This paper considers spectrum sharing for wireless communication between a
cognitive radio (CR) link and a primary radio (PR) link. It is assumed that the
CR protects the PR transmission by applying the so-called
interference-temperature constraint, whereby the CR is allowed to transmit
regardless of the PR's on/off status provided that the resultant interference
power level at the PR receiver is kept below some predefined threshold. For the
fading PR and CR channels, the interference-power constraint at the PR receiver
is usually one of the following two types: One is to regulate the average
interference power (AIP) over all the fading states, while the other is to
limit the peak interference power (PIP) at each fading state. From the CR's
perspective, given the same average and peak power threshold, the AIP
constraint is more favorable than the PIP counterpart because of its more
flexibility for dynamically allocating transmit powers over the fading states.
On the contrary, from the perspective of protecting the PR, the more
restrictive PIP constraint appears at a first glance to be a better option than
the AIP. Some surprisingly, this paper shows that in terms of various forms of
capacity limits achievable for the PR fading channel, e.g., the ergodic and
outage capacities, the AIP constraint is also superior over the PIP. This
result is based upon an interesting interference diversity phenomenon, i.e.,
randomized interference powers over the fading states in the AIP case are more
advantageous over deterministic ones in the PIP case for minimizing the
resultant PR capacity losses. Therefore, the AIP constraint results in larger
fading channel capacities than the PIP for both the CR and PR transmissions.