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Location awareness allows to define a concurrent transmission region where a primary and a secondary networks can coexist. In this paper we investigate the impact of channel rate control on the performance of a cognitive radio ad hoc network overlaying an infrastructure-based system. The proposed algorithm adequately adjusts the secondary user rate to be as large as possible while respecting a given constraint on the achievable primary rate. As a consequence, the rate control scheme expands the concurrent transmission region and increases the average rate of the secondary users, without affecting the primary. Numerical results show that it is possible to increase the throughput of the cognitive ad-hoc network and therefore increase the efficiency of the spectrum utilization.