Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots   Should Be Allocated?
  Massive MIMO is a promising technique to increase the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas, $M$, than scheduled users, $K$, because the users' channels are likely to be near-orthogonal when $M/K > 10$. However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users, $K^\star$, depends on $M$ and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of $K^\star$ in the large-$M$ regime is derived in closed form, while simulations are used to show what happens at finite $M$, in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal $M/K$ is less than 10 in many cases of practical relevance. Interestingly, $K^\star$ depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same $K$. 
Emil Bj\"ornson, Erik G. Larsson, M\'erouane Debbah
cs.IT cs.NI math.IT