Description: In this letter, the error variance of the Minimal
Mean-Square Error (MMSE) channel estimator is analyzed, and
its analytic formula is given. Based on the analytic formula, a
designing criterion on the pilot signals is proposed. When training
time slots can be large enough, our criterion confirms the
well-known fact that orthogonal pilot signals are optimal. But if
training time slots are not enough to support this orthogonality,
our results show that the error variance is lower-bounded away
zero, no matter what kind of pilot signals are used. In this
case, the design of pilot signals should be implemented by using
the line packing on a complex Grassmannian manifold
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