  We address the problem of resource allocation (RA) for spectrum underlay in a
cognitive radio (CR) communication system with multiple secondary operators
sharing resource with an incumbent primary operator. The multiple secondary
operator RA problem is well known to be especially challenging because of the
inter-operator coupling constraints arising in the optimization problem, which
render impractical inter-operator information exchange necessary. In this
paper, we consider a satellite setting for multi-operator CR. In the CR
maturation regime, i.e., the period in which the secondary subscriber density
is growing yet remains much below that of incumbent users, we show that in fact
the inter-operator mutual constraints can be neglected, thus making distributed
(across secondary operators) optimization possible. Furthermore, we establish
analytically that the mutual constraints asymptotically vanish with the primary
user density.
