Statistic Microwave Path Loss Modeling in Urban Line-of-Sight Area Using Fuzzy Linear Regression

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1 ICCAS2005 June 2-5, KINTEX, Gyeonggi-Do, Korea Statistic Microwave Path Loss Modeling in Urban Line-of-Sight Area Using Fuzzy Linear Regression SUPACHAI PHAIBOON, PISIT PHOKHARATKUL Faculty of Engineering, Mahidol University Salaya, Naornprathom, 73170, Thail SURIPON SOMKURNPANIT Faculty of Engineering, King Mongut s Institute of Technology Ladrabang Ladrabang, Bango, 10520, Thail ssuripo@mitl.ac.th Abstract: This paper presents a method to model the path loss characteristics in microwave urban line-ofsight (LOS) propagation. We propose new upper- lower-bound models for the LOS path loss using fuzzy linear regression (FLR). The spread of upper- lower-bound of FLR depends on max min value of a sample path loss data while the conventional upper- lower-bound models, the spread of the bound intervals are fixed do not depend on the sample path loss data. Comparison of our models to conventional upper- lower-bound models indicate that improvements in accuracy over the conventional models are achieved. Keywords: Microwave path loss modeling, urban areas, Fuzzy Linear Regression 1. INTRODUCTION The estimation of microwave path loss is necessary for system cell design of modern mobile communication networ [1]-[9]. However it is difficult to accurately estimate path loss in urban areas because of dispersion caused by reflection blocing due to vehicles, pedestrians, other objects on the road. Therefore, some researchers have measured radio waves statistically modeled their results [10],[11] by using upper lower- bound formulas. However these estimations have still been over estimated because the slopes of the upper- lower- bound are fixed do not depend on the real path loss data. To solve this problem, we propose new upper lower bound models using fuzzy linear regression (FLR). The spread of upper- lower-bound of FLR depends on max min value of a sample path loss data, therefore the FLR is a realistic model suitable for the system cell design of fourth-generation multimedia mobile communication systems in microwave bs. 2. UPPER AND LOWER BOUND MODELS The upper lower bounds for propagation path loss model in UHF microwave b can be calculated by using (1) (2) in [10],[11] d 20 log 10, for d R bp L LOS, l L bp (1) 40 log d, for d 10 Rbp 25log10, d, 20 Rbp LLOS u Lbp 40log d, 10 Rbp for d Rbp for d L LOS, L LOS,u lower upper bouds of LOS path loss; L bp propagation loss at distance between transmitter receiver. In case of no breapoint when the mobile antenna d height approached the effective road height [3], the path loss model can be calculated by d LLOS, u L s log 10, for d Rs R s R S is 20 m based on measurement results using different propagation parameters. L S is the basic propagation loss at R S. The lower limit can be approximated by d LLOS, l L s 30 log 10, for d Rs R s L s 20 log 10 2 R (2) (3) (4) (5)

2 (x) a 0c+ j1 (a jc z ij )-a 0r + j1 (a jr z ij ) y i, i= 1,2,..,n (16) 1 a ic x The parameters a i = [a ic, a ir ] of vector à are determined as the optimal solution of the LP problem (14) (16). Since the LP problem always has feasible solutions, the fuzzy parameters are obtained from the LP problem, for any data. a ir 4. NUMERICAL EXAMPLE Fig. 1. Triangular from of fuzzy number 3. FUZZY LINEAR REGRESSION MODELS Fuzzy linear regression model can be represented in the from [12]-[15] : Y = Zà (6) y i (z I ) = ã 0 +ã 1 z i1 + +ã z i, i=1,2,,n (7) The fuzzy linear regression model (7) is represented using symmetric triangular fuzzy parameters ã i = [a ic, a ir ]as shown in fig. 1 [3] [4] by: y i (z i ) = [a 0c, a 0r ]+[a 1c, a 1r ]z i1 + +[a c, a r ]z i (8) y ic (z i ) = a 0c+ a 1c z i1+ + a c z i (9) y ir (z i ) = a 0r+ a 1r z i1+ + a r z i (10) : y c, a c are center parameters of fuzzy numbers (membership function = 1), y r, a r are spreads of fuzzy numbers (geometrically the spread is a half of the base of the triangular). The parameters ã i of the vector à of the FLR model are determined by a solution of a linear programming (LP) problem which is to minimize the sum of spreads y r (z i ) of elements of vector y Therefore the following LP problem is formulated. C = y 1r (z 1 )+y 2r (z 2 )+ +y nr (z n )Minimum (11) Subject to y i Y(z I ), i = 1,2,,n (12) a ir 0, i = 0,1,2,, (13) from (8) - (10), the LP problem (11) - (13) can be written as follows: n (a 0r+ a 1r z i1+ + a r z i )Minimum (14) i1 a 0c+ j1 (a jc z ij )-a 0r - j1 (a jr z ij ) y i, i=1,2,..,n (15) The FLR model (4) was determined compared with conventional models (1) (2). The FLR model was calculated from measured data in [6]. The fuzzy model was then presented in from: L LOS = [a 0c, a 0r ] + [a 1c, a 1r ]log (d) (17) L LOS,u = [a 0c + a 0r ] +[a 1c +a 1r ]log (d) (18) L LOS,l = [a 0c -a 0r ] + [a 1c - a 1r ]log (d) (19) d = distance between transmitter receiver. The LP problem corresponding to the given data was formulated from (14) (16). By solving this LP problem, the following FLR models are obtained: 4.1 Without Breapoint -for frequency of 3.35 GHz L LOS,u = [63.45] + [37.02]log (d/do) (20) L LOS,l = [41.12] + [34.42]log (d/do) (21) -for frequency of 8.45 GHz L LOS,u = [78.8] + [29.2]log (d/do) (22) L LOS,l = [56.85] + [29.2log (d/do) (23) -for frequency of GHz L LOS,u = [79.97] + [36.44]log (d/do) (24) L LOS,l = [73.16] + [29.6]log (d/do) (25) 4.2 With Breapoint -for frequency of 3.35 GHz d log 10, for d R bp L LOS, u (26) log d, for d 10 Rbp

3 a) frequency 3.35 GHz a) frequency 3.35 GHz Fig. 2 The conventional model without breapoint d log 10, for d R bp Rbp L LOS, l (27) log d, for d 10 Rbp -for frequency of 8.45 GHz Fig. 3 FLR path loss model without breapoint d log 10, for d R bp L LOS, u (28) log d, for d 10 Rbp

4 a) frequency 3.35 GHz a) frequency 3.35 GHz Fig. 4 The conventional model with breapoint d log 10, for d R bp L LOS, l (29) log d, for d 10 Rbp -for frequency of GHz Fig. 5 FLR path loss model with breapoint d log 10, for d R bp L LOS, u (30) log d, for d 10 Rbp

5 d log10, for d Rbp Rbp LLOS, l (31) log d, for d Rbp 10 Rbp The results are shown in Fig for the distance characteristics of the path loss without brea point with brea point respectively. We found that the FLR provide high accuracy within the upper- lower- bound as shown in Fig. 3 5 while the conventional models predict the path loss over estimation at the upper- lower- bound as shown in Fig Conclusions We propose the Microwave path loss models based on measured data in LOS urban environment using the fuzzy linear regression. The models are based on a simple d n exponential path loss vs. distance relationship used for frequency of 3.35, GHz. The spread of the upper- lower- bound of the fuzzy models depends on max min value of a given data while the width of the upper lower regression lines are fixed as shown in eq. (1)-(4) that cause they provide the error prediction at the outside of the boundary. From the reasons above, the FLR is a realistic model suitable for the system cell design of fourth-generation multimedia mobile communication systems in microwave bs. urban quasi line-of-sight environment under traffic conditions, IEICE trans. Commun., vol E84-B, pp , May [10] L. B. Milstein, D. L. Schilling, R. L. Picholtz, V. E.RCEG, m. Kullbac, E. G. Kanterrais, D. S. Fishman, W. H. Biederman, D. C. Ssalerno, On the feasibility of a CDMA overlay for personal communications networ, services IEEE J. Select. Areas Commun.,Vol.10,pp , May [11] H. Masui, T. Kobayashi, M. Aaie, Microwave path-loss modeling in Urban Line-of-sight Environments, IEEE J. Select. Areas Commun.,Vol.20,pp , August [12] J. R. Benjamin. C. A. Cornal, Probability Statistics Decision for Civil Engineers McGraw Hill, Inc., [13] A. Celmins, Least squares model fitting to fuzzy vector data Fuzzy Sets Systems, pp , [14] P. T. Chang, E. S. Lee, A generalized fuzzy weighted least squares regression Fuzzy Sets Systems, pp , [15] P. Diamond, Fuzzy least squares, Infrom. Sci., pp ,1988. [16] P. Diamond, Least squares fitting of several fuzzy variables, Preprints of Second IFSA Congress, Toyo,pp , [17] H. Tanaa, S. Uejima, K. Asai, Linear regress analysis with fuzzy model, IEEE Trans. Syst., Man, Cybern., vol. SMC- 12, pp , June 1982 References [1] R. Prasad, Overview of wireless personal communications: Microwave perspectives, IEEE Commun. Mag., Vol.35, pp , Apr [2] A. J. Rustao, Jr., N. Amitary, G. J. Owens, R. S. Roman, Radio propagation at microwave frequency for line-ofsight microcellular mobile personal communications, IEEE Transaction on vehicular technology, Vol.40, pp , Feb [3] H. Masui, K. Taahashi, S. Taahashi, K. Kage, T. Kobayashi, Difference of path loss characteristics due to mobile antenna heights in microwave urban propagation IEICE trans. Fundamentals, vol E82-A, no. 7, pp , July [4] Y. Oda, K. Tsuneawa, M. Hata, Advance LOS path loss model in microcellular communications, IEEE Transaction on vehicular technology, Vol.49, pp , Nov IEEE J. Select. Areas Commun.,Vol.20,pp , August [5] K. Taira, S. Seizawa, G. Wu, H. Harada, Y. Hase, Propagation loss characteristics for microcellular mobile communications in microwave b, inproc. 5thIEEE ICUPC, Cambridge, MA, Sept.-Oct,1996, pp [6] T. Taga, T. Furuno, K. Suwa, Channel modeling for 2- GHz-b urban line-of-sight street microcells,, IEEE Transaction on vehicular technology, Vol.48, pp , Jan [7] A. Yamaguchi, K. Suwa, R. Kawasai, Received signal level characteristics for radio channel up to 30 MHz bwidth in line-of-sight microcells, IEICE trans. Commun., vol E80-B, pp , Feb [8] E. Green M. Hata, Microcellular propagation measurements in an urban environment, inproc. PIMRC, Sept. 1991, pp [9] H. Masui, M. Ishi, S. Taahashi, H. Shimizu, T. Kobayashi, M. Aaie, Microwave propagation characteristics in an