Spectral Precoding for Out-of-Band Power Reduction Under Condition Number Constraint in OFDM-Based Systems

Orthogonal frequency division multiplexing (OFDM) is a promising technique for dynamic spectrum access due to flexibility in spectrum shaping. However, out-of-band (OOB) power radiation of OFDM introduces significant interference to adjacent users. This is a serious problem in cognitive radio networks, which affects the secondary system to access the instantaneous spectrum hole. Existing methods either do not effectively reduce OOB power leakage or introduce significant bit-error-rate deterioration at the receiver. In this paper, a joint spectral precoding scheme is developed for OOB power reduction by using the matrix operations of orthogonal projection and singular value decomposition. We also propose an algorithm that designs the precoding matrix under receive performance constraint, which is then converted to matrix condition number constraint in practice. This method achieves the desirable spectrum envelope and receive performance by selecting zero-forcing frequencies. Simulation results show that OOB power decreases significantly by the proposed scheme under condition number constraint.