# Energy Efficiency of a Decode-and-Forward Multiple-Relay Network with Rate Adaptive LDPC Codes +
## 4 Simulation Results and Discussion
Lesser power consumption, as less information has to be sent;
4. Shorter time delays. Hence, the OPA approach where the code rate adaptation is done with no intermediate data buffering at relays but post detection combining is done on sequences of unequal lengths, appears to be a promising solution for multiple relays. Moreover, this approach also ensures the maximal energy efficiency by allocating the optimal share of transmit power to the transmitting nodes. In Figure 10, we compare the optimized power allocation technique with a heuristics based approach. The heuristics based method provides the proof of concept that the OPA strategy studied in this research works in the close proximity of the heuristic approach. It is less complex as compared to the heuristics based approach. Nonetheless, the proposed OPA provides a good solution that is energy efficient due to the same power budget of the system in all the cases. Figure 9: OPA (optimized power allocation) Example: Number of effective information bits, received and combined (from three relays), codeword length = 648, \(m_{1}=3\), \(m_{rd}=\{3,3,1\}\), source code rate \(3/4\), and 4-QAM. Figure 11 shows the results of optimized power allocation and adaptive code rates. An identical Nakagami-\(m\) factor is considered on both hops, on all channels between source and multiple relays and relays and destination, i.e., \(m_{1}=m_{2}=3\). This is clear from Figure 11 that when transmit power is allocated optimally, with an increasing number of relays, the BER performance becomes better and better, because of the diversity gain. As the number of paths providing the independent information increases, a diversity gain is achieved, which is actually the change in the slope of BER curve. Hence, the probability of errors decreases with the increasing number of relays. This is worth mentioning here that in Figure 11 the diversity gain curves look more like the power gain curves, but in fact the total power budget for all the cases was kept the same and the additional gain is achieved because of the additional diversity. Figure 12 shows the performance of three different PA schemes studied in this work. As shown in Figure 12, results are collected for n.i.d Nakagami fading, i.e., value of fading factor \(m\) between two hops is different. OPA provides a performance gain of \(\sim\)5 dB and \(\sim\)2 dB as compared to EPA-I and EPA-II, respectively. From the discussion, EPA-I and EPA-II are simpler strategies of power allocation, as compared to the OPA. As, like in EPA-I, there is no transmit power adaptation in EPA-II and only the code rates adaptation is done under the CSI feedback. Table 2 presents an overview of the PA strategies. Positively, OPA not only improves the BER performance of the system but also maximizes the energy efficiency of the system. As we can see, OPA is the superior power allocation technique because it takes into account the real time channel conditions, calculates the instantaneous SNR, and maximizes the energy efficiency of the system. Figure 10: OPA compared with heuristics based approach, LDPC codeword length = 312, \(m_{1}=m_{2}=3\), 4-QAM, and \(C_{R}=1/2\). Figure 3:0 OPA: BER of system with multiple relays, codeword length = 312, \(m_{1}=m_{2}=3\), 4-QAM, and varying code rates \(C_{R}\). Figure 3:1 BER of multiple relays (five relays) with three PA (power allocation) schemes, (independent but not identically distributed (n.i.i.d) channels), and 4-QAM. Furthermore, when there is a code rate adaptation for the relay to destination link, a considerable gain can be attained with post-detection combining even without buffering the information at the intermediate relays. This method not only has many advantages over the technique with information buffering at the relays, but it also reduces the complexity of the overall system and helps the relays to consume less power, reducing the overall system delay.