1Department of Electrical, Electronics and System Engineering ... 2Department of EE, Faculty of Engineering Tech., Al-Balqa' Applied University, Jordan.
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Linear Regression Route Roughness Parameter to Correct Hata Path Loss Prediction Formula for 1800 MHz Mahdi A. Nisirat1 , Mahamod Ismail1 , Liyth Nissirat1 , and Salim Alkhawaldeh2 1
Department of Electrical, Electronics and System Engineering Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia 2 Department of EE, Faculty of Engineering Tech., Al-Balqa’ Applied University, Jordan
Abstract— Propagation path loss models are going under intensive improvement to allow for more accurate predictions. Such improvements should include terrain areas that are not been exposed extensively in most of the earlier models. In this paper the main equation of Hata urban model is modified by a relation that includes the standard deviation of the measuring campaign route elevations (σ). This relation is consisting of two regression formulas, as a function of log(σ), modifying both the intercept point (DC value) and the slope of Hata urban model. Root Mean Square Error (RMSE) difference between this model and the measured filtered raw data path loss has overcome RMSE calculated for Hata suburban model, by up to 13 dB. Areas where data are collected would be assumed suburban by Hata model. Data were obtained from mobile service providers in Amman city and Madaba city, Jordan for the frequency band of 1800 MHz. 1. INTRODUCTION
Empirical path loss models are usually statistical models proposed to calculate average path loss relation. Many of these models are currently going under precise investigation to correct any shortcomings due to different situations such as urban and rough terrain landscape. In addition to that current and future mobile systems are aiming more toward small-cell system layout. Such small area coverage, distance (d) < 1 km, relies heavily on the accuracy of the used path loss model. Hata path loss model was originally proposed for macro-cell coverage, d > 1 km, and lack the adaptation of rough topography [1]. Different studies have shown that Hata model could be used with high accuracy given that transmit antenna height is above average roof top [1, 2]. Single Terrain roughness parameter has been used to correct Hata path loss model for the 900 MHz band for small area coverage in [1]. In that study the standard deviation of the measuring route log(σ) is used to correct the intercept point of Hata suburban relation. In this paper the standard deviation parameter log(σ) is used to correct for both the intercept point and the slope of Hata path loss relation for the 1800 MHz band, where Hata path loss relation is assumed of the general form PL = A + B log 10(d). Here A is inferred to be the intercept point and B is the slope. This paper introduces, in the first section, data collection and authentication process used to assure that data obtained from mobile service providers are valid and can be used for propagation analysis. Secondly, a thorough analysis of standard deviation correlation to path loss phenomena is presented. In the last section, an example of one location route is shown in addition to RMSE analysis. 2. DATA COLLECTION AND AUTHENTICATION
Data are obtained by Umniah mobile company, working as a mobile service provider in Jordan in the frequency band of 1800 MHz. Data are analyzed and collected by Ericsson Test Mobile System (TEMS) software with an antenna mounted on a moving vehicle, with an average speed of 20 km/h, 1.5 meter above ground level. The sample rate was about 4 samples per second. Data were collected from two cities mainly Amman city and Madaba city and it was originally obtained in a form of excel sheets containing different received power levels from different antennas with multi sectors. To make sure that path taken were regular or quasi regular and to assure that latitudes given are correct, a KML code file was generated by MATLAB to show the measurement path on Google Earth. 3. SYSTEM PARAMETERS MODELING AND DERIVATION
In this paper, the effect of the standard deviation of the elevations along the measuring route log(σ) on path loss general relation is analyzed. The analysis covers the effect of route standard deviation, representing path terrain roughness factor, on both parameters of the path loss relation, mainly the
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PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
intercept point, A, and the slope, B. twenty different areas, categorized by Hata as suburban areas, with building elevations less than 9 meter and transmit antenna above roof top are specified. The average of the filtered path loss relation obtained is then subtracted from Hata path loss relation, of the given route, to get an intercept point DC shift difference called δDC (d). This procedure is used again with the slope difference between the average filtered data and Hata path loss relation but after normalizing data over the distance d to get a factor called δs (d). The summary of this procedure is given in Fig. 1 below. Linear regression relation between the standard deviation log(σ) and both of the values δDC (d), and δs (d) are then obtained such that they would be of the form δDC (σ) = K1 + K2 log(σ) and δS (σ) = F1 + F2 log(σ)
(1)
where K1 , K2 , F1 , F2 are the regression parameters and has been found to be 23.36, −16.66, 8.95, and −6.46 respectively. A high correlation factor between the δDC (σ) and log(σ) of 0.995, and between δs (σ) and log(σ) of 0.99 is obtained. This relation is used as a correction factor over Hata urban formula. The new proposed model would be of the form L(proposed) (dB) = L(Hata,urban,smallarea) (dB) + δDC (σ) + δS (σ) log(d)
(2)
Or L(proposed) (dB) = 69.55+26.16 log fc −13.82 log hr −a(hr )+δDC (σ)+[(44.9−log hc )+δs (σ)] log d (3) where L(Hata,urban,smallarea) (dB) is Hata path loss relation for urban areas given in [3], fc is the operating frequency in MHz, hr is the receiving antenna height in meter, ht is the transmit antenna height in meter, d is the distance between transmit and receive antennas in meter, and a(hr ) is Hata correction factor for small areas given as [3] a(hr ) = (1.1 log(fc ) − 0.7)hr − (1.56 log fc − 0.8) dB
(4)
4. RESULTS AND DISCUSSION
One route is chosen as a clarifying example. This route is located in Abdoun area, west of Amman and has a standard deviation parameter of σ = 3.90. The path taken and location is shown in Fig. 2. Over all more than 75 percent of the routes under study are corrected and less RMSE, compared to Hata suburban model, is obtained. Such a result supports the efficiency of this proposed model, where corrections used by Hata for suburban areas are replaced by a correction factor depending on the terrain roughness of the route used to collect the data. Fig. 3 shows the path loss comparison between the proposed model and Hata suburban model. In this example the achieved proposed model RMSE is 2.75 dB, compared to RMSE for Hata suburban model of 13.90 dB.
Figure 1: Procedure followed to implement the proposed model.
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Figure 2: Al — Usra Restaurant Tx at Abdoun area with terrain Standard deviation σ = 3.90, west of Amman. Dimensions are 300 m × 600 m [Google Earth].
Figure 3: Abdoun area proposed path loss compared to Hata suburban path loss. 5. CONCLUSION
In this proposed model, the correction factor used in Hata model for urban areas is modified by a roughness correction factor depending on the standard deviation of the elevations of the measuring route. Better RMSE results are achieved using such correction factor, which highlights the need to include terrain roughness correction factors in any future path loss correction formula. More than 75 percent of the areas under study are corrected with less RMSE of up to 13 dB. REFERENCES
1. Nisirat, M. A., M. Ismail, L. Nissirat, and S. Al-Khawaldeh, “A terrain roughness correction factor for hata path loss model at 900 MHz,” Progress In Electromagnetics Research C, Vol. 22, 11–22, 2011. 2. Fujitani, T., S. Tomisato, and M. Hata, “Experimental study of mobile propagation loss correction formula for a slope terrain area,” IEEE Vehicular Technology Conference, 1–5, 2010. 3. Hata, M., “Empirical formula for propagation loss in land mobile radio services,” IEEE Transaction Vehicular Technology, 317–325, 1980.
