On blind identifiability of multipath channels using fractional sampling and second-order cyclostationary statistics

Considers the problem of blind identifiability of digital communication multipath channel using fractionally spaced samples. Fractionally sampled data is cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. The authors derive a necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process. This result provides an alternative but equivalent statement of an existing result. Using this result, they show that certain class of multipath channels cannot be identified from the second order statistics irrespective of how the sampling rate is chosen. In particular, if the multipath channel consists of time delays that are integer multiples of symbol duration, the channel is not identifiable from the correlation function of the received signal irrespective of how fast the signal is sampled