Energy Efficiency Analysis of Two-Tier MIMO Diversity Schemes in Poisson Cellular Networks

In this paper, the energy efficiency (EE) of different MIMO diversity schemes is analyzed for the downlink of a two-tier network consisting of both macro- and femto-cells. The locations of the base stations (BSs) in both tiers are modeled by spatial Poisson point processes (PPPs). The EE of the system in b/J/Hz is obtained for different antenna configurations under various diversity schemes. Adaptive modulation is employed to maximize both the throughput and the EE across both tiers. Borrowing well established tools from stochastic geometry, we obtain closed-form expressions for the coverage, throughput, and power consumption for a two tier rate adaptive cellular network. Building on the developed analytical framework, we formulate the resource allocation problem for each diversity scheme with the aim of maximizing the network-wide EE while satisfying a minimum QoS in each tier. We consider that both the number of antennas and the spectrum allocated to each tier constitute the network resource which must be efficiently selected for both tiers to maximize network-wide performance. The best performance in terms of the EE is provided by the schemes which strike a good balance between the achievable maximum throughput and the consumed power (both increasing with the number of RF chains used). In addition, the potential savings in EE by using femto-cells with sleeping mode capabilities are analyzed. It is observed that, when the density of active co-channel femto-cells exceeds a certain threshold, the EE of the system can be significantly improved by sleep scheduling.