  This paper investigates the joint power allocation and user association
problem in multi-cell Massive MIMO (multiple-input multiple-output) downlink
(DL) systems. The target is to minimize the total transmit power consumption
when each user is served by an optimized subset of the base stations (BSs),
using non-coherent joint transmission. We first derive a lower bound on the
ergodic spectral efficiency (SE), which is applicable for any channel
distribution and precoding scheme. Closed-form expressions are obtained for
Rayleigh fading channels with either maximum ratio transmission (MRT) or zero
forcing (ZF) precoding. From these bounds, we further formulate the DL power
minimization problems with fixed SE constraints for the users. These problems
are proved to be solvable as linear programs, giving the optimal power
allocation and BS-user association with low complexity. Furthermore, we
formulate a max-min fairness problem which maximizes the worst SE among the
users, and we show that it can be solved as a quasi-linear program. Simulations
manifest that the proposed methods provide good SE for the users using less
transmit power than in small-scale systems and the optimal user association can
effectively balance the load between BSs when needed. Even though our framework
allows the joint transmission from multiple BSs, there is an overwhelming
probability that only one BS is associated with each user at the optimal
solution.
