Pilot Power Allocation Through User Grouping in Multi-Cell Massive MIMO Systems

In this paper, we propose a relative channel estimation error (RCEE) metric, and derive closed-form expressions for its expectation <inline-formula> <tex-math notation="LaTeX">$\rm {Exp}_{rcee}$ </tex-math></inline-formula> and the achievable uplink rate holding for any number of base station antennas <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>, with the least squares (LS) and minimum mean squared error (MMSE) methods. It is found that RCEE and <inline-formula> <tex-math notation="LaTeX">$\rm {Exp}_{rcee}$ </tex-math></inline-formula> converge to the same constant value when <inline-formula> <tex-math notation="LaTeX">$M\rightarrow \infty $ </tex-math></inline-formula>, which renders the pilot power allocation (PPA) substantially simplified and a PPA algorithm is proposed to minimize the average <inline-formula> <tex-math notation="LaTeX">$\rm {Exp}_{rcee}$ </tex-math></inline-formula> per user under a total pilot power budget <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> in multi-cell massive multiple-input multiple-output systems. Numerical results show that the PPA algorithm brings considerable gains for the LS estimation compared with equal PPA (EPPA), while the gains are significant only with large frequency reuse factor (FRF) for the MMSE estimation. Moreover, for large FRF and large <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula>, the performance of the LS approaches to that of the MMSE. Besides, a scheduling strategy is proposed to allocate pilot power in the whole system, which can approach the optimal performance. For the achievable uplink rate, the PPA scheme and improves the minimum achievable uplink rate compared with the EPPA scheme.