## 2 HT Distribution and Simulation Results
### Elements and Linear Array
We  
Figure 3: Structure of the elements with structural parameters (unit: mm; a = 16.4, b = 9.7, c = 26.1, d = 2.9, e = 2.2, f = 3.4, L = 50, L\({}_{2}\) = 13): (a) element A working at 3.5 GHz; (b) element B working at 26 GHz. will introduce the results of these linear arrays with different N values, such as N = 8, 12, 16, and so on, when using the proposed method and analyze the difference. Assuming the linear array is placed on the BS with a height H of 30 m, as shown in Figure 1, and an angle of \(\alpha\) between the antenna and vertical direction, we can use Equation (9) to determine the power distribution in the cell before and after ONF formation at 15 mW of input power:  
\[Power_{dis(i)}=10\times\lg(15)+\text{gain(i)}-\text{lp} \tag{8}\]  
\[|S_{11}|=20\lg|\Gamma| \tag{2}\]0 Gain of the elements. \[|S_{11}|=20\lg|\Gamma| \tag{2}\]1 N element antenna array: (**a**) 3.5 GHz; (**b**) 26 GHz. \[|S_{11}|=20\lg|\Gamma| \tag{2}\]2  
where _Power_dis(i)_ is the power of the \(i\)th point in the horizontal direction, _gain(i)_ is the antenna gain pointing to the \(i\)th point, \(lp\) is the air loss (which can be determine using Equation (8)), and _dis(i)_ is the distance between the antenna and the point \(i\) on the ground, which can be obtained via the trigonometric function. We simulated N unit linear arrays' far-field patterns and used these results to fit the power distribution of them. Figure 7a displays the patterns of 12 units of linear antennas with various processing techniques when the dp is set at \(-60\). From this, we can learn that the maximum gain of the 3.5 GHz uniformly excited antenna is 17.9 dBi and that of the HT-excited antenna is 15.9 dB. The maximum gain of the HT\({}^{2}\) (the square root of HT excitation)-excited antenna, operating at 3.5 GHz, is 14.55 dBi. The maximum gain of the 26 GHz uniformly stimulated antenna is 16.2 dBi, and this is 14.83 dBi for the HT antenna, and 13.64 dBi for the HT\({}^{2}\) antenna. The HT antenna can fill all of the nulls of the all-\"1\" antenna and achieve the ONF beam when the dp is \(-60\), but its gain will be 1.4 dB lower at 26 GHz and 2 dB lower at 3.5 GHz than that of the uniform antenna. The maximum gain becomes lower than that of the HT antenna but the level of null filling is higher when we further increase the proportion of excitation power distribution across units, i.e., by adopting HT\({}^{2}\) excitation distribution. Figure 7b illustrates that the 3.5 GHz antenna, following HT processing, has an obvious advantage in terms of power near the base station range, with a gain of approximately 10-35 dB at the null point, and a range of 400 m. The 26 GHz HT antenna can also further increase the power by 26 dB at the null point. In order to maintain higher communication quality, our ONF beam can simultaneously sustain high radiation power within 200 m: for instance, exceeding \(-75\) dBm at 3.5 GHz and \(-90\) dBm at 26 GHz. Accordingly, the ONF beam can solve the power fluctuation issue in the BS. We additionally investigate the impact of the HT approach on different linear arrays. Table 1 lists the corresponding excitations, and Figure 8a-c show the far-field patterns. As is shown in Figure 8b, the maximum HT gain of 3.5 GHz is 14.03 dBi, which is 2 dB lower than that of the uniformly excited (all-\"1\") array, and the maximum HT gain of the 26 GHz array is 13.76 dBi, which is 1 dB lower than that of all-\"1\" array when N = 8. Furthermore, the far-field gain curve is smoother, and the null-filling effect is improved when the excitation amplitude is squared. The same difference in situation also appears on the 6-, 12-, and 16-element arrays, as shown in Figures 7 and 8. Therefore, we can deduce that the wavelength and the distance between the elements are related to the difference. The maximum gain of the 8-element uniform array is 16.17 dBi in Figure 8b, while the maximum gain of the 12-element HT null-free array is 15.9 dBi in Figure 7a, which is quite near to 16.17 dBi.