# A Metric for Secrecy-Energy Efficiency Tradeoff Evaluation in 3 GPP Cellular Networks
###### Abstract  
Physical-layer security is now being considered for information protection in future wireless communications. However, a better understanding of the inherent secrecy of wireless systems under more realistic conditions, with a specific attention to the relative energy consumption costs, has to be pursued. This paper aims at proposing new analysis tools and investigating the relation between secrecy capacity and energy consumption in a 3 rd Generation Partnership Project (3 GPP) cellular network, by focusing on secure and energy efficient communications. New metrics that bind together the secure area in the Base Station (BS) sectors, the afforded date-rate and the power spent by the BS to obtain it, are proposed that permit evaluation of the tradeoff between these aspects. The results show that these metrics are useful in identifying the optimum transmit power level for the BS, so that the maximum secure area can be obtained while minimizing the energy consumption. secrecy capacity; energy efficiency; metric; cellular networks +
Footnote †: journal: Information Information  
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equal to 2% of global human carbon dioxide emissions and almost equivalent to those of the global aviation industry [8]. Hence, in the last few years, growing attention has been shown by both the Regulatory entities and the Telcos on the impact of the energy saving strategies on the economics [9] and the environment [10]; in the framework of ICT systems, mobile communications networks are the main contributors in terms of energy consumption: their contribution is expected to grow up to 178 Megatons of CO\({}_{2}\) in 2020, while in 2002, it was 64 Megatons. Therefore, in order to reduce the power consumption of cellular networks, several energy efficiency strategies have been proposed that are based on power control and power amplifier sleep mode [11; 12; 13; 14]. Moreover, in order to quantify and compare the energy consumption performance of different components and systems, several Energy Efficient metrics have been defined for component, equipment and system levels: two different BS types have been taken into account for the energy consumption model, as described in [15], the Remote Radio Head (RRH) and the Macro BS. Since telecommunication equipment normally operates at different loads and energy consumption, the introduction of a suitable metric becomes a crucial aspect of the network optimization. In literature, there exist papers evaluating the energy costs of cryptographic algorithms [16], as well as the joint optimization of secrecy rate and energy consumption in cooperative ad hoc networks [17]. To the best of our knowledge, no paper is currently published in international journals dealing with the evaluation of the energy costs of physical-layer security when it is applied to 3 rd Generation Partnership Project (3 GPP) cellular networks. To this end, this paper aims at investigating the tradeoff between secrecy capacity and energy consumption in a 3 GPP cellular network. We focused on secure and energy efficient communications for cellular systems, which are motivated by the fact that most confidential transactions are expected to be conducted over such networks in the very near future. Specifically, we first derived the secrecy capacity of a BS surrounded by another six BSs. Then, we proposed two new metrics which bind the secure area in the BS's sector, the afforded date-rate and the power spent by the BS to obtain it and that allow evaluation of the tradeoff between them. The secure area defines the set of locations in the cell where the eavesdropper cannot leak information to the legitimate user.