## 3 Wireless Channel Analysis
### Radio Coverage Analysis  
To cope with the handover when employing either the DAS or the LWS, it is essential to analyze the effective radio coverage. As for the LWS, the radiated power stemmed from a slot can be expressed as  
\[P=P_{0}e^{-\beta z}, \tag{1}\]  
where \(P_{0}\) is the transmit power, \(z\) means the distance from starting position of the leaky waveguide to the slot position. \(\beta\) is an attenuation constant with a low value [33]. In terms of the DAS, numerous references (e.g., [34]) state that the received power curve is divided into two regions, typically referred to as near and far region, i.e., the two-slope channel model. Two-slope channel models are typical representative of numerous empirical models based on measurements of the received signal strength, which is expressed as  
\[P=\left\{\begin{array}{ll}P_{0}e^{-\beta z},&0\leq z\leq D\\ P_{0}e^{-\alpha_{N}D}\cdot e^{-\alpha_{F}(z-D)}\,z>D\end{array}\right.. \tag{2}\]  
In the near region, the PL slope \(\alpha_{N}\) is steep, which is usually modeled as free space path loss. In the far region, the waveguide effect appears with few lower order modes and the path loss slope is reduced significantly, denoted as \(\alpha_{F}\). The break point, which is a point of transition from near to far region, can be estimated by \(D=a^{2}/\lambda\), where \(a\) is the maximum transverse dimension of the tube and \(\lambda\) is the signal wavelength in free space [34].  
Based on Equations (1) and (2), Figure 4 plots the demonstration of the handover process of both LWS and DAS between two adjacent cells. \(D_{eff-L}\) and \(D_{eff-D}\) mean the effective coverage of the LWS and DAS, respectively. The handover will occur once it satisfies the A3 judgment condition, which is usually adopted in LTE-R [35].  
\[M_{n}+Off_{n}+Oc_{n}-Hys>M_{s}+Off_{s}+Oc_{s}+Off, \tag{3}\]  
where \(M_{s}/M_{n}\) is the signal quality of source/target AAU, \(Off_{s}/Off_{n}\) is the specific frequency offset of source/target AAU, \(Oc_{s}/Oc_{n}\) is the specific offset of source/target AAU. \(Off\) is the offset parameter,  
Figure 3: The leaky waveguide system: (**a**) a schema; (**b**) the radio propagation direction.  
and \(Hys\) is the hysteresis parameter. Obviously, \(M_{s}\) and \(M_{n}\) are determined by the PL. Given that \(\beta<\alpha_{F}<\alpha_{N}\) and \(D=a^{2}/\lambda\), the \(D_{eff-L}\) and \(D_{eff-D}\) can be expressed as based on Equation (3),  
\[P_{0}e^{-\beta(z-z_{L_{0}})}+Of_{n}+Oc_{n}-Hys>P_{0}e^{-\beta(z_{L _{1}}-z)}+Of_{s}+Oc_{s}+Off, \tag{4}\] \[P_{0}e^{-\beta(z-z_{L_{0}})}+Of_{n}+Oc_{n}-Hys>P_{0}e^{-\beta(z_{L _{1}}-z)}+Of_{s}+Oc_{s}+Off. \tag{5}\]  
Based on Equations (4) and (5), the radio coverage of the DAS and LWS between two adjacent cells when processing the handover can be calculated. Obviously, \(D_{eff-L}\) is usually larger than \(D_{eff-D}\) since the received power slope of the DAS is sharper than that of the LWS. Considering that the effective radio coverage of a single AAUs is a constant, one trackside AAU connects to more antennas than that of the leaky waveguides consequently. In addition, the handover failure probability of DAS is higher than that of the LWS. On one side, it can be explained by the low received signal strength of the DAS, on the other hand, this phenomenon derives from the drastic signal variation caused by the time-varying Doppler shift. In conclusion, the LWS is a better wireless access method option compared to the DAS, except for the high expenditure cost.