Efficient parameter estimation of the lognormal–Rician turbulence model based on the k-nearest neighbor and data generation method

In this paper, we propose a novel, to the best of our knowledge, and efficient parameter estimator based on the k-nearest neighbor (kNN) and data generation method for the lognormal–Rician turbulence channel, which is of vital importance to the free-space optical/quantum communications. The Kolmogorov–Smirnov (KS) goodness-of-fit statistical tools are employed to investigate the validity of the kNN approximation under different channel conditions, and it is shown that the choice of k plays a significant role in the approximation accuracy. We present several numerical results to illustrate that solving the constructed objective function can provide a reasonable estimate of the actual values. The mean square error simulation results show that increasing the number of generated samples by two orders of magnitude does not lead to a significant improvement in estimation performance when solving the optimization problem by the gradient descent algorithm. However, the estimation performance under the genetic algorithm (GA) approximates to that of the saddlepoint approximation and expectation–maximization (EM) estimators. Therefore, combined with the GA, we demonstrate that the proposed estimator achieves the best trade-off between the computation complexity and the accuracy.