  In this work, we consider the random access of nodes adapting their
transmission probability based on the local channel state information (CSI) in
a decentralized manner, which is called CARA. The CSI is not directly available
to each node but estimated with some errors in our scenario. Thus, the impact
of imperfect CSI on the performance of CARA is our main concern. Specifically,
an exact stability analysis is carried out when a pair of bursty sources are
competing for a common receiver and, thereby, have interdependent services. The
analysis also takes into account the compound effects of the multipacket
reception (MPR) capability at the receiver. The contributions in this paper are
twofold: first, we obtain the exact stability region of CARA in the presence of
channel estimation errors; such an assessment is necessary as the errors in
channel estimation are inevitable in the practical situation. Secondly, we
compare the performance of CARA to that achieved by the class of stationary
scheduling policies that make decisions in a centralized manner based on the
CSI feedback. It is shown that the stability region of CARA is not necessarily
a subset of that of centralized schedulers as the MPR capability improves.
