A note on uniform power connectivity in the physical signal to interference plus noise (SINR) model

作者：Avin Chen; Lotker Zvi; Pasquale Francesco; Pignolet Yvonne Anne^*

来源：Theoretical Computer Science, 2012, 453: 2-13.

DOI：10.1016/j.tcs.2011.12.066

• Signal to interference and noise ratio (SINR)
• Unit disk graphs
• Network capacity
• Connectivity
• Physical model

In this paper, we study the connectivity problem for wireless networks under the physical signal to interference plus noise ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously. Depending on the interference model, more or fewer colors, corresponding to the number of frequencies or time slots, are necessary. We consider the interference model that compares the received power of a signal at a receiver to the sum of the strength of other signals plus ambient noise. The strength of a signal is assumed to fade polynomially with the distance from the sender, depending on the so-called path-loss exponent alpha. %26lt;br%26gt;We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if alpha %26gt; 1 as well as in two-dimensional grids if alpha %26gt; 2. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(log n) and Omega(log n/ log log n) for alpha = 2 and Theta(n(2/alpha-1)) for alpha %26lt; 2, respectively. If nodes are distributed uniformly at random on the interval [0, 1] a regular coloring of O(log n) colors guarantees connectivity, while Omega (log log n) colors are required for any coloring.

• 出版日期2012-9-28