LAUSR

In this work, the performance evaluation and the optimization of dual-hop LoRa network are investigated. In particular, the coverage probability (Pcov) of edge end-devices (EDs) is computed in closed-form expressions under various fading channels, i.e., Nakagami- $m$ and Rayleigh fading. The Pcov under Nakagami- $m$ fading is computed in the approximated closed-form expressions; the Pcov under Rayleigh fading, on the other hand, is calculated in the exact closed-form expressions. In addition, we also investigate the impact of different kinds of interference on the performance of the Pcov, i.e., intra-SF interference, inter-SF interference (or capture effect) and both intra- and inter-SF interference. Our findings show that the impact of imperfect orthogonality is not non-negligible, along with the intra-SF interference. Moreover, based on the proposed mathematical framework, we formulate an optimization problem, which finds the optimal location of the relay to maximize the coverage probability. Since it is a mixed integer program with a non-convex objective function, we decompose the original problem with discrete optimization variables into sub-problems with a convex feasible set. After that, each sub-problem is effectively solved by utilizing the gradient descent approach. Monte Carlo simulations are supplied to verify the correctness of our mathematical framework. In addition, the results manifest that our proposed optimization algorithm converges rapidly, and the coverage probability is significantly improved when the location of relay is optimized.