## 2 Substrate-Integrated Waveguide Leaky-Wave Antenna Design  
The proposed periodic leaky-wave antenna design based on a substrate-integrated waveguide consists of a repetition of 12 unit cells. The design was conceived employing the 3D full wave electromagnetic simulation tool HFSS (High Frequency Structure Simulator; Ansys, Canonsburg, PA, USA), which is based on the finite element method (FEM). The chosen PCB material was Rogers RT/duroid 5880 (Rogers Corporation, Chandler, AZ, USA) because of its low dissipation factor of 0.0009 at 10 GHz. In order to reduce dielectric losses, a thin laminate with a thickness of 0.254 mm was used, which also represents the height of the SIW [17]. The SIW is designed for a lower cutoff frequency of 40 GHz to allow single mode operation up to 80 GHz with a linear dispersion slope in the frequency range of interest between 50 and 70 GHz [16; 18]. Based on the permittivity of the employed laminate of 2.2, this results in a width \(W\) of 2.6 mm between the via post walls. The via holes have a 0.15 mm diameter and are arrayed with a pitch \(P\) of 0.3 mm. In each unit cell, a 180 \(\upmu\)m wide longitudinal microstrip line is inset in the SIW, as depicted in Figure 1. The microstrip lines act as the radiating elements. Their length \(L\) = 1.67 mm corresponds to the guided wavelength at 61.3 GHz, which is the designed broadside frequency in the center of the 57-66 GHz band. The rectangular slots forming the microstrip lines extend up to the via post walls. The utilization of longitudinal microstrips inset in the SIW is a complementary approach to transversal slot SIW LWAs, which have already been shown, e.g., in [14]. This SIW LWA approach allows for the manipulation of the symmetry of the unit cell, which is a fundamental property for LWAs, in the longitudinal as well as the transversal axis [15]. Here, the microstrip lines are off-centered by 40 \(\upmu\)m in the x-direction, as can be seen in the inset of Figure 1. Due to this asymmetry, the open-stopband is decreased and broadside radiation is increased [15]. For investigating the operational bandwidth and the beam steering behavior of the SIW LWA, Eigenmode simulations were carried out to study the natural resonances of the examined structure. When applied to the SIW LWA unit cell, Eigenmode simulations reveal the waveguide modes with their corresponding Eigenfrequencies [19]. To take into account that, in the LWA, the wave propagates through consecutive unit cells, periodic boundaries are defined at both ends of the unit cell. This allows to enforce a phase difference between the unit cells, which basically relates to the phase taper of an antenna array. The normalized phase difference between two consecutive unit cells is shown in the dispersion diagram in Figure 2. It can be observed, that the Eigenfrequencies change based on the enforced phase difference. Thus, at different frequencies, the phase difference between the radiating elements and consequently the beam angle changes and frequency based beam steering is obtained. In this regard, periodic LWAs have the property to radiate in the left-handed (LH) region, where \(\beta\) is negative, and in the right-handed (RH) region, where \(\beta\) is positive. Thus, for decreasing frequencies in the LH region, the beam is steered towards backfire, and for increasing frequencies in the RH region towards endfire [13]. At the transit from the LH to the RH region, broadside radiation is obtained, which is at 61.3 GHz for this design. The frequency difference between the LH and RH mode at 0\({}^{\circ}\) phase difference is the open-stopband, which generally causes degraded radiation at broadside [13]. Figure 1: Top view of the proposed periodic substrate-integrated waveguide (SIW) leaky-wave antenna (LWA) design based on a printed circuit board (PCB) with top metallization (blue) and dielectric (green), where \(W\) denotes the 2.6 mm width of the SIW, \(P\) the 0.3 mm pitch of the via holes (yellow) with 0.15 mm diameter and \(D\) the 3.9 mm periodicity of the array.