# Differential Evolution in Waveform Design for Wireless Power Transfer
## 5 Conclusions  
In this paper, we evaluated the application of EAs in the problem of optimal waveform design for WPT systems. In detail, we applied various algorithms (DE, CoDE, L-SHADE, and Jaya) for the optimization of the transmitted multi-tone waveforms. A SISO WPT system was utilized and a multipath propagation channel was implemented. From the derived results, EAs seem to successfully obtain the optimal solutions to this non-convex problem, since all four tested algorithms converged to very similar results. However, the differences between the obtained optimal solutions from EAs and the SCP-QCLP algorithm are indiscernible. As a result, we can conclude that the objective function's landscape for the given propagation channels is not very complicated. Consequentially, the complexity of EAs was not beneficial compared to the SCP-QCLP algorithm for the given optimization problem. Also, the results increase the confidence that the SCP approach can provide optimal waveforms despite its simplicity. Finally, CODE exhibited a slightly better convergence speed compared to the other EA algorithms.  
The advantage of using EAs is that they are very flexible and can be used in conjunction with any objective function. To this end, a more realistic model of the rectifier, designed in some simulation software, could be integrated into the objective function. In that case, a charge pump circuit could be used instead of the single diode rectifier. For the given optimization problem, the disadvantage of EAs compared to SCP-QCLP is the longer execution time due to their stochastic nature.  
It would be interesting to examine the application of EAs in waveform design for more complex WPT systems (more challenging objective functions). One scenario would be to examine waveform design in systems that comprise multiple transmitter antennas and/or multiple users like in [9; 17]. However, in that case, it is expected that the computational time for the calculation of the objective function, and consequently the total execution time, would increase. Another scenario could be to apply EAs in systems that require the joint optimization of WPT and some other characteristic, like SNR [15] or information transfer rate [16]. That would require the modification of EAs by integrating some mechanisms for the enforcement of the additional constraints.  
The optimized waveforms demonstrate high PAPR that is beneficial for the receiver rectenna's RF to DC conversion efficiency, but not for the amplifier used in the transmission. This is because the behavior of common amplifiers is nonlinear for these types of signals. Consequently, in a real-world application, an additional constraint on PAPR should be imposed. In that case, since there is a strong limitation on the possible \(s_{n}\) values, it would be interesting to examine if optimizing both \(s_{n}\) and \(\phi_{n}\) using EAs could provide some advantages.  
The conceptualization of the paper was done by [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON], and [PERSON] performed the theoretical analysis and the simulations. [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] validated the theoretical analysis and simulation results. [PERSON], and [PERSON] supervised the process. All authors analyzed the results, and contributed to writing and reviewing the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.