This paper considers spectrum sharing for wireless communication between a cognitive radio (CR) and a primary radio (PR). An effective means known in the literature for the CR to protect the PR is by applying the so-called interference-temperature constraint, under which 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-constraint threshold, the AIP constraint is more favorable than the PIP counterpart because of its more flexibility for dynamically allocating the CR's 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. Some surprisingly, this paper proves that in terms of the achievable ergodic capacity of the PR fading channel, the AIP constraint is indeed superior over the PIP. This proof is based upon an interesting interference diversity phenomenon: 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 loss. Therefore, the AIP constraint results in larger ergodic capacities than the PIP for both the CR and PR.
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