Description

Problem 1: Finding the Path Loss Exponent
The steps followed to find the path loss exponent were as follows:
• I connected my mobile phone with other phone’s hotspot. Then, I identified the hotspot phone to which my mobile device is connected and made sure that the app was able to identify the connected WiFi AP.
• Then, I varied the distance between the transmitter (WiFi AP – hotspot mobile in this case) and the receiver (mobile phone) and measured the RSSI strength of the signal in four different orientations of the mobile phone at each distance.
• Then using the following formula (ignoring the noise term)
(1)
(2)
The above equation is a equation of line with Pr(d) on the y−axis, log10d on the x−axis and slope of −10n.
• I plotted the RSSI strength(in dBm) on y-axis and the log10(d) on x-axis and find the best fit line and divide the obtained slope of line with -10 to get path loss exponent.
• The data observed is attached below along with the graph.

Figure 1: RSSI(dBm) and distance(m) data

Figure 2: Graph for best fit line(RSSI vs log(distance)
From the above plot we can observe that:
(a) Slope of the best fit line = −18.452 Path loss exponent
(b) Variance of the samples wrt the best fit line can be found out by using the following formula.(Calculations can also be seen in the attached excel sheet)
(3)
So by applying the above formula to the graph points, we get
V ariance = 1.994975834 (4)
Problem 2: Range Estimation
The steps followed to do range estimation are as follows:
• Fix d0 = 1m and then find Pr(d0), which is receiver’s RSSI strength at distance of 1m.
• Now by varying the distance, take different samples of RSSI strength at different position(Pr(d)).
• Now log the values in the below formula to find the theoretical calculated distance and compare it with the observed distance values. Use the path loss exponent(n) calculated above.
(5)

Figure 3: Data for calculated distance and average error
From the above table and graph data, calculate the distance as
(a) We calculate the distance using the following formula
(6)
(b) Calculate the average error using
(7)
Average error = 0.5758169 m
Observations
(a) In Problem1, the data was measured in a building by keeping the hotspot phone(the tranmitter) within the line of sight of the receiver. The experiment was performed in a obstruction-free environment, with no obstacles in between the transmitter and receiver. Hence the observed value of path loss exponent is 1.8452 which is close to ideal range of 1.6 − 1.8 in the same environment.
(b) The average error between the distance estimated using the method and the actual distance is 0.5758169, indicating good path loss exponent findings.