  In real-time listening enhancement applications, such as hearing aid signal
processing, sounds must be processed with no more than a few milliseconds of
delay to sound natural to the listener. Listening devices can achieve better
performance with lower delay by using microphone arrays to filter acoustic
signals in both space and time. Here, we analyze the tradeoff between delay and
squared-error performance of causal multichannel Wiener filters for microphone
array noise reduction. We compute exact expressions for the delay-error curves
in two special cases and present experimental results from real-world
microphone array recordings. We find that delay-performance characteristics are
determined by both the spatial and temporal correlation structures of the
signals.
