The proposed beamforming network suitable for 5G mmWave Advanced Antenna System (AAS) should be at least 8 × 8 array supporting mmWave frequency bands allocated to 5G as defined in Section I steering ± 60° and ± 15° in horizontal and elevation planes respectively. Thus, designing an 8-element array, wideband, and wide-angle (± 60) beamformer with dual-polarization capability is a basic demanding requirement for 5G AAS. A novel Rotman lens is designed to meet the basic beamforming requirements for 5G application. The Rotman lens is modeled and optimized with Matlab. The modeled beamformer is simulated and optimized using the Ansys HFSS electromagnetic simulator package. The design procedure consists of the following steps:
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End-fire single antenna element design for dual-polarization capability.
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Lens body design and optimization for wide-angle steering (± 60).
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Beam and array ports and connected transmission line design.
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Dummy port design.
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Non-uniform array port design for SLL reduction.
Single element design
The single antenna element suitable for 5G AAS is recommended to be dual-polarized with a half-power beam width of at least 65° and in line with 3GPP mmWave frequency bands. In addition, the single element is preferred to be integrated into the beamforming network to avoid using large numbers of connectors and associated losses. Thus, an end-fire type antenna element is selected for easy integration to the beamforming network as well as its capability to use in dual-polarization configuration. As a consequence, a novel Vivaldi antenna is designed to be utilized in the AAS beamformer. The proposed antenna is fabricated on Rogers 4350B (\({\varepsilon }_{r}=3.48\)) substrate with a thickness of 0.254 mm. The design methodology, fabrication, and results are comprehensively discussed in Ref.21.
The structure of the proposed Vivaldi antenna element is presented in Fig.3. The antenna has a compact size of 12 × 5.5 × 0.254 mm3. Therefore, the space element is d = 5.5 mm if the antenna is used in the array. The proposed antenna can operate in 23–45 GHz covering 5G n257, n258, n259, n260, and n261 frequency bands and exhibit a nearly constant end-fire radiation pattern with a measured gain of more than 5dBi across the whole bandwidth21.
Fabricated Vivaldi antenna array.
Lens body design
It is intended to design a basic 8-element Rotman lens beamformer between 24 and 30 GHz covering 5G n257, n258, and n261 frequency bands for AAS applications. The Rotman lens is designed for fabrication on a dielectric substrate. The dielectric substrate used is Rogers 4350B (\({\varepsilon }_{r}=3.48\)) with a thickness of 0.254 mm. The design methodology can be presented as a step-by-step process based on the approach detailed in “Rotman lens beamformer design” section.
Determine the requirements
As indicated, the operational frequency band is between 24 and 30 GHz. The number of array elements is N = 8 and the number of beam ports is assumed to be M = 8. The steering angle to meet the AAS requirement is \({\theta }_{0}={60}^{^\circ }\) which is considered to be a wide angle. The 3dB beam width of the N-element array is:
$$M=\left[\frac{{2\theta }_{0}}{{BW}_{array}}\right]\to {BW}_{array}=\frac{120}{8}={15}^{^\circ }.$$
(13)
Considering the array beam width \(({BW}_{array}={15}^{^\circ })\), the maximum coverage angle \({\theta }_{0}={60}^{^\circ }\) can be moderated as \(\theta =60-15/2={52.5}^{^\circ }\). Thus, assuming the steering angle \(\theta ={52.5}^{^\circ }\), the 3 dB beam width of the resultant array can cover the AAS coverage requirement \({(\pm 60}^{^\circ })\).
The element spacing equal to the width of a single antenna element is d = 5.5 mm. The substrate parameters are \({\varepsilon }_{r}=3.48\) and h = 0.254 mm.
- 1.
Calculate the minimum on-axis focal length \({F}_{0}\) using Eq.(1).
$${F}_{0}\ge 2 \left(8-1\right)5.5 {\text{ sin}}{52.5}^{^\circ }=61.08\text{ mm.}$$
- 2.
Set the \({y}_{3}={y}_{3({\text{max}})}\) and \({\zeta }_{\text{max}}=0.5\) and calculate the initial parameters \(\gamma .\alpha \) using (5), and (3) respectively.
$${y}_{3({\text{max}})}=19.25\text{ mm}\stackrel{{\zeta }_{\text{max}}=0.5}{\to } \gamma =1.58\to \alpha ={30}^{^\circ }.$$
The initial \(\beta \) can be selected from Fig.2 as \(\beta =0.88\).
- 3.
Optimize the value of \(\alpha .\beta \) using (9) and (10) to obtain optimum phase and amplitude performance. In this research work, the genetic algorithm (GA) is employed for numerical optimization using Matlab. The optimized parameters are indicated as:
$$\alpha ={29.7}^{^\circ } , \beta =0.91.$$
- 4.
Specify the difference in transmission line length for the side array port compared to the center array port (W) using (7) as:
$$W=1.45\text{ mm}$$
Divide the dimensions by a factor of \(\sqrt{{\varepsilon }_{r}}\). The parameters \({F}_{0}. {F}_{1}. W\) are divided to \(\sqrt{3.66}\) as the designed dielectric constant is recommended 3.66 for Rogers 4350B22.
- 5.
The modeled body lens parameters are summarized in Table 2.
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Beam and array ports and transmission line design
The phase center location of beam ports \(({x}_{1}\cdot {y}_{1})\) can be calculated using (12a) and (12b) as:
$${x}_{1}=25.23\text{ mm }\quad {y}_{1}=14.4\text{ mm.}$$
Also, the phase center location of array ports \(({x}_{2}.{y}_{2})\) can be calculated using (11a) and (11b) as:
$${x}_{2}=0.68\text{ mm } \quad {y}_{2}=14.9\text{ mm,}$$
where the origin is the center of the array port arc. Considering the center location of the ports, the width of the lens port aperture is roughly \({W}_{p}=4.65\text{ mm}\).
The microstrip width (\({w}_{1}\)) of the feed line can be calculated as23:
$${w}_{1}=\frac{7.48\times h}{{e}^{\left({Z}_{0}\frac{\sqrt{{\varepsilon }_{r}+1.41}}{87}\right)}}-1.25\times t\approx 0.55\text{ mm,}$$
(14)
where \({Z}_{0}\) is the characteristic impedance, h, and t are the substrate and track thicknesses respectively. Considering the 50 Ω characteristic impedance and proposed substrate parameters, \({w}_{1}\approx 0.55\text{ mm}\). However, the microstrip line width is slightly optimized as \({w}_{1}=0.53\text{ mm}\) in the simulation process.
After determining the phase center location, lens port width, and feed line width, a horn with the appropriate length \({(L}_{p})\) is tapered toward the feed to overcome the impedance discontinuity problem due to connecting the large lens port width to the small feed line width.
According to Ref.24, the length of the triangular transition \({L}_{p}\) is suggested to be as follows:
$${L}_{p}\approx 4.57{W}_{p},$$
(15)
where \({W}_{p}\) is the width of the lens port aperture.
In this work, the tapering length is optimized based on a model and extracted results as shown in Fig.4 to obtain optimum matching and insertion loss. As a result, the optimized horn length is \({L}_{p}=22\text{ mm}\) where the number 4.57 in Ref.24 is adjusted as \({h}_{p}=4.73\). The schematic of the tapering transition is depicted in Fig.5.
Tapering transition modeling and simulation.
Schematic of the tapering transition.
Due to the very small distance between the ports and easy interconnection purpose, SMPM connectors are used. The impedance matching between the SMPM connector and the microstrip line is very sensitive for mmWave bands. The SMPM connectors are used for the beam ports using the transition procedure as detailed in Ref.25.
Dummy port design
In this design, we employ only a single dummy port on each side of the parallel plate contour with a wide aperture width in order to convene multiple dummy ports and simplify the structure.
The dummy ports are matched using a novel absorber sheet based termination load as described extensively in Ref.26.
The proposed high-performance and cost-effective microstrip termination load is based on the combination of a printed monopole antenna and an absorber sheet as shown in Fig.6 that can be easily integrated with a microstrip line or used with a connector as a termination load for test measurement. The results show a good impedance matching between 20 and 67 GHz that can be effectively used as loaded dummy ports for mmWave applications.
Fabricated SMPM terminator.
In this design, this termination load is integrated into the dummy ports to provide good termination and reflection-less side walls of the Rotman lens.
Once the whole Rotman lens parameters are specified, a mathematic-based geometry of the Rotman lens can be generated by Matlab as shown in Fig.7.
Rotman lens modeling and geometry.
The generated geometry can be imported to full wave simulation packages. Thus, the modeled Rotman lens geometry is imported to Ansys HFSS for simulation and further optimization.
Non-uniform array port design
The side lobe level (SLL) is a challenging parameter in the Rotman lens due to the unwanted reflections from side walls, beam and array ports, and also dummy ports19.
Chebyshev is a famous tapered distribution that can be used to set SLL to a specified value (s). In an N-element array, the peak value of the Chebyshev polynomial of the order N − 1 can be expressed as27:
$${T}_{N-1}\left({z}_{0}\right)={10}^{s/20},$$
(16)
where s is SLL in dB and \({z}_{0}\) is the main lobe position that can be calculated as:
$${z}_{0}={\text{cos}}h\left[\frac{{{\text{cos}}h}^{-1}({10}^{s/10})}{N-1}\right].$$
(17)
The half power beam width (HPBW) of the scanning array can be obtained using:
$$HPBW={\text{cos}}^{-1}\left[{\text{cos}}\theta -0.443\frac{\lambda }{L+d}\right],$$
(18)
$$-{\text{cos}}^{-1}\left[{\text{cos}}\theta +0.443\frac{\lambda }{L+d}\right],$$
where L is the array length, d is the inter-element space, and \(\theta \) is the scanning angle.
In a non-uniform array design, the SLL can be controlled by the amplitude distribution among the elements and there is a tradeoff between SLL and HPBW where by decreasing the SLL, the HPBW is decreased27,28,29.
In this research work, firstly an improved distribution scheme for the target array is achieved based on a Matlab code aiming to enhance the SLL while the HPBW is almost constant. The resultant \(SLL\approx 16\text{ dB}\) as depicted in Fig.8 and the distribution coefficient is presented in Table 3.
Comparison of SLL for uniform and non-uniform array ports.
The improved non-uniform amplitude distribution is applied to the array port by altering the port width. Assuming the relation of power and impedance22:
$$P=\frac{{V}^{2}}{2Z}.$$
(19)
The impedance of microstrip as a function of microstrip width to substrate height \(W/h\) is26:
$$Z=\frac{120\pi }{\sqrt{{\varepsilon }_{eff}}\times \left[\frac{W}{h}+1.393+\frac{2}{3}{\text{ln}}\left(\frac{W}{h}+1.444\right)\right]} \frac{W}{h}>1.$$
(20)
The following relation can be extracted for the width of the microstrip line:
$$\frac{{P}_{1}}{{P}_{2}}\approx \frac{{Z}_{2}}{{Z}_{1}}\approx \frac{\frac{{W}_{1}}{h}+1.393+\frac{2}{3}{\text{ln}}\left(\frac{{W}_{1}}{h}+1.444\right)}{\frac{{W}_{2}}{h}+1.393+\frac{2}{3}{\text{ln}}\left(\frac{{W}_{2}}{h}+1.444\right)}\approx \frac{{\text{ln}}\left(1+4\left(\frac{h}{{W}_{2}}\right)\right)}{{\text{ln}}\left(1+4\left(\frac{h}{{W}_{1}}\right)\right)}.$$
(21)
The width of the array port based on the amplitude coefficient using (21), when the center port width is 4.65 mm can be calculated as indicated in Table 3.
The new Rotman geometry including the non-uniform array ports as indicated in Table 3 is generated for further optimization by the full wave simulation. To this effect, the Rotman lens parameters, and amplitude weighting together with the position of the array ports are optimized using genetic algorithm (GA) by HFSS in terms of phase and amplitude errors and SLLs in the widest angle beam (\({52.5}^{^\circ }\)) as the worst-case for 24 GHz and 30 GHz as the start and stop operating frequencies. The optimized array ports width and corresponding distribution coefficient are shown in Table 4. The symmetrically oriented array port numbers can be found in Fig.7.
The simulated resultant radiation patterns by exciting different beam ports for uniform and improved non-uniform distribution of array ports are presented in Fig.9.
Comparison of SLL for uniform and improved non-uniform array ports.
It is clear that applying an optimized non-uniform distribution coefficient improves the SLL as well as the amplitude and phase performances. The minimum SLL for uniform distribution is around 9 dB while it is increased to around 12 dB for optimized distribution.
The structure of the final Rotman lens beamforming network with optimized parameters is shown in Fig.10. Also, Table 5 summarizes the designed and optimized Rotman lens parameters.
Proposed Rotman lens beamformer structure.
It can be concluded that the optimized values are very close to the designed values confirming a good convergence between the optimized simulation parameters and the proposed design procedure.
