Space-frequency linear dispersion codes for single carrier-frequency domain equalization

This letter addresses the application of Linear Dispersion Codes (LDC) in space and frequency domains in Single Carrier-Frequency Domain Equalization (SCFDE) systems. Space-frequency (SF)-LDCs are more suitable than space-time (ST) LDC in high mobility environments. However, the application of LDCs in space and frequency domains in SCFDE systems is not straightforward as in orthogonal frequency division multiplexing (OFDM) systems because in this case there is no direct access to subcarriers at the transmitter. This letter shows that it is possible to induce a target SF symbol dispersion in SCFDE by using a simple linear pre-coder and a conventional LDC that spreads the symbols in time and space domains according to specific ST dispersion matrices. The letter shows how to derive the ST dispersion matrices to be used at the transmitter as a function of the dispersion matrices describing the target SF dispersion. The presented procedure can be applied to both pure transmit diversity and pure multiplexing schemes, which are special cases of LDCs. Therefore, the proposed scheme provides a low complexity implementation of any dispersion in space and frequency over SCFDE systems, which alternatively would require the use of FFT/IFFT also at the transmitter side. The letter also shows a performance comparison of SF-LDCs and ST-LDCs in a typical propagation environment for future radio systems. The comparison confirms the suitability of using the dispersion in frequency rather than time for a wide range of coherence bandwidths.