Modelo Lee

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Lee s ModelBY

W. C. Y. LeePacTel Corporation

Walnut Creek, CA

bsuact

Lee's Model ) is used to predict the local-mean of areceived signal along a mobile path where the mobile unittravels. The standard derivation of prediction error by com-paring the predicted values with the measured data s approxi-mately 2-3 dB. The model is simple to implement and has ath ory to back t.

Most prediction models are used to predict the pathlossalong the radio path. The radio path is the path fiom the base-station antenna to the mobile-station antenna. The pathlosscurve is generated from the measured data received along themobile path and ploued along the radio path. The standarddeviation is about 6-8 dB. Since a large standard deviationfrom the prediction is hard to use o design a cellular system,Lee's Model(') is used to predict the local mean along themobile path.

11. TheP hilosoDhv of Forming Lee Model

In a mobile radio environment, due U the fact that themobile antenna height is very close to the ground, the mobilesignal received from the base tation is affected by two factors.

One is due to the strong ground reflection which depends onthe natural terrain contour along the radio path. The other isdue to the different human-made structures which result indifferent excessive loss in different geographical areas.

These two causing factors are imbedded in the receivedsignal. In this model we try to predict two factors separately:

A. Caused by the human-made structures only

The human-made structures are different in differentcities and the terrain contours are not flat and vary from areato area. If we try to obtain the received signal attenuation onlycaused by the human-made structures, hen the terrain contourin the area has to be flat which is impossible in reality.However, the average process of elevations at different spotsbut at the sameradio-path distance would wipe out the terrainvariation. Therefore, a pathloss curve with a careful averagingprocess on the elevations would provide the signal attenua-

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e = p,,,(;) a. (in milliwatts)= p , - Oylog ( d / d , )+a in dBm) (1)

tion caused by the human-made structures only as shown inFig. 1.

where P is the received power in milliwatts at the distanceof do which can be 1 mile or 1 km, d is the distance with the

same unit as do and yis the slope of the pathloss in mobile radioenvironment. 1Oyrepresents he dB value per decade. a. s theconnection factor when the actual condition is different fromthe reference conditions which are specified as:

h, - antenna height at the cell site - 100 ft (or 30 m)GI - antenna gain at the cell site - 6 dBdP, - transmission power - l owhz-antenna height at the mobile unit - 10 ft (or 3 m)Gm antenna gain at the mobile unit - 0 dBd

The pathloss curve of the suburban areas can be ex-

p , = (P - 46) - 61.7 dBm - 38.4logd +pressed as:

2 0 1 4 ) + lo log^+ G ,100where P is the ERP in dBm, d in miles, h, and h, in feet andGmin dBd. By setting Gm= dBd, Eq (2) can be simplifiedas follows:

p , = p . 1 0 - ~ . ~ ~d3' h2 (milliwatts) (3)

If PI of 32 dBu is received, then use the conversionbetween dBu and dBm at 850 MHz, dBm (=) dBu - 132, thevalue of 32 dBu converts to -100 dBm.

Substituting PI = 100 dBm into Eq (4) yields

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d = 0. 348 h,0*5m Po*=) in miles 5)

J3q (5) is the contour for a received power P, equals 32mu.

B. Adding the cause of terrain contour

For calmkiting the additional changes in the receivedsignal due to the terraincontour, we need an accurate terraindatabase. There re four Conditions based on the terraincontour situations which c n be t a t ed

1. In a non-obstructive condition

Firstwehavetof~dthespecularrefl~tionpoint(seeFig.2 at which the tangential line of that ground c w m sinterceptingat the cell-site mmna location. 'I 1 heefkc-rive antenna height is o b t a i d by measuring the height fromthe ntercepting point to the antenna.

The antenna-height-gain factor is Ga

hG 2Olog-Lhl

2. In an obstructive condition

We c n fmd the knife-edge diffiraction loss which isillustrated in Fig. 3 with a parameter v

7)

3. The condition of land-to-mobile over water

In this condition, there are wo specular reflected wavesas shown in Fig. 4. The three waves, one direct wave and tworeflectedwavesaddedatthemobilenctiva. esulu n a fkespacelos@.

4. The condition of land-to-boat over water

In this condition see Fig. 3 theR is only one strongspecular eflected wave over the water, the result is the sameas open-area pathloss curve.

III. A Normalell Model

Thed - c e l l model is used for acell gre ter than 1 kmin diameter and c n be f m e d a s shown in Table 1.

VII m Model

When the size of the cells is small, less than 1 Km, thestreet orientation and individual blocks of buildings make adifference n signalreception, smen t idpv ious ly. Thosestreet aientations and individual blocks of buildings do notmake any noticeable difference in reception when this signalis well attenuated t a distance over 1 Km. Over a largedistance, he elatively gre t mobile radio propagation oss of4 dB/dec is due to the situation that two waves, direct andreflected. re more or less equal in strength. The localscatterers, i.e., buildings surrounding the mobile unit, reflectthis signal causing only the multipath fading not the pathlossat the mobile unit. When hc ccb are mall, the ignal arrivingat the mobile unit is blocked by the ndi- buildings whichweakens the signal strength and is considered as part of thepathloss. Therefore we have to take nother approach in ourprediction,tobedescribedinthbsectian. nsmallcellswearecalculating the loss based on the dimensions of the buildingblocks. Since the ground incident angles of the waves are, ingeneral, small due to the low antenna heiihts used in smallcells, the exact height of buildings in the middle of the

propagation paths is not important. as shown in fig. 6. Therefore, only a top-view aerial photo map is used. Wecanuse air photos to calculate the praportional ength of the directwave path being attenuated by the buiiding blocks. When hewave is not being blocked by the building it is a line-of-sightcondition. From the measurement data along the streets n anopen ine-of-sight condition w e find the lineof-sight signalreception P Also, rom the measured signal Pa long thes t r ee t s in out-of-sight conditions within the cells, we find theadditional signal attenuation formula due to the ponion ofbuilding blocks over the direct path by subtracting the re-ceived signal from p,,,,. The steps for forming an additionalsignal attenuation formula a are as follows:

1. Calculate the total blockage lengthB by adding theindividual building blocks. For example, B = a +b +c at pointA shown in Fig. 7.

2. Calculate the signal strength PIa for line-of-sightconditions.

3 Measure the signal strength Pa for out-of-sight con-ditions.

4. The local mean at point A is Pa (at A). The distancefrom the base to the mobile unit is d,. The blockage length Batpoint A isB =a + b+ c. Then the value of for a blockageof B can be expressed as:

a, @ = a + b + c) P (d = d,)- Pa at d,)

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Then the additional signal attenuation curve based on thebuilding blockage is found experimentally as shown in Fig. 8. The curve was obtained at Irvine, California. The curveshows the rapid attenuation occurred while B is less than 500ft- When B is greater than 1 OOO ft-, a nearly constant value of20dB attenuation s observed. It c n be explained by the streetcomer phenomenon as shown in Fig. 9. The rapid attenuationwas seen on he mobile signal during the turning from one

street to anotheras

B starting from 0 and increasing. After Breaches500 thereceivedsignalstrengthP~ illremain 18dBbelow the Pb s he distance d increases. The path losses duetoa lineaf-sight condition for a series of antenna heights havebeen measured along many streets. The 9 dB/oct (or 30 dB/dec) antenna height gain over an antenna height change isusually observed n a sm ll cell, as shown in Fig. 10. It is dueto the fact that the incident angle in the small cell is usuallylarger than 10 . In the smallcell prediction model we use thetwo urves, P and to predict the received signal strength.Therefore, the Microcell (small cell) model can be formed as:

Where P is the line-of-sight pathloss (measured) andis the additional loss due to the length of the total buildingblocks B along the paths.

The expression to be evaluated is:

P = 9 + 10(ye )log dl (From Fig. 9) (9)4

a = 10(y,)logB (From Fig. 9) (10)

Where Po s the intercept point at a distance do d, is thetot l distance. Usually d, is smaller than do n the small cellprediction. yo is the line-of-sight pathloss slope. B is thelength of blocking. y, is the slope due to blocking.

dP = c+ 1 0 ( 7 , ) 1 0 g ~ - 1 0 ( 7 , ) 1 0 g ~ (11)

d.

This Microcell model has been verified in the areas ofki ne and San Diego, California with good results, as shownin Figs. 11 and 12.

In a hilly area, Eq (8) can be modified by adding the termantenna height gain obtained from Fig. 10 as:

(12)h,9 = P, -a , Wlog-h.

The prediction from the Microcell model is not as accu-rate as hat from the normal-cell model. This is due to the facl

that we are using a statistical prediction tool to predict thesignal in more or less deterministic conditions where thepropagation distance is short.

VIII. Full Prediction Model

A full prediction model will be superimposed on thenormal-cell model and the Microcell model to predict thereceived signal strength

narange up to 15 miles. Beyond this

distance, heradio horizon may be considered. Theinterferingsignal is always weaker when it is coming from beyond theradio horizon. It can be neglected in most cases in the mobileradio system design.

Table 1 condil~ns f the normalcell model

Efleded ByReceived

C o n d l i n s Power Human-mado Srudures Natural Terrain

References

1. W. . Y. ee Lee's Model, a condensed version shown nAppendix II written by the Propagation Ad Hoc Committee of IEEEVehicular Technology Society appeared in a special issue of IEEETransactions on Vehicular Technology, February 1988. pp. 68-70.

2. W. . Y. Lee Mobile Cellular Telecommunications Sys-tems, McCraw Hill Co., Chapter 4.

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2 3 4 5 6 7 8 9 1 0, d dhraoeinmilesfonnthelnnsmiUhg.nccant)Figure 1 Propagation Pathloss In Different Areas

Figwe 2 Effective Antenna Height Calculation

figure 5 Land-To-Bo at Over Water

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-50

-60

10

-80

f :B

-90

-100

-110

1lY

i n

348istance from Antenna (feet;

Figure 12 Comparison Of ?he Measured Data AndThe Predicted Curve At Von Karmen, Irvine, CA

Modelo Lee

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