  Carrier Sense Multiple Access (CSMA) MAC protocols are known to suffer from
the hidden station (HS) problem. The complete mathematical analysis of CSMA
networks with HSs is still an open problem, even for broadcast communication
with a simple linear network topology. In this paper we address this challenge
by introducing a MAC layer modeling methodology based on time- and space-domain
Markov processes. Using this methodology we derive the closed-form solution for
the steady-state performance in infinite one-dimensional (1-D) CSMA networks
with HSs. The analytical results are validated by simulation and establish
that: 1) under the assumption of fixed frame duration, if the conditional
channel access probability at each station exceeds a certain threshold, the
CSMA system enters the status of "synchronized transmissions", where a large
number of adjacent stations transmit in overlap and interfere each other
resulting in null system goodput. 2) The maximum system goodput of CSMA
broadcast communication increases with increased station density but becomes
increasingly sensitive to the conditional channel access probability. In [25]
we validate the analytical results gained in this paper by simulation of a
multi-lane highway scenario, and provide quantitative guidance for congestion
control algorithms in vehicular networks.
