Comparison of Orthogonal vs. Union of Subspace Based Pilots for Multi-Cell Massive MIMO Systems

In this paper, we analytically compare orthogonal pilot reuse (OPR) with union of subspace based pilots in terms of channel estimation error and achievable throughput. In OPR, due to the repetition of the same pilot sequences across all cells, inter-cell interference (ICI) leads to pilot contamination, which can severely degrade the performance of cell-edge users. In our proposed union of subspace based method of pilot sequence design, pilots of adjacent cells belong to distinct sets of orthonormal bases. Therefore, each user experiences a lower level of ICI, but from all users of neighboring cells. However, when the pilots are chosen from mutually unbiased orthonormal bases (MUOB), the ICI power scales down exactly as the inverse of the pilot length, leading to low ICI. Further, as the number of users increases, it may no longer be feasible to allot orthogonal pilots to all users within a cell. We find that, with limited number of pilot sequences, MUOB is significantly more resilient to intra-cell interference, yielding better channel estimates compared to OPR. On the other hand, when the pilot length is larger than the number of users, while OPR achieves channel estimates with very high accuracy for some of the users, MUOB is able to provide a more uniform quality of channel estimation across all users in the cell. We evaluate the fairness of OPR vis-à-vis MUOB using the Jain's fairness metric and max-min index. Via numerical simulations, we observe that the average fairness as well as convergence rates of utility metrics measured using MUOB pilots outperform the conventional OPR scheme.