TY - JOUR

T1 - A note on uniform power connectivity in the physical signal to interference plus noise (SINR) model

AU - Avin, Chen

AU - Lotker, Zvi

AU - Pasquale, Francesco

AU - Pignolet, Yvonne Anne

PY - 2012/9/28

Y1 - 2012/9/28

N2 - 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 α. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if α>1 as well as in two-dimensional grids if α>2. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(logn) and Ω(lognloglogn) for α=2 and Θ(n2 α-1) for α<2, respectively. If nodes are distributed uniformly at random on the interval [0,1], a regular coloring of O(logn) colors guarantees connectivity, while Ω(loglogn) colors are required for any coloring.

AB - 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 α. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if α>1 as well as in two-dimensional grids if α>2. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(logn) and Ω(lognloglogn) for α=2 and Θ(n2 α-1) for α<2, respectively. If nodes are distributed uniformly at random on the interval [0,1], a regular coloring of O(logn) colors guarantees connectivity, while Ω(loglogn) colors are required for any coloring.

KW - Connectivity

KW - Network capacity

KW - Physical model

KW - Signal to interference and noise ratio (SINR)

KW - Unit disk graphs

UR - http://www.scopus.com/inward/record.url?scp=84864741904&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2011.12.066

DO - 10.1016/j.tcs.2011.12.066

M3 - Article

AN - SCOPUS:84864741904

VL - 453

SP - 2

EP - 13

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -