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This paper analyzes the fundamental limits of performance of cognitive radios in a multiple access setting. In the traditional information theoretic model for cognitive radio channel, there is a primary and cognitive transmitter-receiver pair, and the cognitive transmitter knows the message transmitted by the primary transmitter. In the multiple access setting, the primary network is an uplink system with multiple transmitters communicating with the primary receiver with the cognitive transmitter having access to the messages of all the transmitters. This paper analyzes a system where two primary transmitters communicate with a primary receiver in the presence of a cognitive transmitter-receiver pair. The capacity region of this system is derived when the channel gain from the cognitive transmitter to the primary receiver is weak.
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