OPTIMIZATION AND APPLICATION OF W.C.Y LEE MICRO-CELL PROPAGATION MODEL IN 850MHZ FREQUENCY BAND

Ivica Kostanic

Florida Institute of Technology, Melbourne, FL

Ivan Guerra, Nizar Faour, Josko Zec and Mladen Susanj Agilent Technologies, Melbourne, FL

ABSTRACT

One of the most popular models for macro-cellular path loss predictions is the Lee model. An extension of this model to the micro-cellular environment requires utilization of building database data. This paper proposes a simple and computationally efficient method for path loss prediction that is based on the Lee micro-cell model and that takes the effects of buildings into account. The performance of the proposed method is validated through extensive comparisons between measured data and model predictions. The comparisons show that, when properly optimized, the proposed approach can achieve an accuracy characterized with standard deviation of the prediction error that is around 6dB.

1. INTRODUCTION

The increase of a cellular system’s capacity requires tighter reuse of the allocated spectrum and deployment of smaller cells. As a result, within high traffic areas, the majority of existing commercial systems deploy a large number of micro-cells. In the micro-cell deployment, the cell site antennas are mounted at low radiation centerlines and therefore, the RF signal propagation is heavily affected by the cell site surroundings. Consequently, for accurate propagation modeling in the micro-cell environment, the effects of buildings have to be taken into account.

There are several approaches to micro-cell propagation modeling ranging from simple two-dimensional statistical predictions to highly sophisticated and computationally intensive ray-tracing techniques. Regardless of which approach is adopted, the model usually faces a tradeoff between the complexity and achievable accuracy. The approach considered in this study is based on the micro-cell model proposed by Lee [1]. To perform the path loss predictions, the model utilizes three-dimensional building data alongside with high-resolution terrain. As such, it represents an extension of the well-known and widely accepted Lee macro-cell propagation model [2].

The outline of this paper is given as follows. Section 2 specifies the proposed implementation of the Lee micro-cell model. Keeping general ideas presented in [1], the implementation uses building correction factors of a more general form. Section 3 provides a methodology for model tuning. Two methods for tuning the Lee micro-cell model are discussed. The derivations of the two methods are

presented along with the guidelines on how they should be used to achieve the highest prediction accuracy. Section 4 documents the results obtained in the validation of the proposed modeling approach. During the validation phase, the model predictions are compared against measurements collected using several micro-cells of a live cellular network. The network considered in this study is deployed in urban and dense urban environments of Miami, FL.

2. LEE MICROCELL MODEL

Generally speaking, a micro-cell is defined as a cell located in a dense urban area that has a relatively small coverage footprint. The radiation centerlines of micro-cells are at low heights and the radiated power rarely exceeds a few watts. In a micro-cell environment the impact of objects that are within the cell’s vicinity is much more pronounced than in the case of macro-cell modeling. For that reason, a standard input to the micro-cell model is a building database. In recent years, the availability of building data information has increased and the data has become considerably less expensive. As a result, micro-cell modeling is becoming a standard part of the network planning process in dense urban and urban propagation environments.

Within Lee’s micro-cell model, the prediction of the path loss is determined as a function of terrain and building database. The actual formula of the model is given as [1]

BLOSp LL α+= (1)

where pL is the median path loss, LOSL is the median path

loss for locations unobstructed by buildings, and Bα is the correction factor due to building blockage. All quantities are expressed in dB.

The path loss for locations that are not obstructed by buildings is calculated in accordance with

( ) ( ) DLhhddrLL BSrefBSrefrefLOS +−+= log15log (2)

where d is the distance between the transmitter and the receiver expressed in feet, r is the slope of the path loss expressed in dB/dec, refL the path loss at the reference

distance in dB, and BSh is the radiation centerline expressed

in feet. The parameters refd and BSrefh are suitable chosen

reference distance and reference antenna centerline. For the work presented in this paper they are set to 100 and 10 feet respectively. The term DL in (2) represents diffraction losses for locations that are obstructed by the terrain.

The path loss expression given in (2) is slightly different from the original Lee’s formulation [1]. The original Lee micro-cell model differentiates between ‘F-zone’ and the far field. The measurements performed as a part of this study did not confirm the existence of a well-defined ‘F-zone’. For that reason, that part of the path loss equation is somewhat simplified. Additionally, it has been noticed that the path loss depends on the radiation centerline. Hence, an additional term that takes the centerline height into account has been added. The added term is consistent with Lee’s macro-cell model [2].

The effects of building obstructions are modeled through a correction term Bα . The value of this correction is proportional to the length of the radio path obstructed by buildings. To clarify the case in point, consider the radio path between transmitter and receiver shown in Fig. 1.

Bd

Ad

X

X

TX

RX

Figure 1. Illustration of the building correction factor

The total normalized length of the obstructed radio path in Fig. 1 is given as

( ) BrefBA dddx /+= (3)

where refBd is a suitably chosen reference distance. For the

study reported in this paper, 10=Brefd feet. Using the

normalized length given in (3), the building loss factor is calculated as

( )xfB =α (4)

where ( )of is a monotonically increasing function of its argument. Within the original description of Lee micro-cell model [1], the format of ( )of is not specified. For the implementation suggested in this paper, the form of the function is provided as

( ) ( )xcbxaxf log++= (5)

The coefficients a, b and c are determined empirically through the analysis of measured data.

3. MODEL TUNING

The goal of model tuning is to minimize the difference between path loss measurements and corresponding model predictions. In the tuning process, the parameters Lref, r, a, b, and c from (2) and (5) are determined so that the overall mean-squared prediction error is minimized. For each measurement point, the difference between measured and predicted path loss values is given by

pimii LL −=δ (6)

In (6), miL represents measured path loss, piL is the path

loss predicted by the model and the index i indicates the ith of N measurement points.

An equation of the form given in (6) can be written for each path loss measurement. By substituting (2) and (5) into (6), the prediction error can be presented in a more compact vector-matrix form given by

ξδ Ay −= (7)

In (7), 1×ℜ∈ Nδ is the vector of differences between measurement and predictions, 15×ℜ∈ξ is the parameter vector given by

[ ]Tref cbarL=ξ , (8)

and 1×ℜ∈ Ny is a column vector in a form

T

BSref

BSmN

BSref

BSm DL

hh

LDLhh

L

+

−+

−= log15,,log151 Ly (9)

The matrix 5×ℜ∈ NA is given by

( )

( )

=

NNNNNref

N

ref

xSxSBdd

xSxSBdd

loglog1

loglog1 111111

MMMMMA (10)

where 1=iS for points obstructed by buildings and 0=iS

for unobstructed points, and 1=iB for points inside the

building and 0=iB for outdoor points. The tuning process seeks to determine values for the

parameter vector ξ that would minimize the norm of the error vector δ . As a part of this study two approaches are considered.

Approach 1 – Joint Local Optimization (JLO). In this approach, the values of the model parameters are obtained through minimization of the cost function given by

( ) δδξ TJ21

= (11)

Substituting (7) into (11) and solving for the minimum, yields [3]

( ) yAAA TT 1−=ξ (12)

The JLO method solves for all parameters of the model simultaneously and generally provides the best fit to measured data. However, although numerically optimal, the values for the parameters may not be physically intuitive and they may vary substantially from cell to cell.

Approach 2 – Two Step Optimization. In this approach, the search for optimum values of model parameters is performed in two steps. In the first step, the values for refL

and r are found using only the path loss measurement obtained at the points that are not obstructed by buildings. Using linear regression, the two parameters of the model can be calculated in accordance with

[ ] ( ) NOTTT

ref rL yAAA 11

11−

= (13)

where 1A is obtained from the first two columns of matrix A given in (10) by retaining only rows corresponding to unobstructed points. The vector NOy is obtained from y in (9) in the same fashion. After refL and r are determined, the

coefficients a, b and c are calculated in accordance with

[ ] ( ) 221

22 yAAA TTTcba−

= (14)

where 2A is obtained from the last three columns of matrix A given in (10) by retaining only the rows corresponding to obstructed points and the vector 2y contains elements given as

iBSref

BS

ref

irefmii DL

hh

dd

rLLy −

+

−−= log15log2 (15)

where obsNi ,,2,1 L= , obsN is the number points obstructed by buildings and the values for refL and r are the ones

obtained from (13).

4. MODEL VERIFICATION

To verify the model proposed in Section 2, a drive-test measurement campaign was undertaken in urban and dense urban areas in Miami and Miami Beach. The purpose was to collect empirical data and compare them with micro-cell model predictions. The model was tuned according to the procedure outlined in Section 3. Both approaches derived in that section were investigated. For this validation, operational on-air transmitters from a major cellular provider were leveraged and measurements of received signal level

(RSL) coming from these transmitters were recorded. From the averaged RSL samples, the mean path losses miL were estimated in local areas.

The Lee micro-cell model and tuning techniques have been implemented in Agilent Technologies WIZARD RF propagation software tool [4]. WIZARD is a flexible platform that, among others features, allows integration of terrain elevation and clutter maps, site configuration and building databases, and various macro- and micro-cell propagation models. A project was generated in WIZARD to reflect the exact configuration of measured 3 sites. Within these sites, a total of 5 transmitters were drive tested sufficiently to establish a statistically valid dataset. Within WIZARD, measured data were averaged into geographical bins. A difference between average measurement and prediction (δi in (6)) is available at each bin containing path loss measurements. The performance of the prediction model can be evaluated from these differences.

Applying the Lee micro-cell model and both tuning methods from Section 3, results summarized in Tables 1-2 are obtained. Table 1 summarizes the Joint Local Optimization and Table 2 applies to the Two Step Optimization. If measurements are accepted as an accurate representation of the path loss in a bin, the mean and the standard deviation of measurement errors is an indication of the prediction accuracy. Both methods will bring the mean measurement error to zero. The standard deviation σ can be defined as:

)var(δσ = (16)

where var(δ) indicates the variance of the vector of differences defined in (7). According to this indicator, both tuning methods give almost identical accuracy. Standard deviations range between 5.3–6.6dB, as seen from the last column of Tables 1-2. These low values for standard deviation of measurement errors rank better than typical standard deviations observed in dense urban environments that are often as high as 8-10dB.

In addition to the standard deviation, tables also report tuned model parameters (elements of parameter vector ξ defined in (8)). This vector includes the path loss at the reference distance in dB (intercept Lref), the rate of increase of path loss with logarithm of distance expressed in dB/decade-of-distance (slope r), building loss factors b and c, and the number of points used in the comparison for each transmitter. Note that since no measurements were taken inside buildings, the constant building attenuation term (a in (5)) was not available for the tuning process.

Table 1. Summary of model optimization using Joint Local Optimization Transmitter Lref Slope b c N σ EFOFR 3 128.4 31.2 2.3 .006 394 5.3 F1 Tx1 125.5 29.3 2.3 .03 87 5.6 F1 Tx2 128.1 37.7 2.5 .01 137 6.5 F1 Tx3 132.4 29.5 2.0 .003 130 6.2 FEFO 1 126.5 35.4 1.3 .007 395 5.5 Table 2. Summary of model optimization using Two-step Optimization Transmitter Lref Slope b c N σ EFOFR 3 132.2 28.7 2.2 .007 394 5.3 F1 Tx1 127.6 27.6 2.5 .026 87 5.6 F1 Tx2 123.6 41.5 2.5 .011 137 6.6 F1 Tx3 131.0 30.7 2.0 .003 130 6.2 FEFO 1 131.0 32.3 1.2 .005 395 5.6

Another illustration of the accuracy of the model is presented in Fig. 2-3. Sector 1 of site FEFO is chosen as the most statistically valid set (395 points taken). Predictions calculated using initial default microcelular propagation parameters and no building loses are compared with predictions from the tuned model. Figure 2 shows a scatter plot of predicted vs. measured points for default and tuned models. The ideal zero-mean, no-scatter line is shown as reference. The default model badly under-predicts when compared with measured data. Improvement introduced by the Joint Local Optimization tuning technique is obvious from the tight fit of tuned predictions to the reference line.

Figure 2. Scatter plot of optimized and default model

predictions vs. measured data

Similar improvement can be observed from the histogram of measurement errors shown in Fig. 3. Histograms for both the default model and the tuned Lee micro-cell model are shown. Removal of the bias and tighter grouping around zero are shown for the optimized model.

Figure 3. Histograms of measurement errors for default

and optimized micro-cell models

The performance demonstrated in Figs. 2-3 clearly qualifies this implementation of Lee micro-cell model as a suitable candidate for propagation prediction in dense urban environments when building data is available.

5. ACKNOWLEDGEMENTS

This work is supported by Agilent Technologies and the Wireless Center of Excellence at Florida Tech. The authors would like to acknowledge the contribution of Tibor Susanj during the measured data collection process.

6. REFERENCES

[1] W. C. Y. Lee and D. J. Y. Lee, “Microcell predictions in Dense Urban Area,” IEEE Transactions on Vehicular Technology, Vol. 47, No. 1, Feb. 1998.

[2] W. C. Y. Lee, Mobile Cellular Telecommunications, McGraw Hill, 1995.

[3] F.M. Ham and I. Kostanic, Principles of Neural Networks for Science and Engineering, McGraw Hill, 2000.

[4] Agilent Technologies, WIZARD Users Manual, Agilent Technologies, 2003