scale devices often provide too few microphones for effective array processing. This study investigates geometry-aware unsupervised loss functions for a neural network-based virtual microphone estimator (NN-VME), aiming to generate virtual microphone (VM) signals without ground-truth recordings at VM positions. Design/methodology/approach Known array geometry is used to construct training constraints. Alongside a previously proposed loss that maximizes linear correlation between estimated VM signals and recordings from other channels, a new loss based on the time difference of arrival (TDOA) of each source is introduced. The losses are compared on simulated multi-source LibriSpeech data, and the generated VM signals are evaluated with multiple beamformers. Findings The correlation-based method generates high-quality VM signals and improves beamforming performance on CHiME-4. The LibriSpeech experiments demonstrate the effectiveness of geometry-aware unsupervised NN-VME under multi-source conditions and show that the generated VM signals can support different beamforming methods. Research limitations/implications The framework assumes known array geometry, and correlation- and TDOA-based constraints may become less reliable under highly reverberant conditions. Future work should improve robustness in diverse real-world environments. Originality/value This study systematically compares geometry-aware unsupervised NN-VME losses across tasks, introduces a TDOA-based constraint for multi-source target speech extraction, and evaluates the applicability of estimated VM signals across beamformers.