Non-contiguous orthogonal frequency-division multiplexing (OFDM) is a promising technique for cognitive radio systems. The secondary users transmit on the selected subcarriers to avoid the frequencies being used by the primary users. However, the out-of-band power (OBP) of the OFDM-modulated tones induces interference to the primary users. Another major drawback of OFDM-based system is their high peak-to-average power ratio (PAPR). In this paper, algorithms are proposed to jointly reduce the OBP and the PAPR for non-contiguous OFDM based on the method of alternating projections onto convex sets. Several OFDM subcarriers are selected to accommodate the adjusting weights for OBP and PAPR reduction. The frequency-domain OFDM symbol is projected onto two convex sets that are defined according to the OBP requirements and the PAPR limits. Each projection iteration solves a convex optimization problem. The projection onto the set constrained by the OBP requirement can be calculated using an iterative algorithm which has low computational complexity. Simulation results show good performance of joint reduction of the OBP and the PAPR. The proposed algorithms converge quickly in a few iterations.

This paper presents a new method for image interpolation based on truncated projections onto convex sets (POCS). By using the convergence property to properly defined convex sets, the proposed algorithm can restore high frequency details in the original high resolution image. In order to apply the POCS method to the interpolation procedure, we first present a two-dimensional separable image degradation model for a low resolution imaging system. According to the model, we propose a truncated POCS-based spatial interpolation algorithm for image sequences. Experimental results with synthetic and real image sequence show that the proposed algorithm gives indiscernible interpolation performance compared with the conventional POCS-base algorithm, while it significantly reduces computational complexity and is suitable for processing image sequences.