Unitary and Non-Unitary Differential Space-Frequency Coded OFDM

In this paper, we present the code design structure of unitary and non-unitary differential space-frequency group codes (DSFCs) for multiple-input multiple-output (MIMO)- orthogonal frequency division multiplexing (OFDM) systems based on optimal coherent space-frequency (SF) group codes. Under the assumption that the transmitter knows only the delay profile of the channel, a differential transmission rule incorporated with subcarrier allocation is obtained that allows data to be sent without channel estimates at the transmitter or receiver. The differential encoding/decoding is performed in the frequency domain within each single OFDM symbol. Therefore, proposed DSFCs can be successfully decoded even for a rapidly fading channel which may change independently from one OFDM symbol to another. Unitary and nonunitary DSFCs, that are constructed based on design criteria, are compared with recently published techniques in the literature and shown to inherit coding gain of optimal coherent SF codes. Due to design structure and energy constraints, our nonunitary DSFCs do not blow up or diminish during the differential encoding.