title: How does this RSSI vs Distance equation work?
body: <p>I came across this equation in a <a href="http://www.ijitee.org/attachments/File/v2i2/A0359112112.pdf" rel="nofollow noreferrer">research paper</a>, and can't seem to make sense of it.  Let me give an argument for why it doesn't make sense, and perhaps someone can tell me where my flaw is?</p>
  
  <p><img src="https://i.stack.imgur.com/PQ0vV.png" alt="Equation"></p>
  
  <p>P_L(d_0) is the RSSI value for distance 0</p>
  
  <p>P_L(d_i) is the RSSI value for distance 1</p>
  
  <p>d_0 is distance 0</p>
  
  <p>d_i is distance 1</p>
  
  <p>So if you put the two RSSI values on the left side of the equation, you have:</p>
  
  <p>(RSSI value 1) - (RSSI value 0) = 10n * log ((Dist 1) / (Dist 0))</p>
  
  <p>Let's consider the case when distance 1 is larger than distance 0:</p>
  
  <p>(Dist 1) > (Dist 0)</p>
  
  <p>Greater distance means less RSSI, so (RSSI 1) &lt; (RSSI 0).  So the left side of the equation is negative.  The research paper states that n is normally between 2 and 4, so the "10n" part of the right side of the equation is positive, which means the log value must be negative, right?</p>
  
  <p>But that leads to a contradiction.  We said Dist 1 is greater, so the number inside the log is greater than 1, therefore the log value itself is positive.  So intuitively, we have found an equation with the left side negative and the right side positive.  What's going on??</p>
  
  <p>(The opposite leads to a contradiction too: if dist 1 is less than dist 0, we get the left side positive and the right side negative)</p>