High precision train positioning is a crucial component of intelligent transportation systems. Tunnels are commonly encountered in subways and mountainous regions. As part of the communication system infrastructure, Leaky CoaXial (LCX) Cable is widely equipped as antenna in tunnels with many advantages. LCX positioning holds great promise as a technology for rail applications in the upcoming B5G (beyond-5G) and 6G eras. This paper focuses on the LCX positioning methodology and proposes two novel algorithms along with a novel communication-positioning integration signal. Firstly, a novel algorithm called Multiple Slot Distinction (MSD) LCX positioning algorithm is proposed. The algorithm utilizes a generated pseudo spectrum to fully utilize the coupled signals radiated from different slots of LCX. This approach offers higher time resolution compared to traditional methods. To further improve the positioning accuracy to centimeter-level and increase the measuring frequency for fast trains, a novel communication-positioning integration signal is designed. It consists of traditional Positioning Reference Signal (PRS) and a significantly low power Fine Ranging Signal (FRS). FRS is configured to be continuous and superposed onto the cellular signal using Non-Orthogonal Multiple Access (NOMA) principle to minimize its interference to communication. A two-stage LCX positioning method is then executed: At the first stage, the closest slot between the receiver and LCX is estimated by the proposed MSD algorithm using PRS; At the second stage, centimeter-level positioning is achieved by tracking the carrier phase of the continuous FRS. This process is assisted by the closest slot estimation, which helps mitigate interference between neighboring slots and eliminate the integer ambiguities. Simulation results show our proposed LCX position methodology outperforms the existing ones and offer great potentials for future implementations.