  Voice Activity Detection (VAD) and Overlapped Speech Detection (OSD) are key
pre-processing tasks for speaker diarization. In the meeting context, it is
often easier to capture speech with a distant device. This consideration
however leads to severe performance degradation. We study a unified supervised
learning framework to solve distant multi-microphone joint VAD and OSD
(VAD+OSD). This paper investigates various multi-channel VAD+OSD front-ends
that weight and combine incoming channels. We propose three algorithms based on
the Self-Attention Channel Combinator (SACC), previously proposed in the
literature. Experiments conducted on the AMI meeting corpus exhibit that
channel combination approaches bring significant VAD+OSD improvements in the
distant speech scenario. Specifically, we explore the use of learned complex
combination weights and demonstrate the benefits of such an approach in terms
of explainability. Channel combination-based VAD+OSD systems are evaluated on
the final back-end task, i.e. speaker diarization, and show significant
improvements. Finally, since multi-channel systems are trained given a fixed
array configuration, they may fail in generalizing to other array set-ups, e.g.
mismatched number of microphones. A channel-number invariant loss is proposed
to learn a unique feature representation regardless of the number of available
microphones. The evaluation conducted on mismatched array configurations
highlights the robustness of this training strategy.
