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.
The radio environment map, which was first proposed by Zhao et al. [
Methods for estimating the parameters of the radio environment map can be divided into three categories [
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 [
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 [
The rest of the paper is organized as follows. Section
The IDW has been considered for radio environment map parameter space estimation in many studies [
Spline interpolation is another widely used method for estimating the parameters of the radio environment map [
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 [
For regionalized variable
The process of solving
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 [
In practice, the most important parameter of the radio environment map is the signal radiation level in units of decibels (
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. [
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 [
In this paper, the loss prediction function of visual distance spread is used, and hence the propagation loss can be expressed as follows:
For given parameters such as the heights of the transmitting and receiving antennae, the value of this function is only related to distance
If the effect of free space propagation loss is taken into account, the overall loss across the propagation path is
Equations (
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 is
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
The final weight coefficient is the product
In this paper, an improved Kriging estimation algorithm for radio environment map parameters is proposed using the new variogram in (
for SEL = (LAGS == end for
The PSO algorithm is used to fit the theoretical variogram models Equations (
better than
and (
In this paper, the proposed algorithm was compared with three kinds of mainstream algorithms, which are IDW [
Five kinds of objective evaluation indexes are used to compare and analyze the estimation results of the various algorithms for the parameters of radio environment map, which are the maximum error (MAX_ERR), the average error (AVE_ERR), the average estimation error percentage (PAEE), the relative mean square error (RMSE), and the root mean square error (RMSPE).
Two sets of data are used to validate all these methods. One is real measured level data of FM radio FM 99.8 MHz and the max level data of bands 87–108 MHz and 1800–1900 MHz. The measuring terminal is a vehicle radio monitoring receiver, and the measurement location is located in Chengdu. The distribution of the sampling points was shown in Figure
Parameters for real measured data.
Measurement area |
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Radio type | FM radio band |
Broadcast | 99.8 MHz, 87–108 MHz |
Number of sources | 1 or |
The average vehicle speed | About 80 Km/h |
Parameters for simulation data.
Calculated area |
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Numbers of points | 1024 |
Carrier frequency | 101.7 MHz |
Path loss model | Free space model |
Shadow model | Log normal model |
Data sampling position distribution map.
The real data set contains a total of 256 sampling points, and the simulation data set contains 1024 level data with range of 100 square kilometers. In order to compare and analyze the estimation results of different algorithms at different sampling granularities, we used 1/2 and 1/4 of the total data as the training data and the remaining data as the validation data. That is, when we used 1/4 data as the training data, the remaining 3/4 data was the validation test data.
Estimation results of level values for 99.8 MHz (1/2 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 19.6973 | 6.3338 | 7.9729 | 0.5122 | 2.0172 |
Spline | 21.2641 | 4.2668 | 5.583 | 0.2512 | 0.9893 |
Kriging | 12.7859 | 3.6714 | 4.5996 | 0.1705 | 0.6714 |
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12.6277 | 3.6488 | 4.5090 | 0.1638 | 0.6452 |
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A quarter of the data (64 samples in total) is used to train the model, and the remaining 3/4 of the data is used for test validation. The results are shown in Table
Estimation result of level values for 99.8 Mhz (1/4 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 26.2765 | 6.3642 | 8.1205 | 0.5381 | 2.0736 |
Spline | 57.8689 | 4.9106 | 7.7875 | 0.4949 | 1.9070 |
Kriging | 16.0234 | 4.0510 | 5.1165 | 0.2136 | 0.8232 |
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16.7655 | 4.0749 | 5.0926 | 0.2116 | 0.8155 |
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In order to reflect the estimation results of various algorithms directly, all the five kinds of algorithms use the same 1/4 training data, the results of which are compared with the same measured data. The comparisons of various algorithms were shown in Figure
Estimation result of level values of 99.8 MHz (1/4 training data)
In the 1/2 data for training, there are 128 sampling points in the range of about 784 square kilometers. A sampling point covers an average of about 6 square kilometers. As could be seen from Table
Estimation results of max level values for 87–108 MHz (1/2 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 12.2333 | 3.3063 | 4.3205 | 0.6093 | 0.2982 |
Spline | 12.3468 | 2.9376 | 3.8746 | 0.4900 | 0.2398 |
Kriging | 11.8977 | 2.6554 | 3.4731 | 0.3937 | 0.1927 |
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10.8254 | 2.5374 | 3.2675 | 0.3485 | 0.1706 |
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A quarter of the data (64 samples in total) is used to train the model, and the remaining 3/4 of the data is used for test validation. The results are shown in Table
Estimation results of max level values for 87–108 MHz (1/4 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 16.3241 | 3.3529 | 4.4390 | 0.6374 | 0.3152 |
Spline | 24.8394 | 3.1712 | 4.3034 | 0.5990 | 0.2962 |
Kriging | 12.6690 | 2.7459 | 3.4564 | 0.3864 | 0.1911 |
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2.6877 | 3.4220 | 0.3788 | 0.1873 |
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11.2699 |
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In order to reflect the estimation results of various algorithms directly, all the five kinds of algorithms use the same 1/4 training data, the results of which are compared with the same measured data. The comparisons of various algorithms are shown in Figure
Estimation results of max level values of 87–108 MHz (1/4 training data).
The maximum signal strength in the frequency band is an important parameter of the radio environment map. In the large scale space, many signal sources constitute the spatial distribution of the maximum signal strength, so it is difficult to make estimation by using the radio propagation model. The spatial interpolation method is more advantageous. The experimental results of 1/2 training data are shown in Table
Estimation results of max level values for 1800–1900 MHz (1/2 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 22.4790 | 5.6729 | 7.5337 | 0.6532 | 1.3643 |
Spline | 18.7473 | 4.9472 | 6.6059 | 0.5022 | 1.0489 |
Kriging |
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4.7758 | 6.3212 | 0.4598 | 0.9605 |
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18.2057 | 4.6203 | 6.1744 | 0.4387 | 0.9164 |
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18.3114 |
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A quarter of the data (64 samples in total) is used to train the model, and the remaining 3/4 of the data is used for test validation. The results are shown in Table
Estimation results of max level values for 1800–1900 MHz (1/4 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 28.2658 | 5.9683 | 7.9227 | 0.7184 | 1.5180 |
Spline | 30.1425 | 6.7523 | 9.0084 | 0.9287 | 1.9626 |
Kriging | 28.8990 | 6.2277 | 8.2594 | 0.7807 | 1.6498 |
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24.1963 | 5.5533 | 7.2744 | 0.6056 | 1.2797 |
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Same as the above, all the five kinds of algorithms use the same 1/4 training data, and the remaining data as the same measured data. The comparisons of various algorithms are shown in Figure
Estimation results of max level values of 1800–1900 MHz (1/4 training data).
The main services in the 1800–1900 MHz band are mobile communications, of which band has more complex electromagnetic environment, and the estimation of the parameters of this band is more difficult. The experimental results of 1/2 training data are shown in Table
Estimation results of level values for 101.7 MHz (1/2 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 26.6984 | 3.4255 | 4.4763 | 0.6184 | 0.3720 |
Spline | 15.5874 | 3.0751 | 3.9084 | 0.4715 | 0.2836 |
Kriging |
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2.7197 | 3.3944 | 0.3556 | 0.2139 |
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12.8846 | 2.5712 | 3.2100 | 0.3180 | 0.1913 |
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13.5290 |
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A quarter of the data (256 samples in total) is used to train the model, and the remaining (768 testing points) is used for testing and validation. The results are shown in Table
Estimation results of level values for 101.7 MHz (1/4 training data).
MAX_ERR | AVE_ERR | RMSPE | RMSE | PAEE | |
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IDW | 26.6254 | 3.3326 | 4.4070 | 0.6072 | 0.3603 |
Spline | 23.1643 | 3.6385 | 4.9289 | 0.7596 | 0.4507 |
Kriging |
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2.8034 | 3.5230 | 0.3881 | 0.2303 |
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11.5091 | 2.7089 | 3.3900 | 0.3593 | 0.2132 |
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13.4562 |
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In order to reflect the estimation results of various algorithms directly, all the five kinds of algorithms use the same 1/4 training data, the results of which are compared with the same measured data. The comparisons of various algorithms are shown in Figure
Estimation results of level values of 101.7 MHz (1/4 training data).
We use 1/2 the simulation data for training model in our experiment, and each sampling point covers about 0.5 square kilometers. As can be seen from Table
In this paper, we proposed a spatial distribution prediction method for radio environment map parameters. It was shown that the IDW, Spline, and Kriging methods are the most effective methods to solve this problem, and, of these, Kriging is the best method. The main parameters of the radio environment map are the signal strength and other parameters are affected by it. In this study, based on the Kriging approach, the definition of a variogram was improved based on the loss characteristics of radio propagation. A new variogram theoretical model was proposed in combination with a radio propagation model. Based on the characteristics of data sampling and signal propagation, a new weighted fitting method for variograms was also proposed. The new method is more suitable for the actual characteristics of radio environment map parameter prediction. Moreover, the proposed model is better adapted to the spatial correlation of radio environment parameters and has better prediction accuracy. Experiments on the signal strength data of a single frequency and the maximum signal strength data of a frequency band and simulation data prove these conclusions. The evaluation indexes of our method are improved by about 10% on average compared with those of the conventional Kriging method.
Radio signal propagation in space is a complex process. There are some intractable problems such as building shadows, same-frequency adjacent channel interference, and multipath propagation. Therefore, to obtain better prediction accuracy, the terrain and station information to the model will be taken into consideration in our future research.
The authors declare that they have no conflicts of interest.
Zhisheng Gao proposed the original idea, Yaoshun Li wrote the paper under the guidance of Zhisheng Gao, Yaoshun Li and Chunzhi Xie designed the experiment and provided all the figures, and Chunzhi Xie checked the manuscript. All authors read and approved the final manuscript.
This work has been partially supported by the Major Project of Education Department of Sichuan (Grant no. 14ZA0118), the Ministry of Education Chunhui project (Grant no. Z2016149), the Xihua University Key Laboratory Development Program (Grant nos. szjj2017-065, s2jj2014-050), and the Graduate Innovation Foundation of Xihua University (ycjj2017070).