# Energy Efficient Resource Allocation for M2M Devices in LTE/LTE-A
## 4 Results and Analysis
### Performance Evaluation  
In this section, we compare the performance of our proposed schedulers to the RME, CBC and RR schedulers. To ensure the minimum of fairness between H2H and M2M devices, both RME-M and CBC-M allocated maximum 60% of the total RBs to H2H modules [13]. The rest of RBs were assigned to M2M devices.  
Figure 5 represents the power efficiency in dBm/bytes. It shows that our proposed schedulers, RME and CBC, allow one to increase the power efficiency for both types of M2M applications compared to the RR scheduler (Figure 5a,b). This efficiency is due to the reduction of power transmission. These schedulers allow one to allocate RBs with best channel quality which has the consequence of using fewer RBs to send data, contrarily to the RR scheduler which does not consider channel quality when allocating resource blocks. Equation (1) shows that the transmitted power is proportional to the number of RBs. So if the number of allocated RBs reduces from N RBs to M RBs, the power can be saved by a value of \(\Delta P_{M,N}\) (Equation (4)).  
\[\Delta P_{M,N}=P_{N}-P_{M}=10*\log_{10}(N/M). \tag{4}\]  
Figure 5: Power efficiency (dBm/byte).  
Figure 6 represents the spectral efficiencies of RR, CBC, RME and our proposed schedulers. We note that our schedulers enable one to have better spectral efficiency than RR scheduler, thanks to the allocation of RBs with the best CQI. [PERSON] (2018) demonstrated that spectral efficiency, which is the measure of wireless network capacity, is proportional to channel quality. Using the Shannon-Hartley theorem (Shannon's Law), the channel capacity is:  
\[C\approx n*B*\log_{2}S/N, \tag{5}\]  
where C is the channel capacity (bits/s), n represents the number of transmit antennas, B is the bandwidth and S/N is the signal-to-noise ratio. This theorem defines the maximum rate at which information can be transmitted over a communication channel, over the air interface in our case, of a specified bandwidth in the presence of noise. Besides, from Figure 6, we noticed that RME-M has better spectral efficiency than RME scheduler thanks to the allocation of a set of RBs with best channel quality.  
Figure 7 represents the number of packets not satisfying delay constraint. We noticed that RME-M allows one to reduce, considerably, the number of packets not meeting their delay constraint. As in addition to taking into consideration power consumption, RME-M takes into account the delay constraint, which allows devices with less delay tolerance to have the highest priority and send their data before their delay expiration. Contrarily to CBC-M scheduler, which does not consider delay constraint, RME-M performs very well and achieves a very high percentage of MTC devices served.  
Figure 8 represents the results in term of fairness. The results show that RR scheduler has the best fairness for M2M periodic devices (Figure 8a). However, all other schedulers have a similar fairness index; this is due to the fact that RR scheduler equally allocates RBs to all devices without considering their channel quality. Our schedulers allow similar fairness for event driven applications (Figure 8b). For H2H devices, RME and CBC have better fairness indexes than our propositional schedulers. This is due the limitation of the number of resource blocs allocated to H2H devices imposed by our proposed schedulers. In CBC and RME, H2H devices are prioritised and if they have better channel quality than M2M devices, the latter will suffer starvation of allocated RBs.  
Figure 6: Spectral efficiency X number of M2M devices.  
Figure 8: Fairness index.  
Figure 7: Number of packets not meeting delay constraint.