## 2 Design Requirements  
In this section, we derive design requirements for a CA radar antenna based on the system operational requirements and ATAR specifications in DO-366. Antennas are a crucial component of any radar system, as they impact detection range and angular accuracy. As assumed in Section 1, the CA function is triggered when the U-space tactical conflict resolution service fails, and the intruder breaches the RWC protection volume, provoking a loss of well clear (LoWC). In this case, the purpose of the CA function is to prevent the intruder from entering the NMAC volume. If the intruder penetrates the NMAC, providence will act as the last barrier before a mid-air collision (MAC) occurs. In aviation, providence is defined as the conditional probability of a mid-air collision (MAC) occurring given that a near mid-air collision (NMAC) has taken place. In safety assessment, providence is usually considered as the last barrier once safety nets have failed. Both the RTCA and EUROCAE approaches use a 2000 ft radius, 500 ft height cylinder centred at the ownship as the protection volume for RWC and a 500 ft radius, 200 ft height cylinder as the near mid-air collision (NMAC) volume for CA purposes, specifically for larger intruders (General Aviation (GA) or UAM/AAM aircraft), as proposed in [12]. Furthermore, DO-396 also proposes a small UA NMAC (sNMAC), consisting of a 50 ft radius, 30 ft height cylinder centred at the ownship, according to [30]. Based on this sNMAC, DO-396 proposes a cylindrical RWC volume with a 200 ft radius and 50 ft height for sUA. Therefore, the CA radar detection range should be 2000 ft (i.e., 619 m) for GA and UAM/AAM intruders, and 200 ft (61 m) for sUA. DO-366 lists the frequency bands in which ATAR radar shall operate, specifically within the C, X, Ka, K, and Ku bands. On the other hand, the International Telecommunication Union (ITU) defines several Industrial, Scientific, and Medical (ISM) bands [31] across the electromagnetic spectrum to prevent high-power applications of electromagnetic energy, such as microwave heating or medical diathermy, from interfering with telecommunication systems. Furthermore, since these bands are unlicensed, certain telecommunication technologies, such as Bluetooth [32] and Wi-Fi [33], also make use of them. In this paper, we use the 24 GHz ISM band, which is very close to the DO-366 K band (24.45-24.65 GHz). The ITU designates this ISM band, among other uses, for radiolocation. No authorisation is required to operate in this band, and there is no power limit. The small wavelength at this frequency (around 12.5 mm) enables the design of compact, lightweight antennas that can be integrated into s UAS without compromising their airworthiness. Since this is an ISM band, a wide range of Commercial-Off-The-Shelf (COTS) components is available, enabling low-cost radar system implementations. For example, the wideband solid-state power amplifier RFLU-PA18G26 GF delivers a typical output of 54 dBm across the 18 GHz to 26.5 GHz range [34]. For the receiving chain, the ADF5904 receiver downconverter offers a noise figure of 10 dB at 24 GHz [35]. The main drawback of this frequency is its high free-space loss; however, due to the relatively short detection range, this does not compromise the feasibility of radar implementation in this band, as we prove at the end of this section. In contrast, designs at 24 GHz can be easily scaled to the DO-366 K band, if required. With regard to the radar cross-section (\(\sigma\)) of the intruder, Annex E to DO-366 [12] provides a value of 5 dBm for GA aircraft at 13 GHz, based on numerical analyses. Given that, according to [12], the radar cross-section remains nearly constant from the X to Ku bands, we assume that such targets operate in the optical region at these frequencies--i.e., \(\sigma\) is determined by the area subtended by the target at the radar location and does not depend on frequency [36]--and we use the same value in the K band.