Adaptive Canonical Correlation Analysis With Application to Time Synchronization for Signal Alignment

Signal Alignment has been recently introduced as a simple and effective means of communicating under powerful and unpredictable (e.g., intermittent) interference. Signal alignment uses repetition coding at the transmitter and canonical correlation analysis (CCA) at the (multi-antenna) receiver to synchronize with and decode the signal of interest. CCAbased synchronization works even in the face of adverse interference, where classical synchronization methods fail; but this requires solving the CCA problem repeatedly, in a sliding window fashion, which is computationally demanding. This paper poses the associated adaptive CCA problem and proposes two computationally efficient and scalable algorithms for solving it. These work by leveraging algebraic properties stemming from shift structures and different reformulations of the batch CCA problem. This enables real-time application of signal alignment as well as applications in other areas where adaptive CCA makes sense. The algorithms are validated in judicious experiments showcasing the computational benefits afforded by the proposed algorithms.