Cyclic Delay Transmission for Vector OFDM Systems

Single antenna vector OFDM (V-OFDM) system has been proposed and investigated in the past. It contains the conventional OFDM and the single carrier frequency domain equalizer (SC-FDE) as two special cases and is flexible to choose any number of symbols in intersymbol interference (ISI) by choosing a proper vector size. In this paper, we develop cyclic delay diversity (CDD) transmission for V-OFDM when there are multiple transmit antennas (CDD-V-OFDM). Similar to CDD-OFDM systems, CDD-V-OFDM can also collect both spatial and multipath diversities. Since V-OFDM first converts a single input single output (SISO) ISI channel to a multi-input and multi-output (MIMO) ISI channel of order/length K times less, where K is the vector size, for a given bandwidth, the CDDV-OFDM can accommodate K times more transmit antennas than the CDD-OFDM does to collect all the spatial and multipath diversities. This property will specially benefit a massive MIMO system. We show that with the linear MMSE equalizer at each subcarrier, the CDD-V-OFDM achieves diversity order dMMSE CDD-V-OFDM = min{⌊2−RK⌋, NtL} + 1, where R is the transmission rate, Nt is the number of transmit antennas, and L is the ISI channel length between each transmit and receive antenna pair. Simulations are presented to illustrate our theory.