## 1 Introduction  
Uniformly excited array antennas inevitably generate radio power nulls, whose signal level is much lower than that of the surrounding area, due to the propagation and coupling characteristics of electromagnetic waves, as seen in Figure 1. This leads to increases in power fluctuations (PFs), poor communication quality, and limitations on the base station (BS) site selection process, which needs to be sure that these regions do not point to user groups [1]. Furthermore, 5G/6G communication technology proposes the large-scale distributed base station (BS) approach to provide faster data rates, reduced latency, and higher reliability communication, but this also results in more nulls at the same coverage [2]. Solving the PF problem in the configuration of directional antenna arrays is important because omnidirectional antennas cannot give better gains and data rates. In the early stages of research in this field, by processing pattern roots, Lawson-Woodward theorem, and Newton iteration, scientists filled the antenna's first null of the lower sidelobe to enhance the power quality near the BS and help reduce signal fluctuations [3; 4; 5; 6; 7; 8; 9; 10]. The first null must now be filled in along with the other nulls in the sector to satisfy the demands for higher communication quality due to the advancements in communication technology. Researchers have employed a variety of algorithms, including genetic, particle swarm, and others, to fill the first null as computational science has advanced. These algorithms need lots of raw data for extensive training and learning [11; 12; 13; 14; 15]. Many experts have proposed or loaded some special structures to fill nulls of the pattern [16; 17; 18; 19; 20; 21; 22], which is suitable to fill a single antenna well but has little effect on the array. In addition, it is possible to solve the coupling problem and fill the null well by constructing particular decoupling structures within the array [23; 24; 25]. Although the cosecant square beam can provide more uniform coverage, it often requires an antenna or a leaky wave reflection surface, neither of which is appropriate for the BS [26; 27; 28]. To compensate for the communication quality of single-beam antennas in nonmain lobe beam directions, multi-input and multi-output (MIMO) technology is proposed in a 5G communication system, causing the emergence of multi-beam array antennas. Generally speaking, there are three methods for creating a high-gain multibeam array: first, by designing antenna units that can produce multiple beams and arranging them into an array [29]; second, by combining linear arrays with beams originating from different directions [30]; and others, by controlling the directions of multiple beams within the array using electrically adjustable components. On the other hand, an increasing number of beams results in complex feeding networks and higher energy consumption. To improve coverage and address communication blind spots well, a reflective intelligent surface (RIS) is considered as a key technology for 6G communication [31]. An RIS can further enhance directionality while achieving beam-switching capabilities depending on numerous electrically adjustable components, instead of using radio frequency channels. A large number of RIS-distributed plans have emerged to obtain better signal coverage [32]; in other words, resolving the vertical beam coverage issue in a way that minimizes the number of beams required vertically or only requires numerous beams horizontally can solve the feeding network energy problems in MIMO and reduce the RIS costs. Therefore, we need to find better base station antenna (BSA) techniques. After repeated numerous simulations and verification, we discovered that the array can generate almost-omnidirectional null-free (ONF) beams, which means its radiation pattern almost contains zero nulls, if its excitations follow the half Tyler (HT) distribution.