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This paper investigates power allocation strategies for secondary users (SUs) in cross-interfering spectrum sharing systems. Addressing limited cooperation between primary users (PUs) and SUs, only instantaneous channel state information (CSi) of the secondary link and statistical CS! of the other links is assumed to be available at the secondary transmitters (STs). We aim at maximizing the secondary achievable rate subject to both a peak power constraint at the ST and an average interference power constraint at the primary receiver. First, the optimal power control strategy is developed. !n order to reduce the complexity, two suboptimal optimization strategies are proposed. The first one, named double threshold waterfilling (DT-WF), is based on an approximation of the optimal solution. The second strategy, named double threshold constant-power waterfilling (DTCP-WF), further simplifies DT-WF. Additionally, the …