## 2 Related Work  
Many researchers have endeavored to reduce the beam alignment overhead or optimize the antenna beamwidth in order to maximize the throughput in multiple antenna systems. Some researchers have focused on reducing the beam alignment overhead in mmWave communication systems [19; 20; 21; 22; 23; 24]. The authors of [19] proposed a new training algorithm that allocates more training resources to the beams with higher beamforminggain. The proposed algorithm of [19] reduces the misalignment probability and thus reduces the beam alignment overhead. The authors of [20] proposed a novel beam alignment scheme that quickly finds a strong propagation path by exploring the angle-of-arrival and angle-of-departure domains. The authors of [21] proposed a low overhead analog beam selection scheme, where they steered two different-width beams: wide beams and narrow beams. They used a convolutional long short-term memory (LSTM) network to construct a narrow beam based on the wide-beam measurements. They reduced the time overhead by reducing the number of measurements. The authors of [22] developed an optimization problem of minimizing the average beam alignment overhead in mmWave networks with a large number of mobile users, where they formulated the problem as a constrained Markov decision process (CMDP). They showed the proposed heuristic algorithm based on the age information of users as approximate to the optimal solution. The authors of [23] proposed a sensor-aided beam-tracking strategy in vehicle-to-vehicle (V2V) communications. A sensor-aided control system, which allows the vehicles to exchange dynamic pose information, tracks highly direct beams without beam alignment procedures. Hence, the proposed sensor-aided beam-tracking does not require the beam-tracking overhead. The authors of [24] proposed a motion-sensor-based beam-tracking strategy. Based on the exchange of attitude information between the transmitter and the receiver, it steers the beam in the right direction without beam searching while the receiver moves. Other researchers have focused on optimizing the beamwidth by taking into consideration the beam alignment overhead in order to maximize the throughput [17; 25; 26; 27; 28; 29; 30; 31; 32]. The authors of [17] addressed the beam alignment-throughput tradeoff and developed an optimization problem that jointly considered the problems of beamwidth selection and scheduling in a mmWave network with multiple transmitter-receiver pairs. The authors of [25] formulated an optimization problem to find the antenna beamwidth in V2I communication, taking into account the time consumption due to beam alignment. They used a recursive algorithm to solve the optimization problem. The authors of [26] formulated a distributed antenna beamwidth optimization problem in device-to-device (D2D) communication and used multi-agent deep RL in order to find the antenna beamwidth of each D2D pair. The author of [27] proposed a joint power and beamwidth optimization algorithm for a NOMA system with limited coherence time. They found the power and beamwidth that maximize the sum rate by iterating between the power allocation and the beamwidth optimization. The authors in [28] proposed a beamwidth-aware scheduling scheme for V2V communications, where the transmitter needs to transmit the same data to several neighboring vehicles at the same time by adapting the beamwidth confirmation. The authors of [29] formulated an optimization problem to jointly determine the beamwidth selection and power allocation in mmWave communication systems. They used the deep Q network (DQN) to solve the optimization problem. The authors of [30] proposed two beamwidth optimization methods to maximize the average throughput in V2V communications with inaccurate vehicular position information. The proposed beamwidth determination method improves the performance compared to the traditional beam-sweeping methods by considering localization errors in order to avoid beam misalignment.