On the Pair-Wise Error Probability of a Multi-Cell MIMO Uplink System With Pilot Contamination

In this paper, a multi-cell multiple-input multiple-output (MIMO) uplink system is considered. For uplink transmission, to implement decoding, the base station (BS) generally needs to estimate channels with the aid of training sequences. Obviously, for full frequency reuse systems, training also suffers from inter-cell interference, namely pilot contamination. In this paper, the impact of pilot contamination on the performance of the considered system is studied based on the maximum likelihood (ML) decoder. Specifically, an exact analytical expression of pair-wise error probability (PEP) is derived, and then, a lower bound and an upper bound of PEP are given, to explicitly show the impact of pilot contamination. With the detailed analysis of these bounds, we can discover: (1) pilot contamination can result in error floor, provided that the number of BSs in the considered system is larger than the length of a frame; and (2) if the length of a frame is larger than or equal to the number of BSs, and an appropriate coding scheme is applied, error floor can be removed. Finally, a coding design criterion is proposed. Based on this criterion, it can be shown that the considered system can achieve the same diversity to what can be achieved by a single isolated cell system.