Virtual Antenna Arrays with Frequency Diversity for Radar Systems in Fifth-Generation Flying Ad Hoc Networks

Abstract

This paper proposes the design of virtual antenna arrays with frequency diversity for radar systems in fifth-generation flying ad hoc networks. These virtual arrays permit us to detect targets from the sky with flying drones. Each array element is composed of a microstrip antenna mounted on quadcopter drones and is virtually connected with the other elements. The antennas are tuned to work at the lower fifth-generation frequency band of 3.5 GHz. The design process considers the optimization of frequency offsets and positions for each element to obtain a side lobe level reduction. This methodology is carried out by particle swarm optimization. Several design examples are presented with random frequency offsets and non-uniform positions. These designs are compared to uniform-spaced arrays excited with Hamming frequency offsets. The simulation results show that using random frequency offsets and non-uniform positions provides a minor side lobe level reduction. This research demonstrates the feasibility of using virtual arrays for radar systems in fifth-generation flying ad hoc networks.

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 VAA 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 λ/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.

2. Virtual Array Model

Each element of the FDVA consists of an elliptic patch antenna assembled on a quadcopter drone, as shown in Figure 1. The maximum size of the drone is 131 mm. The parts of the drone consist of metal and carbon fiber. The antenna is strategically located on the side of the drone to focus the radiation on the front.

The radiation pattern for a VAA of N elements is formulated by the next formula [21],

$$P\left(\theta ,d\right)=\sum _{n=1}^{N}g\left(\theta \right)e^{j{(kx}_{n}sin\theta +2\pi \left(f_0+f_n\right)\left(d-d_0\right)/c)}$$

(1)

where θ is the elevation angle, and the wave number is defined as k = 2π/λ with λ as the wavelength in the initial frequency f₀. The variable x_n is the element position in space. The term f_n is the frequency offset concerning f₀. The difference between frequency offsets is ∆f_n = (f_n − f_n−1). The variable d is the distance variable. The term d₀ is the distance between the array and the maximum radiation. The constant c is the velocity of light in a vacuum. The function g(θ) is the element pattern of the nth antenna in the frequency f₀. This function considers the pattern distortion due to the aircraft structure depicted in Figure 1. The elliptical patch antenna is shown in Figure 2. The antenna material is an FR4 substrate of 1.6 mm thickness, with a permittivity of εr = 4.3, a tangential loss of δ = 0.0025, and a copper layer of 0.04 mm. The physical dimensions are W = 37.5 mm, L = 25 mm, G = 37.5 mm, R = 9 mm, r = 6.5 mm, h = 17.6 mm, x = 1.9 mm, and lg = 9 mm. The antenna parameters were calculated based on the theory reported in [36]. It should be noted that the radiation pattern of the FDVA was simulated in the CST microwave studio. The reflection coefficient is shown in Figure 3; this antenna operates from 3.25 GHz to 3.79 GHz. We selected this element because it is low profile, which is an important characteristic when the antenna is mounted on a drone. Nevertheless, the drone can use a different antenna element. The selection of the best antenna for a frequency diversity virtual array is an open research topic.

3. Problem Statement and Fitness Function

The design problem is to discover the optimum location coordinate x_n and frequency offset f_n for each element of the FDVA, to obtain optimum radiation patterns. The terms f₀ and d₀ are considered constants during the optimization process. In this scenario, the optimization variables are computed as,

$$Q=\left[q^1,q^2,\dots ,q^i\right]$$

(2)

$$q^i=\left[x_n^i,f_n^i\right]$$

(3)

The Q term is a matrix of optimization variables, and each element qⁱ represents the location x_n and the frequency offset f_n. The index term i is an individual from the swarm. During the optimization method, the spacings x_n are searched by defining a spacing s_n = x_n − x_n−1 among the drones within the range of s_n ϵ [1.7 λ, 2.7 λ], where the wavelength λ is considering the frequency f₀ = 3.5 GHz. This constraint is to avoid a possible collision of drones. The frequency offsets, such as f_n ϵ [1 KHz, 20 KHz], are also constrained. The objective function of this optimization is computed with the next expression:

$$of=\max \left(SLL\right)$$

(4)

SLL is the maximum side lobe level for the radiation patterns P(θ,d). The algorithm PSO minimizes the objective function of, obtaining the optimum radiation patterns defined in Equation (1). The methodology of PSO is taken as in [37]. This methodology is very efficient for the design of antenna arrays, as mentioned in [37]. However, we do not claim that PSO is the best algorithm for an FDVA. The design process used the PSO just as a tool to find the optimization variables. The next section will describe the simulation results.

4. Simulation Results

The particle swarm algorithm was coded in MATLAB under a computer with four Xeon processors (model E5-2640) and 256 GB of memory (RAM). The configuration of the PSO was set as follows: number of iterations i_max = 1800, number of agents p_size = 50, inertial weight w varies downward in the range of [0.95–0.4], and acceleration constants c₁ = c₂ = 2. This configuration has been tested with good results in antenna array optimization [37]. We established the FDVA with N = 6, 9, and 12 antenna elements. We performed cases with symmetry and no symmetry of the locations and frequency offsets around the origin. We summarize the results of the optimization in

Table 1. Optimization variables and fitness function values.

N	Symmetry	Normalized SLL	Directivity	Locations xn (λ)	Frequencies fn (KHz)
6	Yes	0.7706	6.56 dB	0, 1.7652, 4.4652, 7.0634, 9.7634, 11.5286	16.248, 12.135, 2.388, 2.388, 12.135, 16.248
9	Yes	0.5828	8.49 dB	0, 2.6582, 5.3208, 7.1053, 8.8719, 10.6385, 12.4230, 15.0856, 17.7438	19.744, 15.234, 12.436, 1.624, 4.664, 1.624, 12.436, 15.234, 19.744
12	Yes	0.5192	9.05 dB	0, 2.6613, 5.1533, 7.4415, 9.1495, 10.8621, 13.5126, 15.2252, 16.9332, 19.2214, 21.7134, 24.3747	10.57043, 19.94567, 17.6699, 1, 1.32935, 9.02219, 39.02219, 1.3293, 1, 17.6699 19.94567, 10.57043
6	No	0.7121	6.95 dB	0, 2.6412, 4.5123, 6.3544, 8.1316, 9.8321	14.3043, 19.217, 1, 1.7049, 11.1150, 2.5609
9	No	0.5904	8.43 dB	0, 2.6994, 5.3944, 8.0934, 9.8727, 12.5459, 14.3622, 16.0889, 17.8965	4.466, 3.308, 19.106, 0.1304, 1, 11.775, 1.171, 07.367, 18.245
12	No	0.5386	9.19 dB	0, 2.6986, 4.3989, 7.0827, 9.1845, 11.2371, 13.7306, 15.7537, 17.4566 19.1796, 20.9382, 23.6236	3.697, 19.408, 3.252, 6.969, 20.000, 13.671, 1, 19.997, 6.018, 17.358, 19.680, 12.929

, which contains numerical values of the optimization variables x_n and f_n. In addition, Table 1 shows the values of the side lobe levels in a normalized magnitude. The cases with symmetry obtained better SLL reductions than those with no symmetry. Figure 4 shows the fitness function values during the optimization process for the cases with no symmetry. The PSO converges at the optimum solution. Figure 5 depicts the optimization variables’ distributions. Using symmetrical distributions would decrease the hardware complexity of the antenna array. The symmetrical random distributions are better than the traditional Hamming distributions regarding SLL reductions.

Now, these distributions generate the radiation patterns shown in Figure 6, Figure 7 and Figure 8 for the cases with different numbers of antennas. Firstly, observe the radiation generated by the Hamming distribution in the three figures. These patterns contain grating lobes due to the spacing of the antennas at greater than λ/2. Nevertheless, it is impossible to use λ/2 as the spacing because this collides with the drones. In this case, the Hamming distributions are not suitable for this application. The random distributions obtain radiation with no grating lobes, as depicted in the three figures. One can infer that these distributions are better solutions for the FDVA. The symmetrical and non-symmetrical distributions generate similar patterns, and the SLL values change only slightly, although symmetrical distributions have the advantage of reducing hardware complexity.

Table 2. Comparison with virtual arrays.

Work	Array Topology	Type of Antenna	Frequency	Drone	Algorithm	Perturbations
Ref. [5]	3D polyhedral and linear	Isotropic	Not included	Not included	DOA	Not included
Ref. [6]	3D random	Isotropic	Not included	Not included	DEMO	Not included
Ref. [7]	3D random in 4 layers	Isotropic	Not included	Not included	Not included	Not included
Ref. [17]	Uniform linear and square with time modulation	Dipole	Not included	Not included	PSO	Not included
Ref. [9]	Non-uniform linear	Isotropic	Not included	Not included	Deterministic	Not included
Ref. [10]	3D random	Isotropic	Not included	Not included	DPINSGA-II	Not included
Ref. [15]	Non-uniform linear	Isotropic	Not included	Not included	Nelder mead simplex method	Included
Ref. [16]	Non-uniform linear	Isotropic	Not included	Not included	SOCP	Included
Ref. [8]	3D random	Square patch	2.4 GHz	Included	DEMO	Not included
Ref. [18]	Non-uniform linear with time modulation	Square patch	2.4 GHz	Not included	IWO	Not included
Ref. [19]	Non-uniform linear with time modulation	Fed-slot	2.4 GHz and 5.5 GHz	Included	DEMO	Included
This Work	Non-uniform linear with frequency diversity	Elliptic patch	3.25 GHz to 3.79 GHz	Included	PSO	Not Included

contains a comparison with previous studies in the field of virtual antenna arrays. The main contribution of this work is the use of frequency diversity in virtual antenna arrays for 5G-FANETs. Moreover, most previous works used isotropic and dipole antennas with no drone structures. However, exploring the scenario of real antennas mounted on a drone is very important before real experimentation. Furthermore, other works utilized patch antennas at a frequency of 2.4 GHz. Here, the designs utilized the recently opened band of 3.5 GHz. Additionally, the previous papers designed virtual arrays with other techniques such as time modulation or only random positions. Previously, frequency diversity was not used in virtual arrays. As such, our contribution represents an advance in this topic, which permits the topic to mature. The frequency diversity in virtual antenna arrays may permit using a FANET as a radar system in future emerging applications.

Finally, it is important to compare this study with previous papers in the field of FDAs. In this case,

Table 3. Comparison with previous FDAs.

Work	Array Topology	Antenna	Frequency Offsets fn	Initial Frequency f0 and Uniform ∆fn	Distance d	Maximum Direction (d0, θ0)	Symmetry	Algorithm	Antenna Spacing
Ref. [24]	Linear N = 5, 10, 15, 17	Isotropic	Hamming and logarithmic	f0 = 10 GHz Δfn = 3 kHz, 2 kHz	0–2 km 2 × 105 km 0–90 km 0–1000 km	θ0 = 0° 1 × 105 km 30° 500 km θ0 = 0° 15 km, 45 km, 745 km θ0 = 30° 500 km θ0 = 0° 500 km	Yes/No	Not applied	λ λ/2 λ/4
Ref. [6]	Square N = 16, 8, 4	Patch Yagui 1–2 GHz 2–4 GHz	Not specified	Not specified	Not specified	θ0 = 0°	Not specified	Not applied	30 mm
Ref. [38]	Linear N = 10	Isotropic	Not specified	f0 = 10 GHz Δfn = 10 kHz	5–15 km	θ0 = 0° 20 km	No	(CMT) algorithm	λ/2
Ref. [29]	Linear N = 10	Isotropic	Random	f0 = 10 GHz Δfn = 5 KHz.	0–25 km	θ0 = 0° 0° θ0 = 0° 1.91° 1 km θ0 = 0° 56.44° 25 km	No	Not applied	λ/2
Ref. [25]	Linear N = 15	Isotropic	Logarithmic	f0 = 5 GHz δ = 30 KHz Δfn = log(m + 1)δ	0–60 km	θ0 = 10° 25 km	Not specified	Not specified	λ/4
Ref. [26]	Linear N = 33	Isotropic	Hamming and logarithmic	f0 = 10 GHz Δfn = 85 kHz.	0–50 km	θ0 = 0° 25 km	Yes	Not specified	0.24 m
Ref. [30]	Linear N = 16	Isotropic	Random	f0 = 10 GHz Δfn ϵ [100 KHz–10,000 KHz]	10–15 km	θ0 = π/3 10.11 km	No	Simulated annealing algorithm	Ref. [26]
Ref. [27]	Linear N = 10	Aperture antennas	Logarithmic and Hamming	f0 = 10 GHz Δfn = 50 KHz.	20–80 km	θ0 = 20° 50 km	Yes	Genetic algorithm	0.015 m
Ref. [21]	Linear N = 20	Isotropic	Hamming	f0 = 10 GHz	300–600 km	θ0 = 0° 450 km	No	PSO	λ/2 = 0.015 m
Ref. [28]	Linear N = 16	Isotropic	Logarithmic	f0 = 10 GHz, Δfn = 30 KHz	50–100 km	θ0 = 25° 75 km θ0 = 0° 30° 82 km	No	Genetic algorithm, MUSIC algorithm
Ref. [34]	Spherical random N = 18 elements	Isotropic	Not specified	Not specified	10–1000 km	θ0 = 90° 100 km	No	Not specified	Not specified
Ref. [31]	Linear- rid N = 51	Isotropic	Random	f0= 37.5 GHz carrier Δfn = 1 MHz	Not specified	Not specified	No	BP-based 3D imaging algorithm	4 m
Ref. [39]	Linear N = 7 and 35	Isotropic	Not specified	f0 = 10 GHz Δfn = 4 KHz	15–45 km	θ0 = 20° 30 km θ0 = 0° 30 km	No	PSO algorithm	λ/2
Ref. [40]	Linear N = 23, 101	Isotropic	Not specified	f0 = 3 GHz Δfn = Not specified	0–20 km	θ0 = 0° 10 km	No	Artificial bee colony (ABC) optimizer	λ/2
Ref. [23]	Linear N = 8	Isotropic	Hamming	f0 = 10 GHz Δfn = 10 KHz	15–45 km	θ0 = 0° 30 km	No	PSO Algorithm	λ/2
Ref. [22]	Linear N = 5	Isotropic	Hamming	f0 = 1 GHz Δfn = 1 kHz, 10 MHz, 200 MHz	0–100 km	θ0 = 0° 60 km	No	CLEAN algorithm	λ/2
This work	Non-uniform linear N= 6, 9 and 12	Elliptic patch	Random	f0 = 3.5 GHz	0–50 km	θ0 = 0° 25 km	Yes	PSO	Non-uniform

compares the most representative works in this field. Most of these works present FDAs with linear topologies and isotropic antennas. The frequency offsets are Hamming, logarithmic, and random distributions. The main difference concerning this work is the combination of random frequency offsets and non-uniform antenna locations, the 5G frequency band, and the use of elliptic patch antennas mounted on real drones.

5. Conclusions

This paper has presented virtual antenna arrays with frequency diversity in the context of 5G communications at 3.5 GHz. We studied the performance of virtual arrays with random frequency offsets and non-uniform locations of the nodes. This combination of variables obtained better results in the radiation patterns than the traditional schemes of Hamming distributions with uniform antenna locations. The results demonstrate that these arrays can form a radar system with a FANET to detect objects from the sky. Future works will focus on validating the findings of this study with experimental tests.