# Context-Aware Beam Selection for IRS-Assisted mmWave V2I Communications
## 3 Scenario Setup and Problem Formulation
where \(p_{0}\) represents the reference power which is the received power at a reference distance of \(d_{0}=1\) m. \(G_{tx}\) and \(G_{rx}\) are the transmitter and receiver antenna gains, respectively, \(N\) is the noise, including thermal noise and the receiver noise figure. As aforementioned, the deployment of mmWave small cells for V2X communication introduces a distinct challenge, as narrow beams are used. The short time a vehicle is present within a beam's coverage results in frequent handovers and increased signal overhead. In addition, due to the fluctuating nature of the channel caused by vehicle mobility, a more conservative approach-using a fixed, robust modulation scheme may be more suitable than an adaptive modulation scheme. Thus, we assume the BS uses a constant, resilient modulation scheme, regardless of the reported SNR. To maximize data transmission in downlink, the radio resource allocation strategy should prioritize vehicles that stay within the beam for the longest periods. Let \(R\) denote the fixed data rate assigned to each beam when serving a vehicle within its beam sector. Vehicles that leave the beam sector experience a zero data rate. Consider a set \(\mathcal{B}(t)\) of available beams from the mmWave small cell BS at time \(t\), where \(|\mathcal{B}(t)|\) can be at most 4, representing the maximum number of simultaneously active beams. Let \(R_{i}(t)\) denote the transmission rate of beam \(i\) at time \(t\), where \(R_{i}(t)=R\) if a vehicle is being served, and \(R_{i}(t)=0\) during handovers, when waiting data from the macro BS, or when no vehicle is within the beam's coverage. The objective of the proposed resource allocation strategy is to maximize the total data transmission across all beams over a given time period \(T\). Minimizing handovers is crucial to achieving this goal, as each handover introduces a data transmission interruption. Let \(S_{i}\) represent the number of serving vehicle switches for beam \(i\) during \(T\) and let \(T_{ij}\) denote the sojourn time of \(j\)th vehicle served by beam \(i\). By maximizing the vehicle sojourn time within a beam sector, the frequency of handovers is reduced, thereby increasing overall transmission time. Consequently, the resource allocation problem can be formulated as:  
\[\max\left(\sum_{i\in\mathcal{B}(t)}\int_{0}^{T}R_{i}(t)dt\right)\text{ or }\max\left(\sum_{i\in\mathcal{B}(t)}\sum_{j=1}^{S_{i}}T_{ij}\right). \tag{3}\]  
To maximize data transmission, the mmBS utilizes all available beams. When a vehicle receives service within a beam sector, the corresponding beam becomes unavailable for other vehicles, and the BS selects another beam from the available set to serve a new vehicle. The BS can either select a vehicle at random or prioritize the vehicle with the highest SNR. However, as we will demonstrate, the conventional strategy of selecting the vehicle with the highest SNR may not be optimal for mmWave vehicular networks due to the narrow beamwidth and frequent handovers. Given the restricted mobility of vehicles within urban street layouts, we propose leveraging vehicle mobility information as an indirect indicator of the street's topology. By constructing vehicle profiles based on their mobility patterns, this contextual information can be utilized for beam selection. Mobility data, such as vehicle orientation, position, and distance from the BS (obtained through local measurements or timing advance), can be employed to enhance the efficiency of beam assignment.