Fisher information analysis for blind channel estimation based on second order statistics

In this contribution we derive a lower bound for the accuracy of blind estimation of communications channels when excess bandwidth is available and exploited through fractional sampling. The estimation methods to which we refer do not rely on the stochastic nature of the transmitted sequence, and performance analysis is generally conducted ignoring this fact, i.e. referring to a particular known transmitted sequence. Since the resulting conditioned (or deterministic) Cramer Rao bound does not take into account the effect of averaging on different transmitted sequences, and since the unconditioned (or stochastic) Cramer Rao bound is too optimistic, herein we derive another bound, namely the diversity variance bound (DVB), which properly takes into account the averaging on different transmitted sequences, without exploiting the Fisher information that they carry on, which is actually taken into account by the unconditioned Cramer Rao bound.