# Context-Aware Beam Selection for IRS-Assisted mmWave V2I Communications
## 3 Scenario Setup and Problem Formulation  
We examine a mmWave small cell designed to improve throughput performance and network capacity for downlink transmission. The small cell BS under consideration is equipped with an antenna array directed along predefined orientations, though the number of radio frequency (RF) chains is fewer than the number of antennas. Each antenna may consist of multiple elements that form a beam directed towards a specific region. As described in [20], the coverage area of a beam, or beam sector, is ideally spatially separated. Given the limited RF chains, only a subset of antennas can be activated for downlink at any time. The scenario is depicted in Figure 1. The mmWave base station (mmBS), located in central London, UK, is equipped with 12 antennas oriented to ensure broad coverage. Due to a limited number of RF chains, the mmBS can activate up to four beams simultaneously, supporting a maximum of four vehicles at once. Beam coverage is determined by the vehicle's presence within a beam's geometric footprint and the achieved SNR meeting the threshold for link activation. We adopt a two-slope path loss model to distinguish line-of-sight (LOS) and non-line-of-sight (NLOS) propagation. If the estimated SNR falls below a threshold (e.g., 2 dB), coverage is not considered valid. The data rate is modeled as a constant value during beam association, consistent with baseline mmWave assumptions and to isolate the impact of connection time from PHY-layer variations. Resource utilization reflects the number of active beams simultaneously serving distinct vehicles, constrained by beamforming hardware limits (i.e., max four beams). A higher beam sojourn time implies better utilization per beam, as it reduces frequent reconfigurations and idle slots. To further enhance signal coverage and alleviate potential blockages in the urban environment, several IRS nodes are strategically deployed within the area. These IRS nodes dynamically reconfigure signal propagation paths, improving beam delivery in NLOS conditions. Note that the illustrated sector areas are approximate; actual coverage depends on the channel model, antenna configuration, and IRS-assisted reflections. This work assumes a carrier frequency of 28 GHz, which has been widely adopted in 5G NR-based mmWave V2X studies [21; 22; 23]. While traditional DSRC (Dedicated Short-Range Communications) and C-V2X (Cellular V2X) systems operate in the 5.9 GHz band, the 3 GPP n257 (26.5-29.5 GHz) is considered a promising band for ultra-high data rate and low-latency vehicular applications, particularly in urban environments with managed infrastructure and directional communication. The adjacent 26 GHz band (n258) is already approved for V2X use in Europe [22]. Field trials such as autonomous beam-steered measurement campaigns [23] further validate the viability of the 28 GHz bands for vehicular communications. Thus, we consider 28 GHz mmWave communication with its path loss model [21] expressed as:  
\[PL(d)=PL(d_{0})+10n\log_{10}(d/d_{0})+X_{g}. \tag{1}\]  
Here, \(d\) refers to the distance between the mmBS and vehicle antennas in meters while \(X_{g}\) represents the channel fading (excluded in our analysis), and \(PL(d_{0})\) denotes the free space path loss (FSPL) in decibels (dBs). The FSPL depends on the carrier frequency \(f_{c}\), and is given by \(10\log_{10}((4\pi d_{0}f_{c}/c)^{2})\), with \(d_{0}=1\) m. We assume a 5 m height difference between the BS and the vehicle, such that the 2D distance \(\hat{d}\) between two points is related to \(d\) as \(d=\sqrt{d^{2}+5^{2}}\). Assuming that vehicles have steerable beam antennas capable of tracking the BS, the signal-to-noise ratio (SNR) for a vehicle being served is given by:  
\[SNR=p_{0}-PL(d)+G_{tx}+G_{rx}-N, \tag{2}\]  
Figure 1: A scenario of a network which consists of a mmBS with 12 beam sectors and multiple IRS nodes shown on a real-world map of around Bedford Square in London.