## 1 Introduction  
Wireless communication has attracted increasing attention in recent years. However, wireless communication occurs in an open environment and broadcasts information to all users in free space [1, 2]. Therefore, wireless communication security has become a serious problem in both civil and military fields. Traditionally, upper-layer encryptions technology has been widely used in wired communication. However, encryption systems are inherited from the traditional computer network and ignores the special physical layer characteristics of wireless communication system, such as the openness wireless channel, time-varying network topology, and resource limitation of mobile terminal [3, 4]. As a result, physical layer (PHY) security was introduced to achieve the confidentiality of messages at the PHY [5]. PHY security enables wireless communications to exploit the properties of physical layer to scramble information content that could be potentially intercepted by eavesdroppers, while simultaneously delivering it to its desired receivers. DM, as a keyless physical-layer security transmitting technique with great potentials, has attracted a great deal of attention over the past decade. It uses antenna arrays to transmit a signal only along the desired directions while distorting signal constellations in all other directions [6, 7]. Traditionally, DM technology has been mainly implemented based on phased arrays (PA) in the past decade [8, 9, 10, 11]. However, the previous communication schemes based on PA can no longer guarantee secure transmission when eavesdroppers locate in the desired direction of LU due to the transmit beampattern being only angle-focusing. Accordingly, it is necessary to investigate other schemes that can prevent eavesdroppers in the desired direction from intercepting messages. Therefore,we depart from PA and apply a frequency diverse array (FDA) into DM implementations because of its extra range dimension dependence, rather than being dependent on only the angle used [12; 13; 14; 15; 16; 17]. FDA delivers a new opportunity for secure wireless communications. However, the beampattern of FDA is still angle-range coupling, which means that confidential messages are accessible to illegitimate receivers that are located at some angle-range pair curves. Several works have focused on frequency offsets to address the coupling problem of FDA [18]. To this end, in [19; 20], the authors proposed a logarithmic frequency increments scheme. Furthermore, with random frequency increments between each element, the author of [21] proposed a new FDA structure, named random FDA, to indicate targets' direction and range without coupling. Besides the radio frequency fronted technology, adding AN at the baseband is another effective technology used to deteriorate the received messages of Eves that has been employed in DM systems [22; 23]. An FDA DM scheme with AN [24; 25] has been proposed to further improve secrecy performance, and a robust synthesis scheme with AN was proposed in [26] for a single user scenario. In summary, the current studies cannot deal with the PHY security problem of multiple receivers obtaining different messages simultaneously, which needs to be addressed in practical applications. The traditional DM schemes with AN need to allocate power to the AN, which will lower the power efficiency of total transmitting power. Furthermore, in practical cases, the Eves would be located as close to LU as possible (even in the same locations as the LUs) to eavesdrop on the confidential signal, and the previous studies have shown that it is difficult to ensure the security of the independent confidential message in this case. In addition, the received power at each LU is not accurately controlled according to the prescribed power. In order to address the limitations of the previous works and further enhance the PHY security, we proposed a spatial modulation (SM) and multiple parameter weighted-type fractional Fourier transform (WFRFT)-aided scheme based on a random frequency diverse array (RFDA).