Efficient spectrum leasing via randomized silencing of secondary users

In this paper, a primary (licensed) user leases part of its resources to independent secondary (unlicensed) terminals in exchange for a tariff in dollars per bit, under the constraint that secondary transmissions do not cause excessive interference at the primary receiver (PRX). The PRX selects a power allocation (PA) for the secondary user that maximizes the secondary rate (and thus its revenue) and enforces it by the following mechanism: Upon violation of a predefined interference level, PRX keeps silencing randomly selected secondary users, until the aggregate secondary interference is below the required threshold. This mechanism ensures that secondary users may not be willing to deviate from the allocated PA. Specifically, the scenario gives rise to a Stackelberg game, in which the primary determines the PA and a Nash equilibrium (NE) constraint is imposed on the PA to ensure that secondary users do not have incentives to deviate, given their knowledge of the silencing mechanism run at the PRX. In principle, the primary should find the set of all PAs that are NE and among them choose the one that maximizes the aggregate secondary utility, and thereby the revenue of the primary. For the most general setting of channel gains, we investigate the conditions for NE for a subset of PAs. When the scenario is symmetric in the sense that all secondary users have the same channel gains in the direct/interfering links, we prove that only two optimal power allocations exist. Finally, for the case of general channel gains with strong interference, we show that there is a unique NE of the game.