# BER Aided Energy and Spectral Efficiency Estimation in a Heterogeneous Network
## 1 Introduction  
It has been a considerable time since it has become evident that homogeneous cellular network architecture cannot adequately fulfill the fast-growing users' demand for capacity and Quality of Service (QoS) [1], as well as for efficient spectrum and energy consumption.  
Starting with the fourth generation (4G) mobile networks, it has become evident that smaller cells enhance network performance and off-load the macro network from excessive traffic. So, for example, simple plug-and-play installed femtocells are more profitable than macro cells, due to the reduced backhaul costs and less transmitted power required in small cells. Specifically, state-of-the-art Radio Access Systems (RAS) encompass cells of different classes to make up a Heterogeneous Cellular Network (HetNet), which includes at least two same-class groups--tiers [2, 3]. The actual explosive growth of data traffic implies severe demand on energy efficiency (EE), so with the 4G Long-Term Evolution (LTE) and its extended version LTE Advanced (LTE-A), as well as with the incoming 5G HetNets, transmission performance enhancements include a reduction in the distance between the transmitting and the receiving antennas.  
With respect to the EE of wireless access networks, the metrics are focused [4, 5, 6] on the energy per information [J/b], enriched by some QoS-related features [7] to improve HetNet's capacity and coverage, which both depend on the Signal-to-Interference-and-Noise Ratio (SINR).  
However, the SINR value is not always available and is not easily measurable. Therefore, we introduce here a novel approach by merging the link abstraction principle into the test scheme, to enable investigating various HetNet performance scenarios using Bit Error Rate (BER) rather than SINR at each User Equipment (UE) [8] within the serving tier area of a BS and a candidate-serving BS. This drastic simplification greatly improves thefield availability of various HetNet performance tests and, so far, has not been used in such an environment.  
We will pursue BER analysis towards network spectral efficiency (SE) and EE. Concretely, instead of the classic hexagonal-grid based cellular network composition with a BS-centered each cell [9; 10], we use stochastic geometry to capture randomness in network topology [9; 10; 11; 12; 13].  
In this regard, the HetNet topology is modeled through the Poisson Point Process (PPP) [8], which describes a non-regular positioning of BSs in a real network, better than the classic hexagonal-grid model [9]. Although the PPP-based analysis of topology is not new [10; 11; 14], it was not long ago when the PPP-distributed BSs were introduced in various HetNets [12; 15; 16; 17; 18] and MIMO-inclusive network scenarios [19].  
In Section 2, we firstly provide a short basic theoretical review, specifically considering the performance limits and related trade-off between SE and EE. The short-term BER-, SE-, and EE-based analytical model is presented as applicable for large HetNets with serving and candidate-serving BSs that have random distribution in the actual serving tier area. Finally, the analytical model is verified in Section 3, by presenting the test results obtained using an ns3 simulation tool that provided the short-term BER values for all UEs of the network under test. Conclusions are summarized in Section 4.