  In this paper, a sequential probing method for interference constraint
learning is proposed to allow a centralized Cognitive Radio Network (CRN)
accessing the frequency band of a Primary User (PU) in an underlay cognitive
scenario with a designed PU protection specification. The main idea is that the
CRN probes the PU and subsequently eavesdrops the reverse PU link to acquire
the binary ACK/NACK packet. This feedback indicates whether the probing-induced
interference is harmful or not and can be used to learn the PU interference
constraint. The cognitive part of this sequential probing process is the
selection of the power levels of the Secondary Users (SUs) which aims to learn
the PU interference constraint with a minimum number of probing attempts while
setting a limit on the number of harmful probing-induced interference events or
equivalently of NACK packet observations over a time window. This constrained
design problem is studied within the Active Learning (AL) framework and an
optimal solution is derived and implemented with a sophisticated, accurate and
fast Bayesian Learning method, the Expectation Propagation (EP). The
performance of this solution is also demonstrated through numerical simulations
and compared with modified versions of AL techniques we developed in earlier
work.
