# Estimating Path Loss from Measured 2.4Ghz/Wlan Signal Strength to get Distance

I want to estimate distances between Wlan Routers based on the RSS (received signal strength) indoors. Im fully aware that I only will get rough estimates. For that I studied some radio propagation models like the ITU model for indoor attenuation which defines path loss as:

$$L \; = \; 20 \; \log_{10}f \; + \; N \; \log_{10} d \; + \; P_f(n) \; - \; 28$$

where,

• ''L'' = the total path loss. Unit: (dB).
• ''f'' = Frequency of transmission. Unit: (MHz).
• ''d'' = Distance. Unit: metre (m)
• ''N'' = The distance power loss coefficient.
• ''n'' = Number of floors between the transmitter and receiver.
• ''P''f(n) = the floor loss penetration factor.

so to get the distance I have the formular

$$d = f^{\frac{-20}{N}} 10^{\frac{L-P_f(n)+28}{N}}$$

Now I only need the Path Loss to get the estimated distance in meters. This is defined in several places as:

Path Loss (dB) = Transimitted dBm + Receive Antenna Gain dBi + Transmission antenna Gain dBi - Received Signal dBm


But the problem is, derived from this formula, if you set 2 Routers next to each other the receiving device should see signal strength of at least 10dBm which NEVER is the case, since RSS is usually between -30dBm and -95 dBm. So therefore this formular is useless for me.

So the question is: Can anybody elaborate how to get the Path Loss from measured RSS in Wlan context? I have the info for antenna gain and transimitted power and usually know the exact model/specs.

Further Detail: The ITU Model works quite well for me when I do not calculate the path loss but just use the absolute value of the RSS (So if -40dBm, I use path loss 40 dB)

Edit: Just for the curious here are my measured RSS for a good signal AP with high sample size of 750: • Just out of curiosity how "steady" is your RSS in a still environment? I have tried something similar in nature and my data was GARBAGE. – tman Sep 30 '14 at 14:23
• See the edit for details. It is usable, I usally get mean = median = mode which can be normal or log normal distriubted with 60/80 conf intervall 2-3dbm/3-5dbm usally. Good enough for educated estimates. Testing indoors in residential area. – Patrick Favre Sep 30 '14 at 14:33
• Addendum: I use high sample size over longer period (sample size 750 over 2-3h) – Patrick Favre Sep 30 '14 at 14:39
• Ahhh thats is a huge difference in time and sample size compared to my previous efforts. – tman Sep 30 '14 at 14:44
• Do you know the transmission power? Do you know the antenna gain, both for the receiver and the transmitter? Their pattern? Can you calibrate your measurement with coaxial cable and known attenuation? – Lior Bilia Sep 30 '14 at 15:30