G Model AEUE-51206; No. of Pages 7
ARTICLE IN PRESS Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Path loss prediction in microcellular environments at 900 MHz Leandro Carísio Fernandes ∗ , Antonio José Martins Soares Departamento de Engenharia Elétrica, Universidade de Brasília, Brasília 70910, Brazil
a r t i c l e
i n f o
Article history: Received 10 March 2014 Accepted 23 April 2014
a b s t r a c t A model is proposed to estimate path loss in urban environments at 900 MHz when the base station antenna is below the average height of the buildings. It shows that the percentage of area occupied by buildings explains more than 20 dB of variation of the mean path loss. © 2014 Elsevier GmbH. All rights reserved.
Keywords: Electromagnetic wave propagation Radiowave propagation Genetic algorithms
1. Introduction In a microcell the base station antenna is usually below the average height of the buildings. In this case the propagation depends less on the vertical plane (rooftop propagation) and more on the horizontal plane (propagation among the buildings). To predict the path loss in such areas it is necessary to use a model that considers some characteristics of the environment. This can be accomplished with numerical methods or with analytical equations. Usually, a detailed description of the environment and a database with the vector data describing the buildings are necessary. Two well-known models used to predict the path loss are the Hata and COST-WI models. Unfortunately, both cannot be used in this case. In microcellular environments, the base station antenna height (hbs ) is usually lower than 30 m. Therefore the Hata model cannot be used to predict the path loss, because it requires that 30 m < hbs < 200 m [1]. Although the COST-WI model is suitable for microcells and small macrocells [2], it fails when hbs < hroof (average height of the buildings) [2,3]. There are some specific models to estimate the path loss in microcellular environments when hbs < hroof . They normally use some characteristics of the environments as inputs. The Berg’s model, for example, assumes that the signal reaching the receiver will cross street canyons in the horizontal plane and will not diffract on rooftops [3]. It replaces the physical distance between transmitter and receiver with a virtual one that depends on the align angle among the streets.
∗ Corresponding author. Tel.: +55 6182205200. E-mail addresses:
[email protected] (L.C. Fernandes),
[email protected] (A.J.M. Soares).
Numerical methods such as ray-tracing can also be used to calculate the path loss in microcellular systems. It is necessary to provide a set of polygons representing the buildings to run a two-dimensional simulation (or solids, for a three-dimensional simulation). Unfortunately it is not even possible to get such data. Sometimes a satellite image of a city is all the information available. In this case, it is necessary to extract the buildings description using image segmentation/classification algorithms and then using the result image to get the external buildings walls. To overcome this issue, we propose a new model to estimate the path loss at 900 MHz frequency band in microcellular systems. It was developed using a genetic algorithm and needs only two input variables, the distance (d) and the information about the buildings between transmitter and receiver (). If the vector data describing the buildings is not available, this variable can be estimated through segmentation of satellite images. The pixels of the image are categorized and can be calculated counting them. It is not necessary to extract the information about the external walls of all buildings (this last step would be necessary to use the ray-tracing algorithm). 2. Proposed model At ultra high frequencies (UHF), when both transmitter and receiver are below the average buildings height, the rooftop propagation can be neglected. The propagation occurs mainly along the streets, reflecting and diffracting at walls and corners of the constructions. For this configuration and d < 500 m, up to 97% of the received power at 2145 MHz is due to a street guided propagation [4]. In fact, this also happens at other frequencies, therefore the buildings can be represented as infinity tall and the rooftop propagation can be neglected [5]. As a result, our model does not take into account the effect of the vertical plane on the propagation of the signal. The influence of the horizontal plane is modeled through the
http://dx.doi.org/10.1016/j.aeue.2014.04.020 1434-8411/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
G Model AEUE-51206; No. of Pages 7
ARTICLE IN PRESS L.C. Fernandes, A.J.M. Soares / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
2
Fig. 1. Footprint of a rectangular area with one transmitter (Tx) and one receiver (Rx).
percentage of area occupied by buildings between the transmitter and receiver. It is suitable for microcellular environments, when hbs < hroof and non-line-of-sight condition. 2.1. Environment representation Fig. 1 shows the footprint of a rectangular area XYZW, with a transmitter (Tx) and a receiver (Rx). The very first attempt to model the propagation environment is through the percentage of area occupied by buildings inside the rectangle. However, our guess is that only a small portion of the environment is necessary to explain most of the path loss.
Fig. 2. Steps to calculate (d,3,30◦ ): (top) calculation of ((1/3)d, 30◦ ); (middle) calculation of ((2/3)d, 30◦ ); (bottom) calculation of (d, 30◦ ).
Fig. 3. Map of Munich, Germany.
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
G Model
ARTICLE IN PRESS
AEUE-51206; No. of Pages 7
L.C. Fernandes, A.J.M. Soares / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
3
Fig. 4. Correlation between (d,N,) and path loss for several values of and N.
To describe the environment between Tx and Rx, we suggest the use of some measure of the percentage of area occupied by buildings in the circular sector AOB, as shown in Fig. 1. Thus, when the transmitter or the receiver moves, the propagation environment is changed, which should somehow be reflected in the path loss. Besides, we suppose that the path loss depends on different parts of the environment in different ways. To test this hypothesis, we suggest that the propagation environment should be modeled through the variable (d,N,): (d, N, ) =
1
1 N
N
d,
+
2
N
d,
+ ... +
N N
d,
(1)
where (r,) represents the percentage of area occupied by buildings in a circular sector with radius r starting from the transmitter and going toward the receiver. is the central angle of the circular sector – see Fig. 1. Fig. 2 illustrates how to evaluate (d,N,) = (d,3,30◦ ). As Fig. 2 shows, the radius of the first, second and third sectors is, respectively, d/3, 2d/3 and d. In the figure, the black and gray colors represent the absence and the presence of buildings. The percentage of area occupied by buildings in each sector is calculated dividing the area occupied by the gray color for the total area of the sector. (d,3,30◦ ) is calculated through the average value of the percentage of area occupied in the three sectors. Note that (1) uses N circular sectors with central angle . Note also that, if (N,) = (1,360◦ ), (d,N,) converges to the percentage of area occupied by buildings in the circle centered at Tx and with radius equals the distance between Tx and Rx. To find the values of (N,) that better models the propagation environment, measurements provided by Mannesmann Mobilfunk in Munich, Germany were used. The database contains vector data of the buildings and the path loss in three routes (about 2300 points) [6]. The measurements were performed at 947 MHz, with hbs = 13 m, hm = 1.5 m (receiver antenna height) and for distance between approximately 100 m and 2 km. Fig. 3 shows the map of Munich, the routes used (black lines) and the base station position (black cross). The value of (d,N,) for all measurements points was calculated for circular sectors with different values of (from 15◦ to 45◦ ) and
N (from 1 to 10). Fig. 4 shows the correlation between the path losses in Munich and (d,N,), calculated using different values of and N. For any , there is not any significant increase in correlation for N > 3. We can also observe that, fixing some N, there is not any significant increase in correlation for > 30◦ , indicating that constructions outside a circular sector with aperture angle of 30◦ is not important enough to calculate the path loss. So, we should consider N = 3 and = 30◦ to calculate (d,N,). Defined N and , from now on we will considerer = (d,3,30◦ ). 2.2. Path loss Fig. 4 shows that there is a relation between and the path loss at 900 MHz when the base station antenna is below the average height of the buildings, but does not quantify it. In this section we discuss how the path loss depends on . According to the log-distance model, the path loss, in dB, is [7]: L(d) = L(d0 ) + 10n log10
d d0
(2)
where L(d0 ) is the path loss at a reference distance (d0 ) and n is an exponent that depends on the propagation environment. For microcells, it is usual to consider d0 = 100 m. As discussed in Section 2.1, the propagation depends mainly on the variable . Thus we can expand (2) to include : L(d0 ) = A + B × f (C + D × ) 10n = E + F × g(G + H × )
(3)
where A, B, C, D, E, F, G and H represent coefficients, f(.) and g(.) represent functions. Considering (3), Eq. (2) can be rewritten as: L(, d) = A + B × f (C + D × ) + [E + F × g(G + H × )]log10
d
100 (4)
This equation shows a generic variation of path loss with the variables and d. For applications at this frequency band (900 MHz) the receiver is usually close to the ground level. Besides, when hbs < hroof and
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
G Model AEUE-51206; No. of Pages 7 4
ARTICLE IN PRESS L.C. Fernandes, A.J.M. Soares / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
Fig. 5. Measured and predicted path loss in Munich.
hm < hroof , the height of the buildings can be considered infinitely tall and the rooftop propagation can be neglected. Therefore, (4) does not use hbs and hm as inputs. The influence of the frequency is quantified by the coefficient A. To find the coefficients and functions in (4), we used genetic algorithms (GAs), one optimization method based on the concepts of natural selection and evolutionary process [8]. In the terminology adopted by GAs, each possible solution is coded as a chromosome. A fitness value is associated with each chromosome and represents how it possible fits the problem. The algorithm starts with a finite set of randomly generated chromosomes (initial population). Then the fitness of each one is calculated. After this step, a new population is created using the previous one. This procedure, called selection, determines which chromosome of the previous
population will be selected to attend the new population. This is done by using the fitness value of the chromosome. The higher the fitness, the higher is the probability of been selected. After that, the crossover operator is applied. With some crossover rate, pairs of chromosomes will cross. This operator exploits the potential of the current population. However, the population may not have necessary information to solve the problem (i.e. the chromosomes may be at local maxima). To bypass this issue, the mutation operator is used. With some mutation rate, one or more bits of a chromosome are inverted. After selection, crossover and mutation, the old population is replaced by the new one. Some versions of the algorithm use the elitism principle, which means that the best chromosomes of the previous population are copied to the new one. This process
Fig. 6. Map of Ottawa, Canada.
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
G Model AEUE-51206; No. of Pages 7
ARTICLE IN PRESS L.C. Fernandes, A.J.M. Soares / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
5
Fig. 7. Measured and predicted path loss in Ottawa.
continues until some stop criteria is reached, which usually is when the number of generations reaches a pre-defined limit or when the fitness of the best chromosome has a desired value. To find the coefficients and functions in (4), the chromosomes were represented by a binary string with 126 bits, 15 bits for each coefficient and 3 bits for each function. f(.) and g(.) can return the logarithmic, exponential, sin, cosine, tangent or square root of the argument. They can also return the argument or zero and can represent an increase, decrease or no dependence of the path loss with the argument. An initial population was generated and each chromosome represents possible equations with the format of (4). To calculate the fitness of the chromosomes, the equations are compared to about 40 measurements point previously selected to represent different values of the pair (,d). These points are marked in the map of Fig. 3. We use the maximum number of generations as the stop criteria. The GA returns the following equation for L(,d): L(, d) = −1.36 + 52.06 log10 (28.59 + 71.24) + [40.69 + 8.91 log10 (30.11 − 28.95)]log10
d 100
Fig. 5 shows the measured and predicted path loss along all the three routes available in Munich (about 2300 measurement points). Note that Eq. (5) describes with good accuracy the mean path loss in the city. Fig. 6 shows the map of Ottawa. The black lines represent the routes and the black cross shows the position of the base station. Measurements were performed at 910 MHz, hbs = 8.5 m and hm = 3.6 m [9]. Fig. 7 shows the measured and predicted path loss along all the three routes. As well as in Munich, Eq. (5) describes with good accuracy the mean path loss in the city. To illustrate the effect of in the path loss, three points 196 ± 4 m far from the transmitter were observed. These points are indicated by a, b and c in Fig. 6. As the variation in distance is low, it is expected that the variation of path loss is caused by the propagation environment. At points a, b and c, the triple (, measured and predicted path loss) is, respectively, (0.22, 98.1 dB, 99.7 dB), (0.637, 111.6 dB, 111.1 dB), (0.444, 110.9 dB, 106.1 dB). Observe that helps to explain the variation of the path loss value.
(5)
As (5) shows, depending on d, can affects path loss in more than 20 dB: L(0.05,100) = 77.1 dB and L(0.7,100) = 97.3 dB. This equation is suitable for microcellular environments, d < 2 km, hbs < hroof , and at 900 MHz frequency band and provides an important insight on how the path loss depends on the percentage of area occupied by buildings. 3. Results Eq. (5) was used to find the path loss in three routes in Munich, Germany, and Ottawa, Canada, and in two routes in Rosslyn, USA. The antennas were surrounded by high rise buildings, so the measurements can be used to validate the proposed model.
Fig. 8. Map of Rosslyn, VA, USA.
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
G Model
ARTICLE IN PRESS
AEUE-51206; No. of Pages 7 6
L.C. Fernandes, A.J.M. Soares / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
Fig. 9. Measured and predicted path loss in Rosslyn.
Table 1 First order statistics of the error. Model
Route 1
Route 2
Route 3
Munich Proposed
(dB) (dB)
−1.8 5.3
−1.5 4.6
0.8 6.0
Ray tracing (PTT-RT) [5]
(dB) (dB)
−6.1 14.6
−6.7 15.5
−1.1 12.3
Ray tracing (Villa GriffoneLab) [5]
(dB) (dB)
−1.7 8.5
−6.3 10.9
−5.5 6.8
Ray launching (Uni.–Karlsruhe) [5]
(dB) (dB)
−4.3 8.5
2.4 9.1
−1.0 8.6
Proposed
(dB) (dB)
−1.5 5.1
0.5 7.0
2.8 5.4
Ray tube [11]
(dB) (dB)
−4.9 10.5
Not available
3.2 7.4
Ottawa
Route 1
Model
Route 2
Rosslyn Proposed
(dB) (dB)
−2.3 3.1
0.2 7.0
Ray tracing 2D [10]
(dB) (dB)
−1.2 6.2
8.6 10.9
Ray tracing 3D [10]
(dB) (dB)
−2.7 5.3
4.5 13.1
Fig. 8 shows the map of Rosslyn. The black lines represent the routes and the black cross shows the position of the base station. Measurements were performed at 908 MHz, hbs = 10 m and hm = 1.5 m [10]. Fig. 9 shows the measured and predicted path loss along all the two routes. As well as in Munich and Ottawa, Eq. (5) describes with good accuracy the mean path loss in the city. In Fig. 8, two points (a and b) are marked on route 1. The distance between
transmitter and receiver is 160 m at point a, decreases to 139 m and is 160 m at point b. The path loss is 108 dB at point a, decreases to 82 dB and is 97 dB at point b. Although the distance varies only 21 m, the path loss varies 26 dB, which can’t be explained only by the distance. In this case the environment is the main responsible for this variation. At point a, is 0.537, it decreases to 0.09 and equals 0.165 at point b, which helps to explains the difference at the measured path loss at these points. The results show a good match between measured and predicted path loss except on route 2 of Fig. 9. Kim et al. also observed poor predictions on this route when they compared measured path loss with the path loss predicted by a 2D and 3D ray-tracing algorithm [10]. They suggested that this difference is because some features of the environment were not take into account (i.e. there are a wire fence and a line of trees along the Arlington River Road). Our model faced the same issue: is the only variable that represents the environment and it only depends on the percentage of area occupied by buildings. The presence of a wire fence and a line of trees influences the path loss but these structures were not considered in the proposed model. Table 1 presents the first order statistics (mean error, , and standard deviation of the error, ) between measured path loss, predicted by this model and using numerical methods. For the proposed model, in all cases the absolute value of the mean error and the standard deviation of the error are less than 3 dB and 7 dB, respectively. Besides, the error given by the estimations using (5) is equivalent with that given by some numerical methods.
4. Conclusions The proposed model was design and tested at 900 MHz frequency band, for distances between 100 m and 2 km, urban areas, and microcellular environments. Although it is restricted to 900 MHz, the algorithm described in Section 2 can also be used to find other equations for other frequency band or environments.
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
G Model AEUE-51206; No. of Pages 7
ARTICLE IN PRESS L.C. Fernandes, A.J.M. Soares / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
The main factor of (5) is the variable , which can be calculated using computational geometry algorithms or image segmentation. The model provides an important insight on how the path loss path loss depends on the percentage of area occupied by building and explains more than 20 dB of variation of the mean path loss due to the environment. The results are consistent with measured path loss. References [1] Hata M. Empirical formula for propagation loss in land mobile radio services. IEEE Trans Veh Technol 1980;29(August (3)):317–25. [2] Cichon DJ, Kurner T. Propagation prediction models – COST 231 final report; 1999, available from: http://www.lx.it.pt/cost231 [chap. 4]. [3] Nawrocki MJ, Dohler M, Aghvami AH. Understanding UMTS radio network – modelling, planning and automated optimisation. 1st ed. Chichester, West Sussex, England: John Wiley & Sons; 2006.
7
[4] Laurila J, Kalliola K, Toeltsch M, Hugl K, Vainikainen P, Bonek E. Wide-band 3-D characterization of mobile radio channels in urban environment. IEEE Trans Anten Propag 2002;50(February (2)):233–43. [5] Athanasiadou GE, Nix AR, McGeehan JP. A microcellular ray-tracing propagation model and evaluation of its narrow-band and wide-band predictions. IEEE J Sel Areas Commun 2000;18(March (3)):322–35. [6] Mannesmann Mobilfunk GmbH COST 231 – urban micro cell measurements and building data. [7] Rappaport TS. Wireless communications: principles and practice. 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall; 2002. [8] Mitchell M. An introduction to genetic algorithms. 3rd ed. Cambridge, MA, USA: MIT Press; 1998. [9] Writteker JH. Measurements of path loss at 910 MHz for proposed microcell urban mobile systems. IEEE Trans Veh Technol 1988;37(August (3)):125–9. [10] Kim S-C, Guarino Jr BJ, Willis III TM, Erceg V, Fortune SJ, Valenzuela RA, et al. Radio propagation measurements and prediction using three-dimensional ray tracing in urban environments at 908 MHz and 1.9 GHz. IEEE Trans Veh Technol 1999;48(May (3)):931–46. [11] Son H-W. A deterministic ray tube method for microcellular wave propagation prediction model. IEEE Trans Anten Propag 1999;47(August (8)):1344–50.
Please cite this article in press as: Fernandes LC, Soares AJM. Path loss prediction in microcellular environments at 900 MHz. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.04.020
