I. Introduction
Investigation of both spatial and temporal spectrum utilization reveals the fact that not all the spectrum is in use all the time. Cognitive radio technology inspired by the observation turns out to be a promising technique for the efficient use of this unused spectrum, potentially allowing a large amount of spectrum to become available for future high bandwidth applications [1] [9]. Some works [2]–[5] make discussions on cognitive radio's achievable rate from information theoretic point. In the seminal work [3], the achievable rate of a single cognitive radio user is provided under such constraints as (i) there is no interference to the primary user, and (ii) the primary encoder-decoder pair is oblivious to the presence of cognitive radio. In [4], they extend the result of [3] to the case with multiple cognitive radio users and characterize the cognitive radio's achievable rate region for Gaussian multiple access channels (MACs). Maximization of the cognitive radio's sum-rate on Gaussian MAC then raises the problem of the allocation of each cognitive user's power ratio [5].