## 3 Omnidirectional and Directional Antennas Issues vs. Round-Robin MAC
### Round-Robin MAC Scheduling Issues  
As largely mentioned in the previous sections, networks containing nodes equipped with omnidirectional antennas are prone to a high waste of energy because the shape of the radiation pattern that does not beamform is only in a specific direction. Although different proposals exist with the aim to solve or at least mitigate the issues derived from the use of omnidirectional and directional antennas at the MAC layer, a deeper analysis is required for highlighting the issues that need to be addressed. For example, let us consider the work [24] that attempts to mitigate the overall network energy consumption using an SAS antenna module along with a round-robin scheduler algorithm. Basically, it works fine under two main assumptions:  
**Assumption 1**. : _Nodes are equipped with high-efficient hardware antennas (SAS)._  
**Assumption 2**. : _Data traffic and nodes are uniformly distributed among sectors._  
**Assumption 3**. : _The size of the sector queues are fixed and equals for all sectors._  
In order to evaluate the implications of the first assumption, it can be useful to analyze the behavior of the RR-MAC in case the omnidirectional antenna is used in place of directional or SAS technologies. For this purpose, we evaluate, through the use of the _Omnet++_ network simulator [41], the energy consumption of nodes of three different run configurations using the same simulation parameters described in [24] (most of the them are illustrated in Table 1 in Section 5 of the present paper); in order to accomplish the analysis, energy simulation modules have been provided for each node. Nodes are initially charged with an energy amount of 300 J; a node turns off when it reaches an energy value of 0 J. In the first configuration run nodes are equipped with the classical omnidirectional antenna; in the second, nodes use the omnidirectional antenna together with the RR-MAC scheduling; the latest run configuration is similar to the second except from the fact that in this case the antenna is the SAS module designed in [42]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline SAS Array Elements Spacing & 0.5 \(\lambda\) \\ Steering Angle & 45\({}^{\circ}\) \\ Transmission Rate & 54 Mbps \\ Message Length & 512 Byte \\ Mobility Model & Random Waypoint \\ Node Mobility speed & from 1 to 10 mps \\ Routing Protocol & AODV \\ Network Load & 50\% \\ Simulation Area Size & 500 m \(\times\) 500 m \\ Simulation Time & 300 s \\ Number of Sectors & 3, 4, 6, 8 \\ Initial Battery Capacity & 300 J \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main simulation parameter set. Figure 3: Directional antennas common issues in mobile ad hoc networks (MANETs). (**a**) Deafness problem. (**b**) Handoff problem. Figure 4 depicts the residual capacity (averaged by all nodes) plot comparison between the three considered cases. As we can expect, when using the omnidirectional antenna without any energy saving mechanism, nodes deplete their battery life very quickly; when the omnidirectional antennas are used in cooperation with RR-MAC the average depletion time is almost doubled (t = 190 s) and improves significantly when SASs are employed by nodes. This is mainly due to the fact that RR-MAC limits the beamforming time for each sector translating into a reduction of the number collisions and interferences. The mentioned assumptions imply that the system could be affected from the queue size and the waiting queue time problems [43] that can affect the overall network consumption in the network. We analyze these issues by creating two more run configurations: in the first one, mobile nodes are uniformly placed in the network; in the same way, the activity degree of nodes is uniformly distributed among sectors; in the second, instead, nodes are periodically concentrated in a certain sector (randomly chosen) of the sectorized plane and the activity degree of nodes is unbalanced among sectors.