# A Symbolic Encapsulation Point as Tool for 5G Wideband Channel Cross-Layer Modeling
Third, analytical expressions for LCR and AFD are often complex, comprising integral functions that diverge [8] and are consequently, computationally intensive. Assuming some typical 5G propagation scenarios (Figure 1), as for contributions of this work, we bring: (i) an additional tool for encapsulating different mobile general channel 5G modeling approaches; (ii) wideband extension of LCR and AFD evaluation for optimal radio resource allocation modeling; and (iii) lower computational complexity and simulation time reduction related to scenario-specific 5G channel models. We begin with [PERSON]'s deterministic model for the narrowband case, as adopted in [9] and then, extend it to the wideband case. The assumptions considered include: vertically polarized signal, point scatterers on the horizontal plane, and a ray tracing approach to compute the distance matrix and signal's complex envelope in each sample point of the mobile route. We discard eventual comments on model's accuracy by keeping a focus on the means to capture the signal's complex envelope and process its statistics, as an object of contribution. However, a scenario that considers multiplane propagation and objects with larger radar cross-sections could be analyzed also, by introducing the vertical axis coordinate (scatterer's height) in distance matrix computation and several point scatterers at a single position. Observations are made on small-scale routes (small area) as common ground when investigating fast fading behavior. After retrieving statistics from the sampled complex envelope, we proceed to define appropriate channel states and derive probability transition matrix as building blocks of the two-state FSMC model. That way, we enter into a more comfortable, information theory environment to estimate QoS performance [10]. Complete observation continues in the direction of unifying the models into one environment. This provides results in one place with the properties to simplify all complex calculations in two  
Figure 1: Examples of typical 5G propagation scenarios: (a) high-speed train; (b) urban vehicle-to-vehicle; (c) crossroad. directions. The first direction is to provide all observations in closed-form expressions. Such expressions are further simplified and manipulated, and this provides a better insight into the observed problem that is being solved. The second direction is to obtain numerical values that give all the characteristics of the process or system. These results are shown in one place. The rest of the paper is organized as follows: in Section 2, we give a short review of related work on second-order statistics application and analysis and achievements in 5G channel modeling, relying on two robust surveys. Section 3 provides the roadmap from the viewpoint of encapsulation and integration of symbolic and numerical analysis. In Section 4, starting from [PERSON]'s well-known deterministic model in the Rayleigh channel, we describe a modeling tool for small areas and steps to capture a complex envelope and evaluate its statistics. Hereafter, we continue with FSMC formulation, correlated to these statistics and in Section 5, we put our simulation setup observing three specific 5G scenarios, transmission schemes, and corresponding measurements in physical resource blocks (PRB). Finally, in Section 6, we take some conclusions on the use of second-order statistics in 5G networks as metadata for higher layer modeling and optimal radio resource allocation.