  In the state-of-the-art interference management schemes for underlay CRNs, it
is considered that all PUs are protected if the cognitive interference for each
primary receiving-point is lower than a maximum threshold, the so called
interference temperature limit (ITL) for the corresponding receiving-point.
This is assumed to be fixed and independent of ITL values for other primary
receiving-points, which corresponds to a box-like FCIR. In this paper, we
characterize the FCIR for {\em uplink} transmissions in cellular CRNs and for
direct transmissions in ad-hoc CRNs. We show that the FCIR is in fact a
polyhedron (i.e., the maximum feasible cognitive interference threshold for
each primary receiving-point is not a constant, and it depends on that for the
other primary receiving-points). Therefore, in practical interference
management algorithms, it is not proper to consider a constant and independent
ITL value for each of the primary receiving-points. This finding would
significantly affect the design of practical interference management schemes
for CRNs. To demonstrate this, based on the characterized FCIR, we propose two
power control algorithms to find the maximum number of admitted SUs and the
maximum aggregate throughput of the SUs in infeasible and feasible CRNs,
respectively. For two distinct objectives, our proposed interference management
schemes outperform the existing ones.
