Non-contiguous OFDM is a promising technique for cognitive radio systems. Nevertheless, the sidelobes of the OFDM-modulated tones cause the out-of-band power (OBP) which can induce large interference to the incumbent communication systems. Another major drawback of OFDM-based systems is the high peak-to-average power ratio (PAPR). In this paper, two algorithms are proposed to jointly reduce the OBP and the PAPR based on the method of alternating projections onto convex sets (POCS). Several OFDM subcarriers are reserved to accommodate the adjusting weights that reduce the OBP and the PAPR. In the first algorithm, the adjusting weights are projected onto two convex sets that are defined according to the OBP and the PAPR limits. Each POCS iteration requires a convex optimization process. In the second algorithm, the frequency-domain OFDM symbol is projected onto multiple convex sets and the adjusting weights are separated into two groups for OBP and PAPR reductions, respectively. The adjusting weights can be obtained in analytical forms so that the computational complexity is lowered. Simulation results show that, within just a few POCS iterations, the proposed algorithms can achieve good performance in the joint reduction of the OBP and the PAPR.
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