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The uplink of a multiuser cognitive radio network, wherein secondary users communicating with a secondary access point coexist with primary users communicating with a primary access point, is considered in this paper. Primary and secondary users' signals coexist in the same frequency band, and the transmit powers of the secondary users are constrained so that the interference from the whole secondary network to each primary user does not exceed a prescribed threshold. Given this constraint, a noncooperative power control game for maximum energy efficiency with a fairness constraint on the maximum received powers for the secondary users has been considered. The considered game is shown to admit a unique Nash equilibrium, also in the case in which energy efficiency is maximized with respect to both transmit power and choice of the linear uplink receiver. Based on large system analysis, a one-shot procedure for computing the users' transmit powers at the Nash equilibrium with no need for iteration among users is also derived. Numerical simulations confirm the theoretical results on the existence and uniqueness of the Nash equilibrium, confirm the effectiveness of the results obtained through the large system analysis, and show that secondary users have a beneficial impact on the whole network throughput, at the price of a moderate degradation in the performance of the primary users.