In this work, we design and analyze transmission range assignments
for broadcasting in wireless multi-hop networks. Moreover, we study different
features of wireless networks. We consider network scenarios in which the exact
location of the nodes is known and others where the nodes location is known
probabilistically. For the former, we propose optimal and near-optimal
algorithms to solve the Minimum-Energy Broadcasting problem for linear
(one-dimensional) networks. We further extend our solutions to encompass cross
networks, in which the nodes are located on two perpendicular lines. The
proposed algorithms have polynomial-time complexity, and are shown to perform
better than previously known algorithms (for some cases, they are the first
polynomial-time solutions).
For probabilistic networks, we propose a transmission range
assignment such that for a given average total consumed power, the linear
network is connected with high probability. We then analyze some features of
these networks, including derivation of exact formulas for the probability of
connectivity of any location of the network to the source, the hop-count
probability mass function (pmf) of an arbitrary
location of the network, and the pdf of the maximum coverage (last reachable
distance from the source) for a given number of hops. The proposed analyses are
applicable to networks with non-identical transmission range assignments, where
the nodes are placed independently and identically according to a Poisson
distribution with an arbitrary density function.
Based on the derived formulas, we then propose localization and
location verification methods. We show that our proposed localization method
not only has a competitive performance for a range-free method, but also
outperforms range-based methods with a local distance measurement error of 10%
or more. Furthermore, the proposed location verification protocol is shown to
have better results compared to the existing verification systems that also use
the hop-count information. We also evaluate the proposed schemes in the
presence of Rician fading and show that their
performance is rather robust with respect to the change in the fading
parameter.