Blind equalization of digital communication channels using fractionally spaced samples

We consider the blind equalization of digital communication channel (systems) using fractionally spaced samples and their second- and fourth-order statistics. A fractionally sampled signal is cyclostationary rather than stationary. Therefore, we first cast the problem into a blind equalization problem of a linear time-invariant (LTI) system with a single input and multiple outputs, by representing the fractionally sampled output process as a vector stationary process. Then we derive a necessary and sufficient condition for the LTI system to be blindly equalizable from the stationary output vector sequence. We propose a constrained maximization problem for solving the blind equalization. To solve the maximization problem, we propose two iterative procedures. The first one is a stochastic gradient algorithm similar to the one proposed by Shalvi and Weinstein (see IEEE Trans. Inform. Theory, vol. 36, p. 312-21, 1990) in the scalar case, while the second one is a super-exponential algorithm similar to the one proposed by them (see IEEE Trans. Inform. Theory, vol. 39, p. 504-519, 1993) in the scalar case.