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In this paper, an underlay spectrum sharing scheme is proposed where both primary and secondary users are discrete power-rate adaptive systems with limited feedback from receivers. By receiving secondary and overhearing primary quantized channel quality information from the secondary receiver and primary receiver, respectively, the secondary transmitter adapts its resource allocation to the current channel quality by selecting a proper power-rate pair from the pre-designed secondary quantization codebook. The secondary quantization codebook is designed to maximize the secondary average achievable rate subject to the long term power constraint of the secondary transmitter and the rate loss constraint at the primary receiver.
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