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

The problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered. Fractionally sampled data are 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. A necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived. This result provides an alternative but equivalent statement of an existing result. Using this result, it is shown that certain class of multipath channels cannot be identified from the second-order statistics irrespective of how the sampling rate is chosen