# Different Object Functions for SWIPT Optimization by SADDE and APSO
## 4 Numerical Results  
In this paper, the wide band system with frequencies ranging from 39 GHz to 40 GHz at millimeter wave are presented and the ray-tracing technique is used to calculate the corresponding channel. Figure 5 shows a simple office environment for simulation. There are three receivers (Rx1, Rx2, Rx3) and one transmitter (Tx) in the office. The coordinates for Rx1, Rx2 and Rx3 are (3.8, 8.8, 1.0) m, (3.0, 7.5, 1.0) m and (3.0, 5.5, 1.0) m respectively. The transmitter is at (7.0, 6.0, 1.0) m in the office. We consider three layers of circular arrays with a vertical distance of 1/4 wavelength. Each layer has 16 wide band short dipole antennas. In other words, there are 48 short dipole antennas. The power harvesting nodes are Rx2 and Rx3. The SWIPT node is Rx1. The SWIPT system is used at Rx1 with the power-dividing architecture (\(\eta=0.5\)). The transmission power to the noise ratio (\(SNR_{T}\)) is set to be 33 dB. We set the same population size and the same generation number for APSO and SADDE. The population is 60 and the iterations are 500. The mutation of APSO and crossover of SADDE are both with the same probability. The weighting \(W\) for the objective function is set to 10 in Equation (9).  
Figure 6 shows the effect of different objective functions for the BER at Rx1. From this figure, we can see that the first proposed criterion can achieve meet the BER constrain for both APSO and SADDE, but the convergent speed for APSO is better than SADDE's. This figure also tells us that the second proposed criterion can also achieve the goal of a large HP and meet the BER constraint as well. In addition to that, the convergent speeds are similar for both APSO and SADDE. Figure 7 shows the total harvesting power ratio for different objective functions. Note that the harvesting power ratio is the power ratio with and without adjusting the feed length at the transmitter. From our simulation, the total harvesting power can be improved about 60 times from the initial array by applying on proposals. Furthermore, it is clear that the total harvesting power for the second proposed criterion is better than that for the first one proposed. Moreover, it is found that APSO converges faster than SADDE in the first proposed criterion.  
Figure 5: Indoor Environment Layout.  
Figures 8 and 9 show the radiation patterns of the first proposed criterion by two different algorithms. Compare Figures 8 and 9, and refer to Figure 5 that indicates the location of the receivers and the transmitter. The adjustment of beams has all been directed to Rx1, Rx2 and Rx3 by SADDE and APSO. However, it is seen that the pattern for Rx3 is the largest compared to the other two receivers. This is because Rx3 is closest to the transmitter. While increasing the total harvesting power, the antenna gain for Rx3 is the largest. On the contrary, the pattern for Rx1 is the smallest. Due to the power being split at Rx1, the algorithm is adjusted to use minimum power to meet the BER criterion. As a result, the gain for Rx1 is smallest compared to Rx2 and Rx3. Note that both SNR and multi-path with  
Figure 6: BER for different objective functions.  
Figure 7: Harvesting power ratios for different objective functions.  
Figure 11: Indoor Environment Layout.  
Figure 10: Antenna pattern by SADDE for the second proposed criterion.  
In the above results, the first objective function is chosen to let two objective values with the same order of magnitude and we also give a weighting \(W\) for adjustment \((1/(W\times BER_{W}\times HP_{T}+HP_{T}))\). However, the weighting must be chosen in advance, with a suitable value for the best optimization. Thus, we attempt to remove \(W\) and the plus term \(HP_{T}\) to keep only the \(BER_{W}\times HP_{T}\) term. Numerical results show that similar optimization results can be found for these two objective functions. However, the second objective function does not need to find the best \(W\) in advance for optimization. Hence, the second function is better for the optimization problem in this paper.