## 1 Introduction  
With the deployment of the Third Generation (3G) wireless systems, it became evident that homogeneous network architectures, based on cells with uniform radiation pattern in service zones, could not fulfill the ever increasing demand of mobile users for capacity, service quality, and economically efficient energy consumption. This evidence has become even more pronounced with the introduction of the Fourth Generation (4G) networks, when implementing smaller cells has become a way to improve network performance, reducing traffic congestion in macro networks. Hence, for example, plug-and-play installation of femto-cells is much simpler and more profitable than whatever can be achieved with macro cells, due to reduced backhaul costs. The smaller the cell, the less power needs to be transmitted, so small cells can serve small groups of users (UE), and thus can improve the quality of service (QoS) [1]. Furthermore, complex Radio Access Systems (RAS) can comprise cells of various classes, thus forming the so-called Heterogeneous Cellular Network (HCN), also commonly referred to as HetNet, where the basic topology concept presumes layering two or more groups of the same-class cells, called tiers [2, 3]. Over the last decade, the rapid evolution of mobile telecommunication services fueled by growing demand for multimedia applications has led to surging data transmission traffic, which (according to annual reports of major network operators and network equipment manufacturers) increases approximately ten times every five years, to reach about 12 Exabytes per month--13 times more than in 2017. The very direct consequence of such data traffic growth is the increasing demand for RAS nodes, which severely affects energy efficiency. Hence, for example, the average annual energy consumption of a single base station (BS) is about 25 MWh [4], which significantly contributes to almost 2% of the global carbon emission currently estimated to be generated by ICT industry. Although HetNet cell planning has been in use even in the Second Generation (2G) mobile networks, it is only the Long Term Evolution (LTE) and its extension LTE Advanced (LTE-A), commonly referred to as 4G standard, which fully define the concept for enhancing the HetNet performance. Such strategies for LTE/LTE-A radio performance planning are centered around reducing the distance between the transmitter and receiver, i.e., improving the service signal coverage of regions demanding more intensive traffic. Accordingly, in Figure 1, examples of a simplified HetNet with a multistandard 4-tier scenario (a), and 3-tier topology (b), are presented. We investigate network energy efficiency according to the following metrics proposed for wireless access networks [5; 6]:  
* energy per information bit [J/b];
* average power used by a device that provides connectivity to a certain covered area [Wm\({}^{2}\)]. Beside service provisioning, the European Telecommunications Standards Institute (ETSI) proposes the following QoS-related metrics [7]:  
* ratio between the throughput of users obtaining the minimal specified (service dependent) QoS within the served area, and the total power consumed by the BSs providing service in that area [b/J];
* ratio between the number of UEs obtaining the minimal specified QoS within the served area, and the total energy consumed by the BSs providing service in that area during the observation time. The essence of the proposed metrics is improving HetNet coverage and capacity, both dependent on signal-to-interference-plus-noise-ratio (SINR). Figure 1: Simplified presentations of an exemplar Heterogeneous Cellular Network (HCN), also commonly referred to as HetNet, (HetNet–); (a) multiple-standard radio access HetNet; (b) 3-tier HetNet coverage with blue lines as service zones’ boundaries, and red spots, green triangles, and black squares as macro-cells, pico-cells, and femto-cells, respectively.