Performance Evaluation of Hata-Davidson Pathloss Model Tuning Approaches for a Suburban Area

In this paper, comparative study of RMSE-base tuning and multi-parameter-based tuning of Hata-Davidson pathloss model for a suburban area is presented. The study was based on field measurement of received signal strength carried out in a suburban area for a GSM (Global System for Mobile communication) network that operates in the 1800MHz frequency band. The results show that multi-parameter-tuned Hata-Davidson model has better prediction accuracy of 98.70720432% and RMSE of 2.177522885 dB as against the RMSE-tuned Hata-Davidson model with prediction accuracy of 97.42722692% and RMSE of 4.256897001dB. However, the RMSE is quite simple and easier to implement even in embedded systems and systems with limited resource.


Introduction
Pathloss models are essential in planning wireless network. The models provide mathematical expressions that enable network designers to determine the amount of pathloss that will be experienced by the signal as it transverse the given terrain [1][2][3][4][5]. Basically, a propagation pathloss model predicts the difference between the transmitted power and the receiver power using empirical and deterministic methods or a combination of both. Empirical models, in general, require adjusting some parameters according to field measurements made in a particular environment. Several empirical pathloss models have been given attention for decades due to their accuracy and environmental compatibility. However, peculiarities of these models give rise to high prediction errors when deployed in a different environment other than the one they are initially built for. For instance, [6] provides the error bounds on the efficacy at predicting pathloss for eight widely used empirical pathloss models based on field strength measurements conducted in the VHF and UHF frequencies in Kwara State, Nigeria. It was concluded that no single model would provide a good fit consistently. Faruk, Adediran and Ayeni, [7] presented similar results to that of [6] and concluded that tuning of pathloss model is necessary to minimize the RMSE value within the acceptable range. For example, Dalela, Prasad and Dalela, [9] presented tuning of COST 231 Hata model based on measurements conducted in 2.3 GHz in Western India. Also. linear iterative method was used in tuning the model and it was found that the tuned model achieved better root mean square errors as compared with the conventional COST 231 Hata model. Isabona and Azi, [10] optimized Walficsh Bertoni model using least squares method. The optimized model predicts pathloss with improved accuracy of about 25-30% compared to the original model. Chen and Hsieh [11] provided a fast and precise dual least-square approach to tune the generally used propagation models, like COST231-Hata model. In this paper, two different least square optimization techniques are used for optimizing the Hata-Davidson model [12]. The first approach is based on addition or subtraction of the RMSE value whereas the second approach is based on the adjustment of some Hata-Davidson model parameters in such a way as to minimise the sum of square error. The performance of the two tuning approaches are compared in terms of their RMSE and prediction accuracy.

Method
The field measurement route is identified with respect to the Cellular Network Base Station (CNBS) selected for the study. Received Signal Strength (RSS) and spatial data (longitude, latitude and altitude) dataset are then collected along the route. Samsung Galaxy S4 mobile phone with Cellmapper android application installed is used to capture and store the RSS and spatial datasets in CSV file. The RSS is converted to the measured pathloss (PL) using the formula [13][14][15]: Again, the Haversine formula in Eq 3 is used to computer the distances (d) between each measurement point and the base station as follows; Where LAT1 and LAT2 are the latitude of the coordinates of point1 and point 2 respectively. LONG1 and LONG2 are the longitude of the coordinates of point1 and point 2 respectively. R = radius of the earth = 6371 km; R varies from 6356.752km at the poles to 6378.137 km at the equator d = the distance between the two coordinates Eventually, the distance (d) data is used in the Hata-Davidson model to generate the predicted pathloss. The prediction accuracy of the pathloss model is evaluated with respect to the measured pathloss. The optimised pathloss model is then develop to improve on the prediction accuracy of the Hata-Davidson model. Finally, the prediction accuracy of the optimised pathloss model is compared with the prediction accuracy of the original (un-optimised) Hata-Davidson model.

Hata-Davidson model is one of the extensions or modified versions of Hata model. Particularly, Hata-Davidson is Telecommunications
Industry Association (TIA) recommended model following modification to the Hata model to cover a broader range of input parameters. The modification consists of the addition of correction terms to the Hata model.
The following equations are used for the computation of the pathloss (in dB) according to the Hata-Davidson model [12]: Where is the pathloss prediction by the Hata model and is the correction factor introduced by Davidson. The following equations are used for the computation of pathloss (in dB) according to the Hata model:

Performance Analysis of the Models
The statistical performance measures or goodness of fit measures for the Hata-Davidson model are defined as follows: i) The Root Mean Square Error (RMSE) is calculated as follows:

Model Optimization Process
The parameters of the Hata-Davidson pathloss model were adjusted (optimized) using least square algorithm to fit to measured data using the following process.
1) First, the residual (or error, e) between measured pathloss, and the Hata-Davidson model predicted pathloss is calculated for each location point, i.
2) Second, the RMSE is calculated based along with sum of errors, that is .
3) Thirdly, if < 0 then the optimised model is obtained by subtracting RMSE from each otherwise, if ≥ 0 the optimised model is obtained by adding RMSE to each . Table 1 gives the measured Received Signal Strength (RSSI), the measured pathloss and the distance of the measurement point from the GSM (Global System for Mobile communication) base station in a suburban area of Uyo, Akwa Ibom state, Nigeria. The GSM network operates in the 1800MHz frequency band. Table 2 and figure 1 show the measure pathloss, the predicted pathloss by untuned Hata-Davidson model, the predicted pathloss by the RMSE-tuned Hata-Davidson model and the predicted pathloss by the multi-parameter-tuned Hata-Davidson model. The results in table 2 show that the multi-parameter-tuned Hata-Davidson model has the better prediction accuracy of 98.70720432% and RMSE of 2.177522885 dB as against the RMSE-tuned Hata-Davidson model with prediction accuracy of 97.42722692% and RMSE of 4.256897001dB. According to experts, pathloss model with RMSE of less than 6dB is acceptable. In any case, the result shows that the multi-parameter tuning approach may be preferred when more accurate prediction result is required. However, the RMSE is quite simple and easier to implement even in embedded systems and systems with limited resource.

Conclusion
In this paper, comparative study of RMSE-base tuning and multi-parameter-based tuning of Hata-Davidson pathloss model for a suburban area is presented. The study was based on field measurement of received signal strength for a GSM network that operates in the 1800MHz frequency band. The results show that the multi-parameter-based tuning performs better than the RMSE-base tuning. However, the RMSE-base tuning is simpler and easier to implement in resource limited systems.