# Evolutionary Game for Content Cache in a mm-Wave-Based Vehicular Fog
## 2 Related Works
### mm-Wave V2X Communications  
The V2X channel model was explored by many researchers. [PERSON] et al. [39] reviewed the state-of-the-art in measurements related to mm-Wave vehicular channels. [PERSON] et al. [40] and [PERSON] et al. [41] proposed channel propagation statistic models for mm-Wave V2X communications using ray-tracing simulations, which include the effects of link blockage, scattering and multipath fading. [PERSON] et al. introduce propagation characteristics of V2V channels, particularly for shadowing effects induced by obstructing vehicles between a transmitter and receiver [42]. In [43; 44], [PERSON] et al. proposed a geometric multiple-input multiple-output (MIMO) channel model for mm-Wave mobile-to-mobile (M2M) applications based on the two-ring reference model. [PERSON] et al. [45] validated the channel model that the 3 GPP has proposed for NR-V2X systems. [PERSON] et al. [46] also validated a vehicle-to-infrastructure (V2I) channel model given by 3 GPP using ray-tracing simulator with 3D environment by OpenStreetMap. The stochastic geometry model for the V2X has been established by many researchers in order to find optimal solutions for the connectivity and throughput under varying blockage, beam direction and vehicle density. [PERSON] et al. [47] proposed a stochastic model of mm-Wave-based V2I, where the blockage probability and throughput were investigated with varying vehicle densities and speeds at a multi-lane highway. [PERSON] et al. [48] presented a theoretical analysis of the Doppler power spectrum in the presence of beamforming at the transmitter and/or the receiver in V2I systems. [PERSON] et al. [49] analyzed the coverage of urban mm-Wave micro-cellular networks based on stochastic geometry with a LOS probability function of randomly oriented buildings for a V2I scenario. [PERSON] et al. [50] proposed an effective spatial framework for mm-Wave V2X in vehicular platoon systems based on stochastic geometry approaches.  
Beam alignment is critical for the mm-Wave communications, especially for the V2V communication as the vehicles move fast. For this, several studies utilize an out-of-band channel or sensors such as radars, GPS, camera, etc. [PERSON] et al. [51] and [PERSON] et al. [52] performed the beam alignment in a V2I using information from the IEEE 802.11 ad module or the LRR radar signal. [PERSON] et al. [53] proposed to use sensors or DSRC for a high-level solution for mm-Wave communication link configuration that can reduce the mm-Wave beam training overhead. [PERSON] et al. [54] leveraged vehicle sensory data of position and the motion for beam-forming by DSRC beacons.  
For the beam scheduling, [PERSON] et al. analyzed the interplay between the beamwidth assignment and the scheduling period in V2V communications [55] and proposed an optimization algorithm to establish a V2V link having optimal beam-width, using swarm intelligence based on the channel and queue state information [56]. [PERSON] et al. [57] proposed a swarm intelligence to efficiently pair vehicles of V2V links and optimize beam widths considering the channel state information and queue state information.  
Several V2X testbed for the mm-Wave communication were built for preliminary study. [PERSON] et al. [58] developed a practical mm-Wave vehicular testbed to evaluate performance, where a fixed beam-steering approach enabled the RSUs to transmit large amounts of data in a considerably short amount of time for a wide range of speeds. [PERSON] et al. [59] investigated mm-Wave blockage characteristics based on measurements collected in a typical V2V environment at 28 GHz. [PERSON] [60] established a V2V testbed using mm-Wave-based IEEE 802.11 ad WiGig and evaluated link connectivity in the driving situation. Several practical works about mm-Wave-based UAV communications and user equipment were introduced [61; 62].