Statistical Characteristics Of Parameters Research Articles

Nonlinear Expression of Groundwater Head Interval Based on the Perturbation Method

An investigation of a groundwater system often requires the prediction of the spatiotemporal distribution of groundwater heads, which determine the groundwater flow direction and magnitude, among other applications. How to quantify the uncertainty of groundwater flow has been an important issue of concern to hydrogeologists for more than 40 years, and many methods based on stochastic and statistical approaches have been proposed to resolve this issue, with considerable progress being made. However, the statistical characteristics of parameters (e.g., hydrogeological parameters, boundaries, and sources/sinks) are often difficult to obtain precisely in practical applications. From a perspective of the interval uncertainty of groundwater, this study proposes a nonlinear expression of the groundwater head interval (GHI) using an interval uncertainty approach to quantify the uncertainty of numerical simulations in groundwater flow. This study uses a steady-state groundwater flow example to analyze the computational effectiveness of the acquired expression of GHI. A comparison of the results with the equal interval continuous sampling method (EICSM) shows that when the changing rate (which is the ratio of the absolute change in the numerical value to the numerical value itself) of a hydrogeological parameter is no more than 0.2, the relative discrepancy of the obtained GHI in this study and EICSM is no more than 5%. When the changing rate is no more than 0.3, such a relative discrepancy can be controlled within approximately 10%. In general, the proposed method is computationally efficient and robust for quantifying GHI. Finally, the method of this study is applied successfully to a real case.

Efficient Parallel Artificial Bee Colony Algorithm for Cooperative Spectrum Sensing Optimization

In this paper, the multiuser linear cooperative spectrum sensing optimization problem in cognitive radio system where the primary user (PU) and cognitive radio (CR) employ multiple antennas is investigated. By optimizing the different weights assigned on the statistic of each CR given a targeted probability of false alarm, the cooperative spectrum sensing optimization focuses on maximizing the probability of detection. Statistical characteristics of parameters in cooperative spectrum sensing for the PU with a single antenna and the CR with multiple antennas (SPMC) system, the PU with multiple antennas and the CR with a single antenna (MPSC) system, both the PU and the CR with multiple antennas (MPMC) system as well as the PU with Alamouti coding system have been investigated. Due to the non-convex characteristic of the cooperative spectrum sensing problem, an efficient parallel artificial bee colony (PABC) method motivated by the intelligent foraging behavior of a honeybee colony is introduced to address the problem without approximations and convexity constraints. Furthermore, classical benchmark functions are presented to validate the searching ability of the proposed algorithm. Simulation results showed that the PABC shows a superior ability when applied in both the typical test functions and the cooperative spectrum sensing scenario. Also, the reliability of spectrum sensing can be significantly promoted with the use of multiple antennas and Alamouti coding.

Optimization of Multiuser MIMO Cooperative Spectrum Sensing in Cognitive Radio Networks

This paper investigates the multiuser multiple-input–multiple-output (MIMO) linear cooperative spectrum sensing optimization problem, in which the primary user (PU) and the cognitive radio (CR) are equipped with multiple antennas. By optimizing the different weights assigned on the received signals of CRs, the cooperative spectrum sensing optimization aims at maximizing the probability of detection given a targeted probability of false alarm. Statistical characteristics of parameters in MIMO cooperative spectrum sensing systems have been determined for the PU with a single antenna and the CR with multiple antennas, the PU with multiple antennas and the CR with a single antenna, and both the PU and the CR with multiple antennas. Because of the non-convex characteristic of the optimization problem, an alternative approach based on a genetic algorithm (GA) instead of convex approaches is proposed to find the optimal weight vectors without solution domain restrictions and convexity constraints. Furthermore, several classical GA crossover operators have been provided to investigate their effect on sensing performance. The simulation results show that, the reliability of spectrum sensing in cooperative spectrum sensing system can be significantly improved with multiple antennas. Furthermore, the GA method is a promising approach in addressing the cooperative spectrum sensing problem.