  Implementation cost and power consumption are two important considerations in
modern wireless communications, particularly in large-scale multi-antenna
systems where the number of individual radio-frequency (RF) chains may be
significantly larger than before. In this work, we propose to deploy a single
low-noise amplifier (LNA) on the uplink multiple-input-multiple-output (MIMO)
receiver to cover all antennas. This architecture, although favorable from the
perspective of cost and power consumption, introduces challenges in the LNA
gain control and user transmit power control. We formulate an energy efficiency
maximization problem under practical system constraints, and prove that it is a
constrained quasi-concave optimization problem. We then propose an efficient
algorithm, Bisection -- Gradient Assisted Interior Point (B-GAIP), that solves
this optimization problem. The optimality, convergence and complexity of B-GAIP
are analyzed, and further corroborated via numerical simulations. In
particular, the performance loss due to using a shared LNA as opposed to
separate LNAs in each RF chain, when using B-GAIP to determine the LNA gain and
user transmit power, is very small in both centralized and distributed MIMO
systems.
