# Energy Efficiency of D2D Multi-User Cooperation
## 1 Introduction  
As multimedia communication develops, traditional cellular networks will not be able to handle large amounts of data and support high-speed transmission. D2D communication can help enhance data rate, system capacity and spectrum efficiency through short-range communication among users directly by reusing the spectrum of cellular network [1; 2; 3], which gives users a better communication experience than the traditional cellular network. Furthermore, D2D pairs can build a self-organizing system by establishing connections with the help of a cellular network. Due to flexibility, multiple D2D users who want to receive the same data from an Evolved Node B (eNB) can organize a cluster, and a cluster head is chosen to receive the data from the eNB to share with cluster members by dividing the data into multiple data packets, which is the mesh D2D service introduced in Reference [4]. Regarded as a proximity service, D2D services are sufficiently flexible to adapt to various complex heterogeneous networks in the future. D2D communication is an important part of heterogeneous networks. The spectrum efficiency, throughput and energy efficiency can be improved by interference suppression, resource allocation and relay selection schemes [5; 6; 7; 8]. Many studies show that most researches on short-range communication systems focus on improving communication reliability and data rate among users [9; 10; 11]. As D2D users communicate directly with each other through short-range communication (which consumes a small amount of energy due to the short distance [12]), whether the users can provide enough energy for the packet transmission or not is usually ignored. In fact, though the cooperation among a largenumber of D2D users can effectively enhance the spectrum efficiency and throughput of heterogeneous networks [13], the amount of consumed energy of each D2D user obviously rises with the number of cooperative users. Hence, it is necessary to take the energy availability of each user into account when there are multiple cooperative users. Traditional ways of choosing relaying users were based on the maximum SNR [14; 15], which resulted in high energy consumption. On one hand, particular users are chosen by multiple users simultaneously, which results in energy waste. On the other hand, particular users will be chosen at different times, which will cost these particular users a large amount of energy. Hence, it is not appropriate to choose relaying D2D users based on the maximum SNR when there are multiple cooperative users. In the D2D cluster, some D2D users will consume additional energy as the relaying of other D2D users to receive data from the base station and then relay the data to corresponding D2D user. Which will cost these part of relaying D2D users a large amount of energy. In order to avoid excessive energy consumption of some D2D users and decrease of the system lifetime, this paper reduces the energy consumption of the single D2D user by preventing a D2D user from being chosen as a relaying by multiple D2D user at the same time and always being chosen at different times. So, we restrict that the relaying D2D user only relays data for one of the other D2D users. Then the key is how to match multiple relaying D2D users with the rest of multiple D2D users. The Kuhn-Munkres algorithm is a classic algorithm in graph theory to find the optimal match of weighted bipartite graph. Motivated by the application of the Kuhn-Munkres algorithm in Reference [16], where the Kuhn-Munkres algorithm was introduced to solve the matching problem of maximizing transmission capacity, this paper adopts the Kuhn-Munkres algorithm to deal with this issue. Hence, the D2D multi-user cooperation issue is transformed into a MWM problem. This paper aims to solve the energy problem of D2D users when there are multiple D2D users cooperating. In the D2D communication system, D2D users who want to receive the same data form a cluster by a self-organizing connection with the help of a cellular network.