Performance Analysis of Minimum Hop Count-Based Routing Techniques in Millimeter Wave Networks: A Stochastic Geometry Approach

Operating beyond-5G networks at the millimeter wave (mmWave) band imposes technological challenges while offering great opportunities. The nature of millimeter waves renders the communication quality susceptible due to blockage caused by obstacles. Hence, multi-hop relaying is likely to play a significant role in improving the performance of mmWave networks. In this paper, we investigate the performance of two appropriate routing techniques for mmWave networks, namely minimum hop count (MHC) and nearest LoS relay to the destination with MHC (NLR-MHC). Analytical models are provided to evaluate the performance of the two routing techniques using tools from stochastic geometry. We model the distribution of hop count using phase-type distribution, and then we use this distribution to derive analytical results for the coverage probability and spectral efficiency. Results reveal the significant impact of densities of relays and blockages on the performance of the aforementioned routing techniques in-terms of spectral efficiency, connectivity probability, and average hop count. It is also demonstrated that NLR-MHC achieves a superior coverage probability and spectral efficiency compared to MHC. However, MHC provides better performance in-terms of connectivity probability and average hop count.