Computational complexity reduction of orthogonal precoding for sidelobe suppression of OFDM signal

Spectrum sculpting (SS) is a precoding scheme for sidelobe suppression of orthogonal frequency division multiplexing (OFDM) signals and can shape a spectrum with deep notches at chosen frequencies. However, the SS method will degrade the error rate as the number of notched frequencies increases. Orthogonal precoding of the SS has both a notched spectrum and an ideal error rate, but the computational complexity of the precoder matrix is very large. This paper proposes a matrix decomposition of the precoder matrix of the orthogonal precoding to reduce the computational complexity. Numerical experiments show that the proposed method can drastically reduce the computational complexity.