Capacity bounds for large scale wireless ad hoc networks under Gaussian channel model

Abstract

We study the capacity for both random and arbitrary wireless networks under Gaussian Channel model when all wireless nodes have the same constant transmission power P. During the transmission, the power decays along path with attenuation exponent beta > 2. We consider extended networks, where n wireless nodes {v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,hellip, v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> } are randomly or arbitrarily distributed in a square region B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> with side-length a. We randomly choose n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> multicast sessions. For each source node v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , we randomly select k points p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</sub> (1 les j les k) in B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> and the node which is closest to p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</sub> will serve as a destination node of v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> . We derive the achievable upper bounds on unicast capacity and an upper bound (partially achievable) on multicast capacity of the wireless networks under Gaussian Channel model. We found that the unicast (multicast) capacity for wireless networks under Gaussian Channel model has three regimes.