## 1 Introduction  
Flying ad hoc networks (FANETs) facilitate many activities in society, such as agricultural processes, security, communications, and so on. This is possible with a swarm of drones wirelessly connected with low-gain antennas. In these swarms, the antenna system is crucial for effective performance; thanks to the antenna, it is possible to collect data from the sky with drones. However, reaching far targets is impossible when low-gain antennas are used. In recent years, the concept of virtual antenna arrays (VAAs), comprising a group of nodes formed by the low-gain antennas of each drone of the swarm [1; 2; 3; 4], was introduced. This permits the antenna system to increase the directivity to reach far targets. Some interesting studies are being published on this topic; for instance, a polyhedral AAA with isotropic sources was studied with a direction-of-arrival estimation scheme [5]. In addition, the positions of isotropic sources were optimized to obtain high directivity and side lobe level reduction [6; 7; 8]. In [9], a comparison was made of a single element and a virtual linear array with the optimum service time when both used the same power. A non-uniform virtual array of isotropic sources was designed for an optimum side lobe, transmission power, and motion energy consumption [10]. A demonstration of the feasibility of VAA for multi-port input and multi-port output radars was reported in [11; 12]. Previous research [13] proposed a sizeable VAA using a GPS to communicate over long distances. Research on forming a VAA to maintain an air object was reported in [14]. Other important papers have published VAAs based on the drone cluster approach in the presence of position errors [15; 16]. Recently, the effects of the drone structure in virtual arrays were studied in [8]. In addition, new research presented time-modulated VAAs with dipoles [17] and patch elements [18; 19]. In summary, the previous works mainly proposed VAAs for communication systems of FANETs. However, the topic of VAAs is still maturing and has many opportune areas for research. In that context, this paper presents the application of VAAs for radar systems mounted on a FANET at 3.5 GHz. This frequency is very suitable for emerging radar systems in the fifth generation (5G). Previously, this scenario has not been studied in the literature. New FANETs will require communication with new 5G systems soon at the band of 3.5 GHz. To that end, we propose the design of frequency diversity virtual arrays (FDVAs) to detect objects in far targets with a 5G-FANET. It is important to highlight that frequency diversity has been utilized in traditional arrays [20], but not with virtual arrays. For instance, different frequency diversity arrays (FDAs) with a uniform linear topology were designed by using Hamming [21; 22; 23], logarithmic [24; 25; 26; 27; 28], and random frequency offsets [29; 30; 31]. These approaches generally utilize the spacing among the antennas of \(\lambda/2\). On the other hand, two-dimensional topologies of FDAs, such as concentric rings [32] and rectangular [33], have been studied. In addition, three-dimensional spherical topologies were proposed in [34]. A novel FDA was also synthesized with time modulation [35]. These previous papers analyzed FDAs with isotropic antennas. Moreover, one piece of research [33] proposed an FDA with Yagi patch antennas. Here, the main contribution is the design of a non-uniform FDVA with elliptic patch antennas mounted on quadcopter drones. The main challenge was to find the optimum frequency offsets and positions of the nodes. This was achieved to obtain a side lobe level reduction. The methodology was carried out by particle swarm optimization (PSO). Several design examples with different numbers of antennas are presented.