Characterization of single-carrier block transmission under the precoded OFDM architecture

The orthogonal frequency-division multiplexing (OFDM) transmission has better spectral efficiency than traditional single-carrier (SC) transmission. However, one can implement an SC block transmission under the architecture of precoded OFDM (POFDM) [1] and attain the same spectral efficiency as the typical OFDM system. This gives us the motivation to characterize the SC block transmission and compare it with the conventional SC transmission. Since the discrete-to-continuous-time (D/C) conversion is the essential part in the transmitter of SC block transmission, we first derive the ideal interpolation pulses of the D/C conversion for two POFDM systems based on the approach in [2]. We then derive the correlation functions of the interpolation pulses, and extend the results in [2] for the matched filter that can implement the ideal sampling, or C/D conversion, of the POFDM signal. Based on the ideal forms of D/C and C/D conversions, we characterize the SC block transmission. Comparing with the conventional SC transmission, we show that for the SC block transmission the amplitudes of the interpolation pulses are periodic with the period identical to the block duration. Within the block duration, the interpolation pulses either shift circularly or have circularly shifted amplitudes. In addition, the SC block transmission also has the multi-carrier forms, and the the condition of zero intersymbol interference (ISI) only needs to be satisfied within one block duration for the interpolation pulses.