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In this letter, we investigate the optimal power allocation for interference-limited cognitive multiple access channels. The objective is to minimize the outage probability of cognitive users (CUs) while satisfying the interference constraint on the primary user (PU). The formulated optimization problem is non-convex, but can be efficiently solved by the aid of logarithmic transformation. For comparison, we also analyze two suboptimal power allocation schemes by assigning equal interference (EI) or equal transmit power (ETP) to each CU. We derive closed-form expressions for both schemes, and asymptotically analyze their performance. Simulations results confirm the correctness of our analysis and effectiveness of the proposed schemes.