# Optimization of Different Deployments and Resolution of Antenna Arrays in SWIPT
## 4 Numerical Results  
The office environment is shown in Figure 4. We take the mm-Wave system of frequencies ranging from 39 to 40 GHz and used the ray tracing technique to compute the environment channel. There are three receivers (Rx1, Rx2, Rx3) and one transmitter (Tx) in the office. We then consider two kinds of nodes for SWIPT and WPT. The Rx1 uses 50% power-splitting for information decoding and harvests the half power with 60% power efficiency. The WPT nodes Rx2 and Rx3 can harvest 100% power at 60% power efficiency. The transmitter uses three different deployments as shown in Figure 5. Each antenna array has three layers with a vertical distance of \(\lambda/2\). Additionally, each layer has 16 antennas. The unit of the antenna uses the wideband dipole antenna with a \(\lambda/2\) distance separated at least. In other words, there are 48 antennas for each deployment. The transmission power to the noise at receiver (SNR_T) is set to 33 dB. For the feed length adjustment, we use SADDE to optimize the objective function and set the total iteration to 500. The population size is 60 and the adjustment parameter is 48 for each antenna array. Note that the low resolution of feed lengths only has four phases with 0o, 90o, 180o, 270o. Figure 4: Indoor environment layout. Figure 5: Three different antenna array deployments: (**a**) circular; (**b**) triangular; and (**c**) rectangular. Figure 6 shows the total harvesting power ratio by high resolution feed length for different deployments. The harvesting power ratio is based on the harvesting power under the zero phase of a circular array. It can be seen that the circular array has the best harvesting power ratio and the convergence speed. The harvesting power ratio for the triangular deployment is better than that for the rectangular deployment. However, the convergence speed of the triangular deployment is the slowest. For the low-resolution feed length, the harvesting power ratio for the circular, triangular and rectangular antenna array is shown in Figure 7. Compared to the high resolution, the harvesting power ratios are all decreased by approximately 30% and have a slow convergence speed for all three different deployments. Then, we compare the criterion for BER. In Figure 8, we can see that the BER constraint for high-resolution feed length adjustment is satisfied no matter what the deployments are. It can be seen that the BER and harvesting power are both almost converged after 400 iterations. In the low resolution, as shown in Figure 9, it seems that the optimization for the BER is still good. According to the results, it is clear that the objective function shown in Equation (10) is useful for different layouts of the antenna array. Additionally, it does prove that the different deployments do affect the final harvesting power ratio. Figure 10 illustrates the optimized pattern with different resolutions for the circular array. Figure 10a shows the pattern focused on Rx1, Rx2 and Rx3 for the high-resolution case--where the gain for Rx3 is the largest and the gain for Rx1 is smallest. This is because Rx3 is closest to the transmitter in the environment and Rx1 has split the power for SWIPT. The pattern gains are similar at the three receivers in Figure 10b for the low-resolution case. It can be seen that the harvesting power with low resolution is less than with high resolution. Figure 11 displays the pattern for the triangular array. The pattern can be focused on three receivers, as shown in Figure 10, but the total harvesting power ratio is less than that for the circular array. The optimized pattern for the rectangular array is depicted in Figure 12. Figure 12a shows that the pattern cannot simultaneously be focused on three receivers--even in the high-resolution case. The rectangular deployment has the worst harvesting power ratio, though it does reach the BER constraint. For the low-resolution case, optimization has found the local solution instead of the global solution, as shown in Figure 12b, in which the pattern is focused on Rx2.