Orthogonal precoding for sidelobe suppression in DFT-based systems using block reflectors

Abstract

Sidelobe suppression has always been an important part of crafting communications signals to keep interference with users of adjacent spectrum to a minimum. Systems based on the discrete Fourier transform, such as orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-division multiple access (SC-FDMA) are especially prone to out-of-band power leakage. Although many techniques have been proposed to suppress sidelobes in DFT-based systems, a satisfactory balance between computational complexity and out-of-band power leakage has remained elusive. Orthogonal precoding is a promising, linear technique in which the nullspace of a precoding matrix with orthonormal columns is designed to suppress the sidelobes. In particular, Xu and Chen [1], van de Beek [2] and Ma et al. [3] have proposed orthogonal precoders that yield excellent out-of-band suppression. However, they suffer from high arithmetic complexity-quadratic in the number of active subcarriers-which has limited their application. In this paper, we find that the arithmetic complexity can be made linear instead of quadratic if a block reflector is used to perform the precoding instead of an otherwise unstructured unitary transformation. There is no penalty to be paid in achieved bit-error rate. We show by numerical simulation that the penalty in peak-to-average power ratio is also very small for OFDM.