Lee’s Model

         The approach of this model [1] in prediction of the received signal is different from others’ approaches. In this model, dimensions of building blocks get more important. Since the ground incident angles of the reflected waves are, in general, small due to the low antenna heights used in micro cells, the exact height of the buildings in the middle of the propagation path is not important [1].  Received signal is calculated as the subtraction of attenuation due to buildings from line of sight case. It is formulated as follow:

                           Pos(non-los) = Plos-aB(B)

 

where aB is attenuation due to buildings and has B blockage length.

Model is measurement based model and attenuation value based on measurements.

            Calculation of aB from measurements value as follow:

i. Calculate the total blockage length B by adding the individual building blocks as shown in figure 1. B=a+b+c

ii. Measure the signal strength Plos

iii. Measure the  signal strength Pos

iv. local means value at point A is Pos(A) , distance from the base station to mobile is d=dA, then attenuation is defined as

 

aB( B=a+b+c) =  Plos(dA)-Pos(dA)


Figure 1 [1]. Building Block Occupancy at location A

 


By depending on measurements, following formulas are derived for received power for los case and attenuation values aB.

100£d<200

 

 

200£d<1000

 

 

1000£d<5000
 

And

 


 

B < 1

1£B< 25

25£B<600

600£B<3000

3000£B

 
 
        aB = 0

             = 1+0.5log(B/10)

             =1.2+12.5log(B/25)

             =17.95 + 3log(B/600)

             =20 dB

 

             where, Pt is the ERP in dBm, d is the total distance in feet, hb is base station height in feet, B is the length of blocking in feet.

        In order take effect of hilly terrain into account, antenna height gain term is defined and overall formula becomes

Pr=Pt-aB ,

 

 

Comparison of the model with measurements carried out in different cities is given in following figures.


 


Figure 2 [18]. Comparison of the model with measurements carried out at Main Street , Irvine CA


 

 


Figure 3 [1]. Comparison of the model with measurements carried out at Main Von Carmen, Irvine CA

 

 

Moreover, in [2] comparison of the model with measurements for different routes, which are zigzag, Los, staircase, and random, are given. Following figures proves how model give accurate results.


                   Figure 4[2], Comparison of the Lee model with measurements for zigzag case


 


                     Figure 5[2], Comparison of the Lee model with measurements for Los case


 


                      Figure 6[36], Comparison of the Lee model with measurements for Stair case


 


                    Figure 7[2], Comparison of the Lee model with measurements for Random case

 

 

 

 

 [1] Lee William C.Y., “ Mobile Communications Design Fundamentals”, Wiley, New York,1993.

 

[2] W.C.Y.Lee, D.J.Y.Lee, “Microcell Prediction in Dense Urban Area”, IEEE Trans. Veh. Techno. Vol.47, No.1,1998,pp.246-253