Wireless Communications and Mobile Computing

Volume 2017 (2017), Article ID 2475439, 13 pages

https://doi.org/10.1155/2017/2475439

## Parameter Estimation for the Field Strength of Radio Environment Maps

School of Computer and Software Engineering, Xihua University, Chengdu 610039, China

Correspondence should be addressed to Zhisheng Gao

Received 21 July 2017; Revised 13 October 2017; Accepted 1 November 2017; Published 29 November 2017

Academic Editor: Gianluigi Ferrari

Copyright © 2017 Zhisheng Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The parameters of a radio environment map play an important role in radio management and cognitive radio. In this paper, a method for estimating the parameters of the radio environment map based on the sensing data of monitoring nodes is presented. According to the principles of radio transmission signal intensity losses, a theoretical variogram model based on a propagation model is proposed, and the improved theoretical variation function is more in line with the attenuation of radio signal propagation. Furthermore, a weight variogram fitting method is proposed based on the characteristics of field strength parameter estimation. In contrast to the traditional method, this method is more closely related to the physical characteristics of the electromagnetic environment parameters, and the design of the variogram and fitting method is more in line with the spatial distribution of electromagnetic environment parameters. Experiments on real and simulation data show that the proposed method performs better than the state-of-the-art method.

#### 1. Introduction

The radio environment map, which was first proposed by Zhao et al. [1], is mainly used in cognitive radio [2, 3]. A radio environment map is an integrated database that is used to describe the electromagnetic environment. Because of its wide range of applications for radio [4–8], it has been further extended. The radio environment map is a comprehensive database that contains many fields of information, such as the available spectrum profile, geographical features, rules, relevant laws and regulations, radio equipment situation, and expert experience [9]. The radio environment map is fundamental to the construction of a communication network, improving operation efficiency, and managing radio resources. Ojaniemi et al. [10] believe that the core content of the radio environment map is the field strength estimation, so accurately estimating the field strength of the radio signal in the geospatial space with a certain granularity is key. Pesko et al. [11] called this problem the construction of the radio frequency layer. In this paper, we call it radio environment map parameter estimation. This problem, especially since 2012, has been increasingly studied in depth [11–15].

Methods for estimating the parameters of the radio environment map can be divided into three categories [11]. The first are based on direct spatial interpolation, the second are based on the propagation model, and the third are the hybrid combinations of the first two methods. Propagation-based methods require a large amount of information, including the signal transmission source, latitude and longitude coordinates, antenna height, transmitting power, and even geographical information and climate information on the propagation path, which greatly limits the scope of application of this method. At the same time, because most propagation models are empirical models based on radio transmission, their universality is not strong. Ojaniemi et al. [10] showed that, under certain conditions, this method has lower prediction accuracy than spatial interpolation methods.

In recent years, the focus of research on radio environment map parameter estimation has transferred to spatial interpolation-based methods, especially methods based on geostatistics. In this kind of method, the measured values of ground truth are obtained by radio monitoring sensors, and then the spatial environment parameters of the remaining locations are obtained using spatial interpolation estimation. Comparative studies of spatial interpolation methods were made in [15–17]. Comparative studies of the inverse distance weighted (IDW) method, Spline interpolation method, and Kriging interpolation method were presented in [15, 16, 18], and the IDW, gradient plus inverse distance squared (GIDS), and Kriging methods were compared in [17]. Prediction experiments on indoor and outdoor electromagnetic environments showed that the IDW method is more robust, while the Kriging method is the most accurate method. Reference [19] presented an approach that uses the spatial dependence of ground truth data and constructs the signal intensity map using Kriging. In [20], several spatial interpolation methods based on IDW were analyzed and used to estimate the spatial distribution of radio field strength. Reference [21] proposed a geostatistical method for the radio environment map and through an actual case study demonstrated that the method is superior to the method based on path loss model and data fitting. At the same time, this kind of method relies on the data collected by the monitoring sensor, so the distribution and quantity of the monitoring sensors affect the predication accuracy of the radio environment map parameters. In [22], the relationship between the number of sensors and construction error of the radio environment map is analyzed in detail.

Existing studies show that the Kriging method is the best way to estimate the parameters of the radio environment map. However, the radio transmission process is affected by various factors such as the number of transmitting stations, geographical environment, and weather. In practice, the number of monitoring sensors is limited, so the data sampling points are sparsely distributed, which increases the difficulty of estimating the parameter space distribution. At the same time, because the Kriging algorithm is based on a variogram, its linear quadratic optimization is based on the assumption that the data set conforms to the normal distribution and meets the second-order stationary hypothesis or quasi-second-order stationary assumption. Therefore, a nonnormal distribution will affect the stability of the data and cause the variogram to produce a proportional effect. That is, it will improve the sill and nugget values and increase the estimation error [23]. To solve this problem, we propose a method to estimate the parameters of the radio environment map based on the radio propagation model and the Kriging method. This method retains the advantages of both the propagation model and the Kriging method and hence obtains better parameter space prediction precision than the single method. The main contributions of this paper are as follows: Using the radio propagation model to improve the variogram of the Kriging algorithm, a new theoretical variogram model for radio environment map parameter estimation is proposed. Based on the characteristics of radio signal propagation and data acquisition, a weighted optimization of the variogram is proposed, and particle swarm optimization (PSO) is applied to fit the modified variogram. The modified Kriging algorithm can hence be better adapted to the spatial distribution of the radio environment parameters.

The rest of the paper is organized as follows. Section 2 describes the related research on interpolation-based prediction of the radio environment. Section 3 introduces the improved Kriging method based on the electromagnetic propagation model and PSO-based weighting variogram fitting. Section 4 presents the results of some comparative experiments on real and simulation data to examine the effectiveness of the proposed method. Finally, Section 5 concludes this work.

#### 2. Related Works

The IDW has been considered for radio environment map parameter space estimation in many studies [14–18, 20, 21, 24]. The estimated value of the forecast point parameter can be calculated by the weighted sum of the actual observation values of nearby observation points. This method considers that the contributions of the observation points closer to the prediction point are greater; otherwise, the contribution is smaller, which can be expressed as follows:where is a sampled value of the actual parameter at the th observation point, is the Euclidean distance between the th observation point and the predicted point, and is a strength parameter that defines the decrease in weight as the distance increases. When equals one, the method is called IDW, and when it equals two, the method is called the inverse distance squared weight.

Spline interpolation is another widely used method for estimating the parameters of the radio environment map [16, 20, 25]. In these methods, the Spline is generated using the actual measured values of all observation points to guarantee global smoothness, and then the parameter values of the predicted points are calculated using polynomial fitting.

The Kriging method is a method based on the spatial analysis of a variogram, which is an unbiased optimal estimation of regionalized variables over a finite area, and is considered to be the best method for estimating the parameters of the radio environment map [11–13, 13–21]. The Kriging method is divided into ordinary Kriging and universal Kriging depending on the existence of space field drift. Ordinary Kriging is more commonly used than universal Kriging [11]. The following is a description of the ordinary Kriging method.

For regionalized variable , the sample values for a series of observation points are , . Then, the estimated value of grid point in a region can be estimated by a linear combination; that is,where is the th weighting coefficient. According to the principle of optimal unbiased estimation, the value of should satisfy the following conditions:where is the real sample value. Assuming that satisfies the intrinsic hypothesis, then according to the Lagrange theorem, the ordinary Kriging equations can be expressed as follows:where is the value of the variogram between sampling points and and is the Lagrange constant. Weighting coefficient can be calculated by (4). When is substituted into (2), the estimation value of grid point can be obtained.

The process of solving shows that the key of Kriging interpolation is how to obtain the best estimate of variogram .

#### 3. Proposed Method

##### 3.1. Improved Variogram for Parameter Estimation of Radio Environment Map

In geostatistics, a variogram is a tool used to study the autocorrelation structure of regionalized variables. The value of a variogram function is only related to the distance between two regionalized variables. Larger values of the variogram indicate smaller autocorrelation. The variogram function is defined as follows [10]:where is the number of pairs of observation data points with lag distance , is the value of the regionalized variable at position , and is the value of the regionalized variable at a distance from . When the data distribution is relatively uniform, the basic lag distance can be equal to or slightly larger than the minimum distance between the observed data points. Alternatively, the basic lag distance can be obtained by comparing and analyzing the variability and stability of the experimental variogram of several candidate basic lag distances.

In practice, the most important parameter of the radio environment map is the signal radiation level in units of decibels (). If the Kriging algorithm is used directly, the expression of can be simply obtained by (5) in units of . However, this is not consistent with the units of propagation loss that are calculated by the radio propagation model. Hence, the variogram is not dimensionally consistent with the propagation model. We believe that the transmission loss of the propagation model represents the correlation between the two radio environment parameters. Therefore, to combine the variogram with the propagation model, the definition of the variation function used in traditional geostatistics is modified as follows:The newly defined variogram is called the parameter estimation variogram of the radio environment map, and the dimensions of the value calculated by the new variogram are consistent with the dimensions of the transmission loss obtained by the propagation model.

##### 3.2. Theoretical Variogram Model Based on Propagation Model

It is necessary to use the theoretical variogram model to fit the actual variogram. The commonly used theoretical models for a variogram are the Gaussian, exponential, and spherical models. In practice, the most commonly used model is the spherical model proposed by Pesko et al. [11].

In this paper, two new theoretical variogram models are proposed based on the Longley–Rice model: one uses the Longley–Rice to model the theoretical variogram directly, and the other introduces free space transmission loss into the first model. The Longley–Rice model, also called the irregular terrain model [7], is mainly used to predict the median path loss over irregular terrain. The median value of the propagation loss in free space for different path lengths is calculated as follows:where is the visual distance spread, is the diffraction propagation distance, and is the scattering propagation distance. In addition, , , and are propagation losses for sight, diffraction, and scattering in free space, respectively, and are propagation loss coefficients, and and are loss coefficients for diffraction and scattering, respectively. If the influence of the free space transmission loss is not taken into account, the loss on the whole transmission path can be expressed by (7).

In this paper, the loss prediction function of visual distance spread is used, and hence the propagation loss can be expressed as follows:where all other variables are defined as in (7).

For given parameters such as the heights of the transmitting and receiving antennae, the value of this function is only related to distance . Hence, the loss prediction can be rewritten as follows:where is the distance of two data points and is a very small constant, which prevents division by zero. Note that, in practice, the two data sampling points may be in the same coordinate position, and is equal to 0 in this case. Coefficients , , and are coefficients to be determined. The value of is set to 14,000, which is used to simulate the distance of sight.

If the effect of free space propagation loss is taken into account, the overall loss across the propagation path iswhere is the loss of free space propagation, is the propagation distance, and is the emissive frequency. According to the same ideas above, (11) can be rewritten as where is a coefficient to be determined and the other variables are defined as in (9).

Equations (9) and (11) are the two theoretical variogram models proposed in this paper. The new models are more consistent with the parameter change behaviors in the radio environment map and more accurately reflect the relationship between parameter space changes.

##### 3.3. Weighted Fitting Algorithm for the Theoretical Variogram

Using the ground truth data, the theoretical variogram is fitted and the undetermined coefficients in the model are obtained. In traditional methods, the least-squares method is mainly used to fit the function. Its fitness function iswhere is the fitness function value of the th variable, is the th lag of the th variable, is the estimated value of variogram at position , and is the real value of the variogram at position . The disadvantage of this method is that it considers the contribution of all data to be equal without considering outliers and specific data points as well as the specificity of the radio environment parameters.

In practice, because of building occlusion and the effects of an uneven distribution of sampling nodes, abnormal noise exists. To overcome this problem, the method proposed in this paper increases the corresponding weight coefficient of the fitness function to strengthen or reduce some environmental factors or meet the distribution characteristics of the variogram. To address the problem of uneven sampling point distributions of the radio environment parameters, the first weight coefficient is introduced, where is the number of sample point pairs that correspond to a certain lag distance and is the total number of sample point pairs. The second weight addresses the inconsistencies and inaccuracies in the sampled point data, which is caused by the electromagnetic shadowing of buildings and reflections, multipaths, and radio propagation diffraction. For example, there could be some abnormally large or unusually small sampled values. To reduce the impacts of unreasonable sample points on the fitness function, the weight coefficient is , where is the mean value of the variogram and is the value of the variogram at lag distance . The third weight is added because point pairs with smaller lag distances often better reflect the degree of variability of regionalized variables. To increase the contribution of data point pairs with small lag distances, the proposed method adds weight coefficient , where is the mean value of the lag distance and is the corresponding lag distance.

The final weight coefficient is the product . Then, can be computed byHence, a new fitness function is obtained, expressed as follows: For the fitness function defined by (14), the PSO algorithm is used to fit the weighted variogram. In the particle swarm, the position of the* i*th particle can be expressed as , where is the dimension of the solution space and is the number of particles. The previous most optimal position of the th particle is denoted as and the optimal position of the swarm is denoted as . Each particle has a moving speed, and the moving speed of the th particle is . At each iteration, the particle velocity and position changes are updated by the following equation:where is the number of iterations and* C*_{1} and* C*_{2} are learning factors (or acceleration coefficients) that determine the learning ability of each iteration of the algorithm.

##### 3.4. Radio Environment Map Field Strength Estimation Algorithm

In this paper, an improved Kriging estimation algorithm for radio environment map parameters is proposed using the new variogram in (6) and the modified theoretical variogram model in (9) and (11). The algorithm includes the following main steps: (i) calculating the value of the variogram by sampling data; (ii) fitting the theoretical variogram curve equation using PSO; and (iii) calculating the test weight parameters using the theoretical variogram curve equation. The complete process is shown in Algorithm 1. The inputs of the algorithm are sample point coordinates and , sampling value , and coordinates of the point to be estimated. The output of the algorithm is the estimated value . In the algorithm, is the basic lag distance, is the maximum multiple of the lag distance, and matrix vectors , , and are expressed, respectively, as follows:where is the value of the variogram between sampling points and and is the Lagrange constant.