Delay-locking: Unraveling Multiple Unknown Signals in Unknown Multipath

Given a mixture of co-channel user signals subject to frequency-selective multipath, sensed through an array of co-located antennas, how can we recover the user signals? This is a difficult problem, especially when some of the user signals are much weaker than others, and we know little about the transmitted signal properties. The setup is relevant in a number of settings, including non-cooperative communications, signal intelligence, passive radar using illuminators of opportunity, and convolutive speech and audio separation. This paper considers the problem of unsupervised signal recovery in unknown multipath and (possibly strong) multiuser interference. Leveraging the fact that multiple independently faded copies of each signal are received through distinct paths at different times, this paper shows that relative path delays and the user signals can be identified via canonical correlation analysis (CCA). CCA is a powerful statistical learning tool that can efficiently estimate a common subspace even in the presence of noise and strong co-channel interference. The proposed approach provides rigorous recovery guarantees, can tolerate strong co-channel interference and low SNR, and is computationally tractable for practical implementation. Simulations reveal that the proposed approach achieves much better performance than independent component analysis, which is the only baseline that works under similar assumptions in this setting.