Capacity of large scale wireless networks under Gaussian channel model

In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes <i>v<sub>i</sub></i>(1 ≤ <i>i</i> ≤<i> n</i>) are randomly located in a square region with side-length <i>a</i> = √<i>n</i>, by use of Poisson distribution with density 1. All nodes transmit at constant power <i>P</i>, and the power decays along path, with attenuation exponent α > 2. The data rate of a transmission is determined by the SINR as <i>B</i> log(1 + SINR). There are <i>n<sub>s</sub></i> randomly and independently chosen multicast sessions. Each multicast has <i>k</i> randomly chosen terminals. We show that, when <i>k</i> ≤ θ<sub>1</sub> <i>n</i>/(log <i>n</i>)<sup>2α+6</sup>, and <i>n<sub>s</sub></i> ≥ θ<sub>2</sub><i>n</i><sup>1/2+β</sup>, the capacity that each multicast session can achieve, with high probability, is at least <i>c</i><sub>8</sub>√<i>n</i>/<i>n<sub>s</sub></i>√<i>k</i>, where θ<sub>1</sub>, θ<sub>2</sub>, and <i>c</i><sub>8</sub> are some special constants and β > 0 is any positive real number. Our result generalizes the unicast capacity [3] for random networks using percolation theory.

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