Optimal training for affine-precoded and cyclic-prefized block transmissions

In block-mode transmission, inserting a cyclic prefix (CP) between two consecutive blocks provides an efficient way of removing inter-block 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. Apart from the CP insertion, no redundancy is introduced in the precoding. 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, data-rate (or bandwidth) has to be traded off to accommodate training. We propose full-rank orthogonal single-carrier (FROSC) precoding. 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. Finally, simulation results show that the bit error rate of the DROSC method can be quite close to that of the FROSC scheme. The former is however spectrally more efficient