Disjoint Pilot Power and Data Power Allocation in Multi-Cell Multi-User Massive MIMO Systems

In this paper, we consider pilot and data power allocation in multi-cell multi-user massive multiple-input multiple-output (MIMO) systems to maximize the summation of spectral efficiency (sum SE). In conventional massive MIMO systems, equal pilot and data power is assigned to all users so the sum SE is not good. A common way to maximize sum SE is forming a maximization problem with the sum SE objective function containing both pilot and data power as variables. However, pilots are only used for channel estimation so pilot power should be allocated based on channel estimation quality instead of sum SE. Moreover, improving significantly channel estimation quality also helps to indirectly improve the sum SE. This motivated us to propose a disjoint pilot and data power allocation where pilot powers are optimized based on the sum normalized mean squared error (sum NMSE) channel estimation minimization problem and data powers are optimized based on sum SE maximization problem. We consider least squares (LS) and minimum mean squared error (MMSE) estimation methods which are commonly used in massive MIMO. In the first step, we formulate a minimization problem to minimize the summation of NMSE of the system under maximum pilot power per user constraint. Minimization problem for MMSE method is non-deterministic polynomial-time (NP) hard so we propose an algorithm to find the local optimum point. First step is only related to pilot powers and indirectly improves the sum SE by improving channel estimation quality. In second step, we further improve the sum SE by formulating a sum SE maximization problem with data powers as variables under maximum data power per user constraint. Since this problem is NP-hard, we derive a lower bound on the sum SE and maximize this bound instead Numerical results show the advantages of our proposed approach in comparison with existing schemes.