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Existing works design the pilot pattern for sparse channel 6 estimation, assuming that the power of all pilots is equal. However, equal 7 power allocation is not optimal in cognitive radio (CR) systems. In this cor8 respondence, we jointly design the pilot power and pilot pattern for sparse 9 channel estimation in orthogonal-frequency-division-multiplexing-based 10 CR systems, based on the rule of mutual incoherence property that 11 minimizes the coherence of the measurement matrix used for the sparse 12 recovery. Under the sum power constraint and peak power constraint, the 13 pilot design is formulated as a joint optimization problem, which is then 14 decoupled into tractable sequential formations. Given a pilot pattern, we 15 formulate the design of pilot power as a second-order cone programming. 16 Then, we propose a joint design algorithm, which includes discrete opti17 mization for pilot pattern and continuous optimization for pilot power. 18 Simulation results show that the proposed algorithm can achieve better 19 channel estimation performance in terms of mean square error and bit 20 error rate and can further improve the spectrum efficiency by 2.4%, 21 compared with existing algorithms assuming equal pilot power. 22