  In mobile millimeter wave (mmWave) systems, energy is a scarce resource due
to the large losses in the channel and high energy usage by analog-to-digital
converters (ADC), which scales with bandwidth. In this paper, we consider a
communication architecture that integrates the sub-6 GHz and mmWave
technologies in 5G cellular systems. In order to mitigate the energy scarcity
in mmWave systems, we investigate the rate-optimal and energy-efficient
physical layer resource allocation jointly across the sub-6 GHz and mmWave
interfaces. First, we formulate an optimization problem in which the objective
is to maximize the achievable sum rate under power constraints at the
transmitter and receiver. Our formulation explicitly takes into account the
energy consumption in integrated-circuit components, and assigns the optimal
power and bandwidth across the interfaces. We consider the settings with no
channel state information and partial channel state information at the
transmitter and under high and low SNR scenarios. Second, we investigate the
energy efficiency (EE) defined as the ratio between the amount of data
transmitted and the corresponding incurred cost in terms of power. We use
fractional programming and Dinkelbach's algorithm to solve the EE optimization
problem. Our results prove that despite the availability of huge bandwidths at
the mmWave interface, it may be optimal (in terms of achievable sum rate and
energy efficiency) to utilize it partially. Moreover, depending on the sub-6
GHz and mmWave channel conditions and total power budget, it may be optimal to
activate only one of the interfaces.
