  In this paper, we consider the design of joint resource blocks (RBs) and
power allocation for dual-mode base stations operating over millimeter wave
(mmW) band and microwave ($\mu$W) band. The resource allocation design aims to
minimize the system energy consumption while taking into account the channel
state information, maximum delay, load, and different types of user
applications (UAs). To facilitate the design, we first propose a group-based
algorithm to assign UAs to multiple groups. Within each group, low-power UAs,
which often appear in short distance and experience less obstacles, are
inclined to be served over mmW band. The allocation problem over mmW band can
be solved by a greedy algorithm. Over $\mu$W band, we propose an
estimation-optimal-descent algorithm. The rate of each UA at all RBs is
estimated to initialize the allocation. Then, we keep altering RB's ownership
until any altering makes power increases. Simulation results show that our
proposed algorithm offers an excellent tradeoff between low energy consumption
and fair transmission.
