Selected Propagation Models Modification for Application in Container Terminal

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XV Poznań Telecommunications Workshop - PWT 2011 1

Abstract—It is particularly important to look for any propagation model that could be useful for designing mobile radio systems in container terminal environment. The selected propagation models have been investigated. The applied research methodology has been described too. Results of the statistical adjustment in terms of signal loss determination in such environment have been analysed. The analysis have proved effectiveness of adjustment by increasing the accuracy of path loss estimation.

Index Terms— radio waves propagation, measuring research, container terminal environment, propagation models adjustment

I. INTRODUCTION

Container port area should be treated as a very difficult radio waves propagation environment, because lots of containers made of steel are causing very strong multipath effect and there is time-varying container arrangement in stacks of different height. There is a number of propagation models, mainly for urban, suburban or rural environments, there is also propagation model destined for container port environment, but this model has been developed for designing only fixed radio links. Modelling path loss in mobile radio links is more complicated, so it is particularly important to look for any propagation model that could be useful for designing such links. To solve this issue there is a need to adjust existing models based on measuring research. Such tests have been carried out in Gdańsk Deepwater Container Terminal (DCT) in accordance to normative requirements [1, 2], which have to be met during research. The analysis contained in [3] has been also taken into account.

At the outset of the paper, in section II, the applied research methodology has been shortly presented. This part describes both the measuring equipment and measurement procedures. Next, in section III, selected propagation models have been evaluated in terms of designing mobile radio networks in investigated environment. These models are: ITU-R P.1411 models for the case of propagation over roof-tops for urban and suburban areas [4], COST231 – Walfisch-Ikegami model [5] and the above mentioned multi-variant empirical model for designing fixed radio links in container terminal [6].

The main part of the paper (section IV) presents results of statistical adjustment of selected models, which relies on adding correction functions to original path loss formulas. At

the end of the paper, results have been summarized and discussed. Additionally, authors mentioned further work aimed at developing new propagation model for designing mobile radio links in container terminal environment.

II. PROPAGATION RESEARCH METHODOLOGY

Propagation research have been carried out in years 2008-2009 in DCT Gdańsk. Structure and power description of measuring radio link have been presented in [7, 8]. This link was built with a fixed transmitting section, a mobile receiving section and a propagation environment, which was the subject of research.

The fixed transmitting section of test equipment consisted of signal generator connected to transmitting antenna through RF amplifier. Transmitting antenna was a monopole vertical antenna with electrical length of one-quarter of a wavelength. The mobile receiving section (Fig. 1) consisted of a spectrum analyser with built-in GPS receiver, an industrial computer, a rotary encoder with its controller and test wheel, a LCD display, a safety lighting and a battery with DC/AC converter. Receiving antenna was the same type as transmitting antenna. Whole receiving section has been carried by hand-cart.

Measurement results should include information about slow and fast changes of power flux density of electromagnetic field (slow and fast fading, respectively) [3]. For obtaining 1 dB confidence interval around the real mean value, test points have been chosen at each 0.8 λ (wavelength), over 40 λ averaging interval [2]. Spectrum analyzer MS2721B Receiving antenna Industrial computer GPS antenna LCD display Encoder controller Rotary encoder Battery DC/AC converter (12V/230V) 3m (N-N) 5m (BNC) LAN RS232 RS232 Test vehicle Test wheel Safety lighting

Fig. 1 Block diagram of mobile receiving section

During the research in the DCT nearly 290 thousand propagation cases have been collected. These cases concern propagation routes with various lengths (up to 620 m), various frequencies of test signal (from a range of 500 MHz up to 4 GHz) and various heights of transmitting antenna installation (from a range of 12 m up to 36 m).

III. EVALUATION OF SELECTED MODELS

The container terminal is a non-typical radio wave propagation environment. Due to its structure, consisting of

Selected Propagation Models Modification

for Application in Container Terminal

Sławomir J. Ambroziak and Ryszard J. Katulski, Member, IEEE

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XV Poznań Telecommunications Workshop - PWT 2011 2 containers' stacks placed on a flat surface and cut by a uniform

grid of routes, it seems to be similar to urban areas [9]. However, fact that the containers are made of corrugated steel is the reason to suppose that the conditions of radio waves propagation in such environment might be quite different. It is also important that both the layout of containers' stacks, as well as their height are variable in time. After considering above mentioned issues, four well-known propagation models have been selected [10].

A. COST 231 Walfisch-Ikegami for NLOS situations

The COST231 Walfisch-Ikegami model allows for improved path loss estimation by consideration of more data to describe the character of the urban environment. For non-line-of-sight (NLOS) situation the basic transmission loss is depended on a free space loss L0 [dB], a multiple screen diffraction loss Lmsd [dB], and a roof-top-to-street diffraction and scatter loss Lrts [dB] [5]. It is expressed by:

> @

0 rst msd rst msd WI 0 rst msd L L L for L L 0 L dB L for L L 0 ! ® _d ¯ . (1)

B. ITU-R P.1411 for NLOS1 (§4.2.1)

Recommendation [4] includes propagation models destined for designing short-range outdoor radiocommunication systems for different types of environments. Two models for typical NLOS cases, where the base station antenna is mounted above roof-top level have been selected.

The first one is the model described in §4.2.1 of Rec. [4]. This model should be used to estimate the basic transmission loss in a highly urbanized city centres, medium-sized cities and suburban areas, where the roof-tops are all about the same height. It is a modified version of the Walfisch-Ikegami model, extending the frequency range of its applicability up to 5 GHz. Main formula expressing the basic transmission loss for this model is the same as (1):

> @

0 rst msd rst msd 1411,4.2.1 0 rst msd L L L for L L 0 L dB L for L L 0 ! ® _d ¯ , (2)

but calculation of each component is more complicated.

C. ITU-R P.1411 for NLOS1 (§4.2.1)

The second model has been characterized in §4.2.2 of Rec. [4]. It may be used to calculate the basic transmission loss in suburban environment. Depending on the distance between base station and mobile station this model distinguishes three regions in terms of the dominant arrival waves at the mobile station, namely: a direct wave dominant region, a reflected wave dominant region, a diffracted wave dominant region. It may be expressed by simplified expression:

> @

0 1411,4.2.2 rw

dw

L direct wave dom. reg. L dB L reflected wave dom. reg.

L diffracted wave dom. reg.

° ® ° ¯ . (3)

D. Multi-variant empirical model for LOS1 and NLOS

In context of this paper, particularly noteworthy is empirical model for designing fixed radio links in container terminal. This model makes the basic transmission loss dependent on a frequency f [MHz], a propagation path length d [km], a path type qualification (LOS or NLOS condition) and a difference between transmitter antenna height ht [m] above terrain level and average height hav [m] of container stack [6]. From among four model variants, two describes propagation situations occurred during tests in the DCT, namely: x LOS1, for htt hav:

> @

1 55.2 20lg 5.8lg 22.1lg( ) LOS t av L dB f d h h , (4) x NLOS1, for htt hav:

> @

1 32.6 20lg 7.9lg 0.8lg( ) NLOS t av L dB f d h h . (5)

Above described models are going to be adjusted in order to use them for designing of mobile radio links in container terminal environment. But firstly they should be evaluated in this scope. This evaluation is based on two measures of matching measured data to mathematical models, namely: mean error (ME) and standard error of estimate (SEE). These errors are commonly being used to verify accuracy of the path loss models and they are defined by (6) and (7) respectively:

> @

,

> @

,

> @

1 1 ( ) N m i c i i ME dB L dB L dB N

¦

, (6)

> @

2 , , 1 1 ( ) 1 N m i c i i SEE dB L dB L dB N

¦

, (7)

where Lm,i is the measured value of the basic transmission loss in i-th position of the receiver equipment (i=1,...,N), Lc,i means the basic transmission loss value computed using propagation model for i-th position, and N is the sample size [9]. Mean error value reflects the expected average difference between path loss values obtained using proposed model and real path loss measurement results, while standard error of estimate is the measured of path loss values dispersion and describes how good the model matches to experimental data [10].

Table 1 summarizes values of mean error and standard error of estimate for selected propagation models. Although the Walfisch-Ikegami model is quite good for its range of applicability it should be noted that we are looking for the best matching model for all measured data, inter alia for frequencies from a range of 500 MHz up to 4 GHz. In this regard the best matching model is the multi-variant empirical model for fixed radio links in container terminal environment. But in this caseobtained mean error is positive, which means underestimation of the path loss. Obviously, this situation isn’t good from the viewpoint of radio network designer. The SEE is about 8 dB and in the light of [11] this result may be acknowledged as acceptable. Results obtained for the others models are much worse. This short analysis points the necessity of statistical adjustment of the selected models.

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TABLE 1VALUES OF MEAN ERROR AND STANDARD ERROR OF ESTIMATE FOR SELECTED PROPAGATION MODELS

Model Scenario Data range Sample size ME [dB] SEE [dB]

COST 231 Walfisch-Ikegami

Medium sized city and suburban areas

All measured data 287582 -5.3 10.6 Range of applicability 130968 -2.2 7.9 Metropolitan centres All measured data 287582 -10.1 16.0

Range of applicability 130968 -3.9 9.3 ITU-R P.1411

NLoS1 situation (§4.2.1 of [4])

Medium sized city and suburban centres

All measured data 287582 -8.4 13.4 Range of applicability 254184 -8.9 13.7 Metropolitan centres All measured data 287582 -8.8 13.9 Range of applicability 254184 -9.4 14.3 ITU-R P.1411

NLoS1 situation (§4.2.2 of [4])

Suburban areas All measured data 287582 -4.5 10.0 Range of applicability 190581 -5.9 10.8 Multi-variant empirical

model

LOS1 All measured data

(Range of applicability) 287582

3.8 8.3

NLOS1 3.0 7.6

IV. STATISTICAL ADJUSTMENT OF SELECTED MODELS

In order to increase accuracy of path loss estimation in investigated environment selected models have been adjusted by adding correction functions to original path loss formulas. Coefficients of these functions were calculated on the basis of empirical data and using multivariate linear regression. The statistical significance of particular coefficients was proved (with 95% confidence) using the Student's t-test.

A. Adjustment of the COST 231 Walfisch-Ikegami

The Walfisch-Ikegami model has been modified by adding to (1) two correction functions, as follows:

> @

0 rst msd c1 rst msd WI 0 c2 rst msd L L L L for L L 0 L' dB L L for L L 0 ! ® _d ¯ . (8)

These function are expressed by following polynomials:

1 1 1 1 1 1 1 lg lg lg lg , c t b L a f b d c h d h e I f ' ' (9)

2 2 lg 2 lg 2 c L a f b d , (10) c

where f [MHz] – frequency, d [km] – distance between base station antenna and mobile terminal, Δht [m] – difference between average buildings height and mobile terminal height,

Δhb [m] – difference between base station antenna height and average buildings height and ϕ [°] – street orientation angle.

TABLE 2CORRECTION FUNCTIONS COEFFICIENTS FOR WALFISCH-IKEGAMI

Medium sized city and suburban areas scenario a1 b1 c1 d1 e1 f1

-17.91 -15.01 -12.89 5.19 -0.077 48.21

a2 b2 c2

2.33 -9.09 -8.68

Metropolitan centres scenario a1 b1 c1 d1 e1 f1

-31.91 -16.71 -8.81 5.51 -0.088 86.65

a2 b2 c2

5.86 -7.47 -16.82

Coefficients of correction functions for two versions of the Walfisch-Ikegami model are presented in table 2.

B. Adjustment of the ITU-R P.1411 (§4.2.1)

In case of propagation model, described in §4.2.1 of ITU-R P.1411, adjustment has been done by adding to (2) one

correction function, as it is outlined below:

> @

0 rst msd rst msd 1411,4.2.1 c3 0 rst msd L L L for L L 0 L' dB L L for L L 0 ! ® _d ¯ .(11)

This function is expressed by following equation:

3 3 3 3 3 3 3 lg lg lg lg c t b L a f b d c h d h e I f ' ' . (12) Function parameters have the same meaning as in (9) and (10).

TABLE 3CORRECTION FUNCTION COEFFICIENTS FOR ITU-RP.1411(§4.2.1)

Medium sized city and suburban centres scenario a3 b3 c3 d3 e3 f3

-5.98 -19.69 -6.92 0.72 -0.22 9.97

Metropolitan centres scenario a3 b3 c3 d3 e3 f3

-5.96 -19.97 -9.39 -0.12 -0.23 11.87

Coefficients of correction function for two different versions of the ITU-R P.1411 (§4.2.1) model are presented in table 3.

C. Adjustment of the ITU-R P.1411 (§4.2.2)

Adjustment of model described in §4.2.2 of Rec. [4] has been done by adding correction functions to (3), as follows:

> @

0 c4

1411,4.2.2 rw c5

dw c6

L L direct wave dom. reg. L dB L L reflected wave dom. reg.

L L diffracted wave dom. reg.

° ® ° ¯ . (13)

These function are expressed by following polynomials:

4 4 lg 4 lg 4 c L a d b O , (14) c

5 5 5 5 5 5 lg lg lg , c b t r t L a d b h h c h h d I e (15)

6 6 6 6 6 6 6 lg lg lg lg , c b t r t L a d b c h h d h h e f O I (16) where λ [m] – wavelength, hb [m] – base station antenna height, hr [m] – average buildings height, ht [m] – mobile terminal height. Other parameters have the same meaning as in the previous cases.

Coefficients of correction functions for the ITU-R P.1411 (§4.2.2) model are presented in table 4.

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TABLE 4CORRECTION FUNCTIONS COEFFICIENTS FOR ITU-RP.1411(§4.2.2)

a4 b4 c4 -6.51 0.75 21.45 a5 b5 c5 d5 e5 -22.53 15.64 -16.59 -0.21 46.2 a6 b6 c6 d6 e6 f6 -3.84 0.68 1.69 -15.09 -0.02 6.24

D. Adjustment of the empirical model

The empirical model for designing fixed radio links in container terminal has been modified by adding correction functions to two investigated variants, as follows:

> @

1 1 7 '_LOS _LOS _c L dB L L , (17)

> @

1 1 8 '_NLOS _NLOS _c L dB L L . (18) These function are expressed by following polynomials:

7 7 lg 7 lg 7 lg c t av L a f b d c h h , (19)

8 8 lg 8 lg 8 lg 8 c t av L a f b d c h h . d (20) Function parameters have the same meaning as in (4) and (5).

TABLE 5CORRECTION FUNCTION COEFFICIENTS FOR THE EMPIRICAL MODEL

a7 b7 c7

-0.2 14 11.32

a8 b8 c8 d8

-0.17 11.89 -11.56 22.46

Coefficients of correction function for two different versions of the empirical model are presented in table 5.

E. Comparison of adjusted models

Comparison of error values for selected models before and after adjustment is presented in table 6. For all adjusted models values of ME are equal or nearly equal zero and depending on particular model this error is smaller from 3 to 10 dB. However the SEE for all models have been reduced from 2 to 10 dB depending on particular model as well.

TABLE 6VALUES OF MEAN ERROR AND STANDARD ERROR OF ESTIMATE FOR SELECTED PROPAGATION MODELS BEFORE AND AFTER ADJUSTMENT

Model Original scenario Before adjustment After adjustment ME[dB] SEE[dB] ME[dB] SEE[dB] R2

COST 231 Walfisch-Ikegami

Medium sized city and suburban areas -5.3 10.6 0.0 5.2 0.758

Metropolitan centres -10.1 16.0 0.0 5.7 0.718

ITU-R P.1411 NLoS1 (§4.2.1 of [4])

Medium sized city and suburban centres -8.4 13.4 0.0 7.6 0.5

Metropolitan centres -8.8 13.9 0.0 7.8 0.46

ITU-R P.1411

NLoS1 (§4.2.2 of [4]) Suburban areas -4.5 10.0 -0.1 5.0 0.785

Multi-variant empirical model

LOS1 3.8 8.3 0.0 5.3 0.752

NLOS1 3.0 7.6 0.0 5.3 0.752

Apart from these two parameters, very important is a coefficient of determination R2, which is a statistical measure of how well the adjusted model approximates the real path loss values. The coefficient of determination is calculated as a ratio of the regression sum of squares and total sum of squares, what may be expressed by following equation [12]:

2

2 2 , , , , 1 1 N N c i m av m i m av i i R

¦

L L

¦

L L , (21)

where Lm,av – averaged value of measured path loss and other parameters have the same meaning as in (6) and (7).

Taking this parameter under consideration, as well as the ME and the SEE, the adjusted ITU-R P.1411 (§4.2.2) model is the best matching to experimental data.

V. CONCLUSION

There is no propagation model for designing mobile radio networks in container terminal environment, so in practice other models are used. Four of them have been selected to adjustment in order to estimate the path loss in investigated environment. Firstly – basing on measurements results – they have been evaluated in this scope and the analysis has shown, that the adjustment is needed. This modification improved significantly the accuracy of path loss modelling. For the best adjusted model – ITU-R P. 1411 (§4.2.2) – the mean error equals -0.1 dB, the standard error of estimate equals 5 dB, and the coefficient of determination is 0.785. This results means that the adjusted model fits very well to experimental data.

Currently, further work focuses on developing new

propagation model for designing mobile radio links in container terminal environment, taking into account additional independent variables, specific for this environment.

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