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Due to limited cooperation between the primary users and the secondary users (SUs) in practical spectrum sharing systems, the secondary transmitters and receivers are assumed to have partial channel state information related to the primary receiver. Under such an assumption, this work investigates power allocation strategies for the SUs subject to an outage probability constraint on the primary transmission and a peak transmit power constraint on the secondary transmission. The challenge lies in the non-convexity of the outage probability constraint. Firstly, we prove that strong duality holds and that the Karush-Kuhn-Tucker (KKT) conditions are necessary for optimality. The optimal solution is then derived by addressing the optimality issues of the KKT solutions. Secondly, in order to further reduce the algorithmic complexity, two suboptimal strategies are proposed. The first one is designed based on several …