Distributed compression and maximum likelihood reconstruction of finite autocorrelation sequences

Estimating the autocorrelation of wide-sense stationary time series is important for a wide range of statistical signal processing and data analysis tasks. Distributed autocorrelation sensing strategies are of interest when multiple pieces or realizations of the time series are measured at different locations. This paper considers a distributed autocorrelation sensing scheme based on randomly filtered power measurements, each compressed down to one bit, without any sensor coordination. A Maximum Likelihood (ML) reconstruction scheme is proposed and is shown to work well, even at high overall compression ratios and with a substantial fraction of bit errors. Whereas the ML formulation appears non-convex, it is proven that it in fact possesses hidden convexity, which enables optimal solution. Simulations are used to illustrate the performance of the proposed ML approach.