## 2 Related Works  
Relating to MAC layer communications, most causes of excessive energy consumption in mobile network scenarios include the use of omnidirectional antennas, data processing, high protocol overhead, and a high level of interference in the channel. Data processing implies the large usage of a central processing unit (CPU), memory, hard drive, etc. To partially solve this issue, regarding energy consumption, the most actual solution is to find a compromise between data processing and radio communication [21]. In this regard, in [20], the authors present a data compression mechanism in order to minimize packet length with the aim to limit energy consumption in radio communication. In [25], the authors highlight the large protocol overhead introduced by this kind of system. Generally, to design an energy efficient MAC protocol, some of the following expedients are employed:* **Reducing collisions and retransmissions:** This is one of the most common objective of MAC protocols for limiting the probability of interfering nodes. In this context, the work [26] proposes a novel deafness-aware (DA-MAC), with the goal to mitigate the deafness problem through a discrete-time Markov chain model. The model uses a double-channel schema in order to handle the directional RTS (DRTS); more specifically, the single channel provided by the directional MAC is split into two different logical channels used for filtering the data traffic and the control packets, respectively; the designed DA-MAC algorithm provides for several features that allows one to recognize and mitigate efficiently the collisions occurred because of deafness. The results highlight a reduction of the deafness duration and a good improvement of the aggregate throughput compared with some of the most significant existing works. * **Reducing overhearing:** Wireless mobile nodes deplete battery life also because they overhear transmissions of their neighbors. One possible solution to mitigate this problem is to use dedicated and separated channel distinguishing control and data traffic so that nodes do not overhear undesired information. For example, the authors in [27] propose a schedule-based broadcast mechanism including data transmission timers for each node. In [28], two schemes are proposed in order to mitigate the deafness caused by persistent hearing of data and for handling the short retry limit (SRL) in directional environments. * **Minimize control overhead:** Limiting the protocol overhead represents a critical challenge, especially when small packets are used [29; 30; 31]. Because of the important channel acquisition overhead, the high amount of small packets to be transmitted translates into a significant waste of energy. However, if mobile nodes perform multiple transmission slot requests with a single reservation message, the control overhead can be limited [32]. In [22], the authors propose two MAC protocols in which nodes use directional sectorized antennas. The scheduler and the protocols are designed with the aim to minimize the co-site interference issue that could arise in some directional contexts also by limiting the overall overhead in the network. * **Reducing beamforming time:** In [3], the authors propose a tone DMAC mechanism that enable the transmission of special packets (out-of band tones) by nodes in omnidirectional mode; these tones can be processed by neighbors reducing considerably the large backoff time introduced by deafness. In [24], a round-robin MAC (RR-MAC) approach is presented with the goal to minimize the impact of deafness in directional MAC contexts. The round-robin mechanism was implemented by an algorithm that manages the assignment of the beam toward a certain sector also handling the incoming frames that could not temporally be transmitted in the channel by using waiting queues. The RR-MAC (Figure 1) allows for the communication plane to be divided into identical sectors, each of them having a certain amplitude \(w\) (sector width) and a beamforming duration time \(T_{i}\) (sector time).