1. INTRODUCTIONInteraction of EM waves with materials having dierent electrical properties than the material through which the wave is traveling leads to transmitting of energy through the medium and reection of energy back in the medium of propagation. The amount of energy reected to the amount of energy incidence is represented by Fresnel reection coecient , which depends upon the wave polarization, angle of incidence and frequency of the wave. For example, as the EM waves cannot pass through conductors, all the energy is reected back with angle of incidence equal to the angle of reection and reection coecient = 1.

Figure 1: two-ray ground reflection model

Seldom in communication have systems encountered channels with only LOS paths and hence the Friis formula is not a very accurate description of the communication link. A two-ray model, which consists of two overlapping waves at the receiver, one direct path and one reected wave from the ground gives a more accurate description as shown in Figure 4.2. A simple addition of a single reected wave shows that power varies inversely with the forth power of the distance between the Tx and the Rx. 2. RESULT AND ANALYSIS

Matlab codeclear all;clc; ht=50;hr=1.5;x=0:200:2000;d=2000;d0=1000;e0=1e-3;Gr_db=2.55;gr=1.8;gt_db=0;fc=900e6;c=300e6; lamda=c/fc;e=(2*e0*d0*2*pi*ht*hr)/(d^2*lamda)ae=(gr*lamda^2)/(4*pi);pr=(e^2*ae)/(120*pi)pr_db=10*log10(pr)pl_db=40*log10(d)-(gt_db+Gr_db+20*log10(ht)+20*log(hr))pl_db_1=40*log10(x)-(gt_db+Gr_db+20*log10(ht)+20*log(hr)); plot(x,pl_db_1,'--')xlabel('Distance between transmitter and reciever');ylabel('Pathloss in dB');title('Two-ray ground reflection modle');

The result obtained in this experiment was finding the followinga) The electric field variationb) The received power in W at mobile station c) The received power in db at mobile station d) Path loss in dbe) Analyze the results above when the carrier frequency is changed to i. 1800MHzii. 1900MHzTherefore the results obtained for the path loss will be plotted against the distance between the transmitter and the receiver as shown in figure 1.The result that will be obtained is three parts which are the three carrier frequencies an the results above will be obtained for each carrier frequency.Firsly, I simulated the for 900MHz and then 1800MHZ and 1900MHz.a) 900MHz

Figure 2: Calculation result in matlab for 900MHz signal

As you can see the results are summarized belowf) Electric field=0.70686mV/mg) Received power=2.1094x10-11h) Received power in db =-106.7585dbi) Path loss in db= 87.4025dbThe path loss plotted against the distance is shown below

Figure 3: path loss vs. distance for 900MHz signal

b) 1800MHz

Figure 4: results for 1800MHz

a) Electric field=1.4mV/mb) Received power=2.1094x10-11c) Received power in db =-106.7585dbd) Path loss in db= 87.4025db

Figure 5: path loss vs. distance for 1800MHz signal

c) 1900MHz

Figure 6: results for 1800MHz

a) Electric field=1.4mV/mb) Received power=2.1094x10-11c) Received power in db =-106.7585dbd) Path loss in db= 87.4025db

Figure 7: path loss vs. distance for 1800MHz signal

When the carrier frequency was changed the only thing that changed was the electric field while the rest such as the received power and path loss didnt change.

3. DISCUSSIONThis experiment was about two ray modelling, which is useful propagation model that is based on geometric optics and considers both the direct path and ground reflected propagation path between transmitter and receiver as shown in figure 1. This model has been found to be reasonably accurate for predicting the large scale signal strength over distances of several kilometers for mobile radio systems that use tall towers (height which exceed 50m), as well as for line of sight microcell channel in urban environments.Therefore, in this experiment, I have calculated the electric field variation, the received power in Watt and decibels at mobile station and path loss in decibels for the signal. The carrier frequency was also changed to 1800MHz and 1900MHz. the path loss of the two ray model for a 2km distance was also plotted. The path los graph shows that as the distance between the transmitter and the receiver increases, the loss will increase.When the carrier frequency was changed to 1800MHz and 1900MHz, the path loss didnt change that much but the electric field will change.The received signal in the receiver contains two signals which are the one received directly from the transmitter antenna at a line of sight while the other one is the one that reflected from the ground. The one reflected from the ground is not as strong as the one that was obtained directly from the transmitter and it contains a lot of losses.

4. CONCLUSIONThis experiment was about two ray ground propagation modelling. We have learned how to calculate the electric field variation, the received power at mobile station and the path loss. The path loss increases as the distance between the transmitter and the receiver increases. The received signal in the receiver contains two signals which are the one received directly from the transmitter antenna at a line of sight while the other one is the one that reflected from the ground.

5. REFERENCES

[1]. T. S. Rappaport, Wireless Communications: Principles and Practice, 2nd ed. [2]. J. W. Mark and W. Zhuang, Wireless Communications and Networking. New Delhi: PHI, 2005.[3]. Goldsmith, Andrea (2004).Wireless communications(1. publ. ed.). Cambridge, U.K.: Cambridge University Press. [4]. S. Ahmed, G. C. Karmakar, and J. Kamruzzaman.[5]. An Environment-Aware Mobility Model for Wireless Ad Hoc Network. Elsevier Computer Networks, 54(9):1470{1489, May 2010.

6. APPENDIXFormulas used to calculate the electric field, received power and the path loss are shown belowPath loss in dB

Received power

Electric field when the distnance is much greater than the square root of the product of transmitter and receiver height.