Full-Rank and Rank-Deficient Precoding Schemes for Single-Carrier Block Transmissions

In block-mode transmission, inserting a cyclic prefix (CP) between two consecutive blocks provides an efficient way of removing interblock interference and simplifies equalization of frequency-selective channels at the receiver. Here, we address optimal training design for channel estimation in such systems. Our investigations focus on affine precoding schemes. In designing the precoder, least squares channel estimation is constrained to be decoupled from symbol detection, which results in orthogonal precoding schemes. If the precoding matrix is full-rank, the data rate (or bandwidth) has to be traded off to accommodate training. We propose a full-rank orthogonal single-carrier (FROSC) precoding with a low peak-to-average power ratio. Then, in order to improve bandwidth efficiency, we propose a rank deficient orthogonal single carrier (DROSC) precoding scheme. Symbol recovery is still possible thanks to the finite alphabet property of the data symbols.