# Optimal Power Allocation with Hybrid Relaying Based on the Channel Condition
## 4 Simulation Results
destination \(\gamma_{da}\) for the DF-AF relay network has a similar form of harmonic mean between \(\gamma_{s1}\) and the SNR of the third hop when \(\gamma_{s1}\) is less than the SNR of the second hop. For a given \(\gamma_{s1}\), \(\gamma_{da}\) can be increased by increasing \(|h_{3}|^{2}\). Therefore, \(\gamma_{ad}\) has a greater value than \(\gamma_{da}\) when \(|h_{2}|^{2}\) is sufficiently larger than \(|h_{3}|^{2}\). On the other hand, \(\gamma_{da}\) has a greater value than \(\gamma_{ad}\) when \(|h_{3}|^{2}\) is sufficiently larger than \(|h_{2}|^{2}\). Figure 8a,b show the achievable rates of the equal power allocation schemes for hybrid three-hop relay networks when the SNRs of the first hop \(\gamma_{s1}\) are \(0\,\mathrm{dB}\), \(-3\,\mathrm{dB}\) and \(-6\,\mathrm{dB}\). As shown in Figure 7a,b, the achievable rate of the DF-AF relay network is greater than for the AF-DF relay networks when \(|h_{3}|^{2}\) has a greater value than \(|h_{2}|^{2}\) and vice versa. It is observed that the achievable rates of the equal power allocation schemes are lower than for the proposed power allocation schemes. From Figures 5-8, it is noted that the proposed optimal power allocation scheme uses less \(P\) than the equal power allocation scheme to keep same achievable rate. Also, the results consider achievable rate per unit bandwidth. Therefore, the advantage of proposed schemes increases linearly according to the bandwidth of systems. Since the bandwidth of recent communication systems has been increased continuously to accommodate future data traffic, the proposed optimal allocation scheme can contribute to increase the power efficiency of the recent wideband systems. The simulation results in Figures 7 and 8 show that the appropriate hybrid relaying according to the channel condition provides a significant performance improvement compared with other power allocation schemes. For further comparisons, the power allocation schemes in [24; 25] are referenced. Since the system model for each paper is different, we refer to the simulation results of each paper. In [24], the proposed power allocation is used to improve a diversity gain by cooperative transmission in the hybrid DF cooperative communication system. Simulation results for the achievable rates according to power usage show an around 3 dB performance improvement compared with equal power allocation. Also, in [25], the proposed power allocation is used to improve a diversity gain by cooperative transmission with relay selection in the multiple relay system. Simulation results for the achievable rates according to power usage show a performance improvement of less than 1 dB. In addition, as the cooperative communication has complicate structure, the problems of sophisticated schedulers and additional overhead occur. However, from the simulation results of Figures 7 and 8, according to channel condition, we confirm an performance improvement of over 5 dB in the range of 5\(\sim\)10 dB of used power by using appropriate hybrid relaying, as compared with other types of hybrid relaying. Therefore, the analysis of hybrid relaying and power allocation according to the channel condition yields meaningful results.