  This paper investigates spectrum-power trading be- tween a small cell (SC)
and a macro-cell (MC), where the SC consumes power to serve the macro-cell
users (MUs) in exchange for some bandwidth from the MC. Our goal is to maximize
the system energy efficiency (EE) of the SC while guaranteeing the quality of
service (QoS) of each MU as well as small cell users (SUs). Specifically, given
the minimum data rate requirement and the bandwidth provided by the MC, the SC
jointly optimizes MU selection, bandwidth allocation, and power allocation
while guaranteeing its own minimum required system data rate. The problem is
challenging due to the binary MU selection variables and the fractional form
objective function. We first show that in order to achieve the maximum system
EE, the bandwidth of an MU is shared with at most one SU in the SC. Then, for a
given MU selection, the optimal bandwidth and power allocations are obtained by
exploiting the fractional programming. To perform MU selection, we first
introduce the concept of trading EE. Then, we reveal a sufficient and necessary
condition for serving an MU without considering the total power constraint and
the minimum data rate constraint. Based on this insight, we propose a low
computational complexity MU selection algorithm. Simulation results demonstrate
the effectiveness of the proposed algorithms.
