On Design of Non-Orthogonal Pilot Signals for a Multi-Cell Massive MIMO System

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 from 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.