# Second-Order Statistical Properties of Vehicle-to-Vehicle Rician Fading Channel
## 1 Introduction  
Vehicle-to-vehicle (V2V) communication is a critical component of emerging intelligent transportation systems, enabling safety-critical applications such as collision avoidance and traffic optimization, and their communication network failure has the potential to cause fatal injuries [1]. However, the vehicular channel is subject to rapid and severe fading due to the high mobility of the nodes, the dynamic scattering environment, and intermittent obstructions, a phenomenon termed time-variant fading [2]. An accurate modeling of these time-varying channel characteristics is essential for the design of reliable V2V communication systems. The level crossing rate (LCR) and average fade duration (AFD) are two important second-order statistical properties that quantify the time-variant nature of the channel. The LCR represents the rate at which the signal envelope crosses a specified threshold in the positive direction. The AFD measures the average time duration for which the signal level remains below a specified threshold [3]. Modeling V2V channels is challenging and requires complex models for high mobility and varying environments [4]. This is necessary because the V2V channels exhibit dynamic and complex characteristics due to the changing nature of the environment, vehicular velocities, antenna heights, sizes of surrounding vehicles, and roadside obstacles [5]. These factors result in rapid fluctuations in signal strength and short stationary intervals, posing significant challenges for V2V channel modeling. The literature on V2V channel modeling shows a variety of approaches, with recent research focusing on two main techniques:non-regular shape geometric-based stochastic channel modeling (NS-GBSM) and regular shape geometric-based stochastic channel modeling (RS-GBSM) techniques. The NS GBSM approach provides higher accuracy in modeling complex V2V environments by accounting for the irregularities and dynamic changes in the propagation environment [6]. On the other hand, the RS-GBSM models, though simpler and mathematically tractable [7], offer accuracy and ease of use, making them more suitable for theoretical analysis and preliminary simulations, and they have been widely adopted. RS-GBSMs assume that the scattering objects in the environment are arranged in a regular geometric pattern, such as rings, spheres, ellipses, or a combination of both, and the channel statistics are derived from the resulting geometry. The RS-GBSM has been extensively used in the literature for modeling narrow-band V2V channels [8; 9; 10]. In this study, the design and implementation of the RS-GBSM consider the different V2V classification scenarios, which include carrier frequencies, frequency selectivity, channel statistics, Tx/Rx antenna environments, and direction of motion according to the IEEE 802.11p standard. The Tx-Rx separation distance (d) scenarios can thus be classified as a large spatial scale (LSS, d \(>\) 1000 m), medium spatial scale (MSS, 1000 m \(\leq\) d \(\leq\) 300 m), and small spatial scale (SSS, d \(<\) 300 m), and has been importantly captured in the model. The advantages offered by RS-GBSM techniques have gained significant attention, with a strong focus on investigating first-order statistical properties, such as correlation function (CF) and power spectral density (PSD). However, second-order channel statistics are also of immense importance, as they provide valuable insights into the degree of channel variations, the probability of deep fading, and the duration the channel is likely to remain in a fade. Despite this, limited research exists in the literature on LCR and AFD for RS-GBSMs, and only a few studies have investigated these second-order statistics in the context of V2V flat fading channels with respect to the influence and impact of several key parameters, including vehicle traffic density (VTD) and Tx-Rx separation distance (d) [11; 12; 13; 14; 15]. In [11], [PERSON] investigated LCR and AFD in Rayleigh fading channels under LSS. However, refs.