An Efficient Approximation for Nakagami-mQuantile Function Based on Generalized Opposition-Based Quantum Salp Swarm Algorithm

With the further research in communication systems, especially in wireless communication systems, a statistical model called Nakagami-m distribution appears to have better performance than other distributions, including Rice and Rayleigh, in explaining received faded envelopes. Therefore, the Nakagami-m quantile function plays an important role in numerical calculations and theoretical analyses for wireless communication systems. However, it is quite difficult to operate numerical calculations and theoretical analyses because Nakagami-m quantile function has no exact closed-form expression. In order to obtain the closed-form expression that is able to fit the curve of Nakagami-m quantile function as well as possible, we adopt the method of curve fitting in this paper. An efficient expression for approximating the Nakagami-m quantile function is proposed first and then a novel heuristic optimization algorithm—generalized opposition-based quantum salp swarm algorithm (GO-QSSA)—which contains quantum computation, intelligence inspired by salp swarm and generalized opposition-based learning strategy in quantum space, to compute the coefficients of the proposed expression. Meanwhile, we compare GO-QSSA with three swarm intelligence algorithms: artificial bee colony algorithm (ABC), particle swarm optimization algorithm (PSO), and salp swarm algorithm (SSA). The comparing simulation results reveal that GO-QSSA owns faster convergence speed than PSO, ABC, and SSA. Moreover, GO-QSSA is capable of computing more accurately than traditional algorithms. In addition, the simulation results show that compared with existing curve-fitting-based methods, the proposed expression decreases the fitting error by roughly one order of magnitude in most cases and even higher in some cases. Our approximation is proved to be simple and efficient.