  Fixed low-resolution Analog to Digital Converters (ADC) help reduce the power
consumption in millimeter-wave Massive Multiple-Input Multiple-Output (Ma-MIMO)
receivers operating at large bandwidths. However, they do not guarantee optimal
Energy Efficiency (EE). It has been shown that adopting variable-resolution
(VR) ADCs in Ma-MIMO receivers can improve performance with Mean Squared Error
(MSE) and throughput while providing better EE. In this paper, we present an
optimal energy-efficient bit allocation (BA) algorithm for Ma-MIMO receivers
equipped with VR ADCs under a power constraint. We derive an expression for EE
as a function of the Cramer-Rao Lower Bound on the MSE of the received,
combined, and quantized signal. An optimal BA condition is derived by
maximizing EE under a power constraint. We show that the optimal BA thus
obtained is exactly the same as that obtained using the brute-force BA with a
significant reduction in computational complexity. We also study the EE
performance and computational complexity of a heuristic algorithm that yields a
near-optimal solution.
