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.

In this paper, we apply extended regularized channel inversion precoding to address the multiuser multiantenna downlink transmission problem. Different from conventional regularized channel inversion precoding, extended RCI precoding considers non-homogeneous channels, adjusts more regularization parameters, and exploits the information gained by inverting the covariance matrix of the channel. Two ways of determining the regularization parameters are investigated. First, the parameters can be determined by solving a max-min SINR problem. The constraints of the problem can be transformed to the second-order cone (SOC) constraints. The optimal solution of the problem can be obtained by iteratively solving a second-order cone programming (SOCP) problem. In order to reduce the computational complexity, a one-shot algorithm is proposed. Second, the sum-rate maximization problem is discussed. The simple gradient-based method is used to solve the problem and get the regularization parameters. The simulation results indicate that the proposed algorithms exhibit improved max-min SINR performance and sum-rate performance over RCI precoding.