A link between Multiuser MMSE and Canonical Correlation Analysis

Recent work has shown that repetition coding followed by interleaving induces signal structure that can be exploited to separate multiple co-channel user transmissions, without need for pilots or coordination/synchronization between the users. This is accomplished via a statistical learning technique known as canonical correlation analysis (CCA), which works even when the channels are time-varying. Previous analysis has established that it is possible to identify the user signals up to complex scaling in the noiseless case. This letter goes one important step further to show that CCA in fact yields the linear MMSE estimate of the user signals up to complex scaling, without using any explicit training. Instead, CCA relies only on the repetition and interleaving structure. This is particularly appealing in asynchronous ad-hoc and unlicensed setups, where tight user coordination is not practical.