## Section: New Results

### Interference modeling in multi-hop wireless networks

As interference plays a crucial role in ad hoc networks, these
networks are often referred to as interference limited networks.
Indeed, the network capacity is related to the radio channel reuse
which is limited by the interference. As interference results from
the summation of signals issued by concurrent transmitters, it
strongly depends on the transmitters location. The point process
used to model the nodes location is thus fundamental in any study of
such networks. In previous works, the spatial distribution of the
radio nodes has generally been modeled thanks to a Poisson point
process. However, the Poisson point process is accurate for very
sparse networks only and suffers from a lack of realism in dense
ones. It relies on the assumption that transmitters are
independently distributed whereas in practice, the Medium Access
Control (MAC) protocol defines medium access rules to avoid
collisions and by this way introduces a spatial correlation between
the transmitters. Therefore, the spatial independence does not hold.
Recent works already tackle this problem by modifying the initial
Poisson process according to the mechanisms of a CSMA/CA protocol
and use the well known Matérn point process. However, this
approach still suffers from two strong limitations. First, it tends
to underestimate the number of concurrent transmitters and as a
consequence, the interference level is strongly under-estimated in
dense networks. Second, it assumes that a transmitter defers its
transmission if it detects a busy medium due to the nearest
previously selected transmitter. Albeit, medium access policies may
rely either on carrier detection or on energy level. In the case of
carrier detection, the inhibition model can be effectively related
to the strongest signal, according to the Matérn selection
process. However, in the case of energy detection, the candidate
transmitter does not defer its transmission according to the
strongest interference but rather to the interference level induced
by all effective transmitters. In this case, the inhibition process
should be related to all concurrent transmitters and inhibition
balls are not adequate. In [12] , we
investigate original processes that comply with the CSMA/CA
policies. We propose the use of the *Simple Sequential
Inhibition* point process to model CSMA/CA networks where carrier
detection depends on the strongest emitter only. This point process
is then extended to a family of new point processes modeling
effective transmitters in a busy medium detection mode based on the
strength of all concurrent signals. The impact of these different
models on the interference distribution is evaluated and we
highlight large variations with respect to the different point
processes. In particular, we show that the use of a Poisson process
is generally inaccurate to model CSMA/CA networks. We finally study
the theoretical Bit Error Rate resulting from the different point
processes.