Matrix Decomposition of Precoder Matrix in Orthogonal Precoding for Sidelobe Suppression of OFDM Signals

Abstract

The spectrum sculpting precoder (SSP) is a precoding scheme for sidelobe suppression of frequency division multiplexing (OFDM) signals. It can form deep spectral notches at chosen frequencies and is suitable for cognitive radio systems. However, the SSP degrades the error rate as the number of notched frequencies increases. Orthogonal precoding that improves the SSP can achieve both spectrum notching and the ideal error rate, but its computational complexity is very high since the precoder matrix is large in size. This paper proposes an effective and equivalent decomposition of the precoder matrix by QR-decomposition in order to reduce the computational complexity of orthogonal precoding. Numerical experiments show that the proposed method can drastically reduce the computational complexity with no performance degradation.