Distribution of Path Loss for Wireless Personal Networks Operating in a Square Region

Path loss plays fundamental roles in system design, spectrum management, and performance evaluation. The traditional path loss model has a slight inconvenience; it depends on the unknown distance. In this letter, we explore the probability distribution function (PDF) of path loss in an indoor office environment by randomizing out the distance variable. It is shown that the resulting PDF is not Gaussian-like but is skewed to the right, and both the PDF and the moments are related to the size of the office instead of the unknown distance. To be specific, we incorporate the IEEE 802.15.4a channel parameters into our model and tabulate the cumulative distribution function with respect to different room sizes. Through a simple example, we show how our model helps a cognitive spectrum user to infer path loss information of primary users without necessarily knowing their transmitter-receiver distance.