Spectrum-Power Trading for Energy-Efficient Small Cell
  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. 
Qingqing Wu, Geoffrey Ye Li, Wen Chen, and Derrick Wing Kwan Ng
cs.IT math.IT