  We consider a spectrum-sharing network where n secondary relays are used to
increase secondary rate and also mitigate interference on the primary by
reducing the required overall secondary emitted power. We propose a distributed
relay selection and clustering framework, obtain closed-form expressions for
the secondary rate, and show that secondary rate increases proportionally to
log n. Remarkably, this is on the same order as the growth rate obtained in the
absence of a primary system and its imposed constraints. Our results show that
to maximize the rate, the secondary relays must transmit with power
proportional to n^(-1) (thus the sum of relay powers is bounded) and also that
the secondary source may not operate at its maximum allowable power. The
tradeoff between the secondary rate and the interference on the primary is also
characterized, showing that the primary interference can be reduced
asymptotically to zero as n increases, while still maintaining a secondary rate
that grows proportionally to log n. Finally, to address the rate loss due to
half-duplex relaying in the secondary, we propose an alternating relay protocol
and investigate its performance.
