Multiple Complex Symbol Golden Space-Time Labeling Diversity

The Golden code is a full-rate space-time block code (STBC), which achieves a diversity order of <inline-formula> <tex-math notation="LaTeX">$2N_{r}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$N_{r}$ </tex-math></inline-formula> is the number of receive antennas. The multiple complex symbol Golden code (MCS-Golden code) is a generalized Golden code. The MCS-Golden code not only achieves full-rate but also achieves a diversity order of <inline-formula> <tex-math notation="LaTeX">$2^{n}{N_{r}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$n\ge {1}$ </tex-math></inline-formula>, is an integer, and <inline-formula> <tex-math notation="LaTeX">$2^{n}$ </tex-math></inline-formula> is the number of multiple complex symbols in the MCS-Golden code system. In this paper, we apply the labelling diversity technique to the MCS-Golden code to form a new type of STBC, named as multiple complex symbol Golden space-time labelling diversity (MCS-GSTLD). The proposed MCS-GSTLD achieves a diversity order of <inline-formula> <tex-math notation="LaTeX">$2\times {2^{n}}{N_{r}}$ </tex-math></inline-formula>, and further improves error performance compared to the MCS-Golden code. We also formulate the theoretical average bit error probability (ABEP) for the proposed MCS-GSTLD system. Furthermore, we apply sphere decoding with sorted detection subset (SD-SDS) to detect the transmitted symbols in the MCS-GSTLD system. Simulation results show that the SD-SDS scheme achieves the theoretical ABEP for <inline-formula> <tex-math notation="LaTeX">$N_{r}&gt;2$ </tex-math></inline-formula>. Both theoretical and simulation results demonstrate that with the same spectral efficiency and four receive antennas, the 2CS-GSTLD achieves at least 1.3 dB signal-to-noise ratio (SNR) gain compared to the 2CS-Golden code at a BER of <inline-formula> <tex-math notation="LaTeX">$3\times {10^{-6}}$ </tex-math></inline-formula>, while the 4CS-GSTLD achieves at least 0.7 dB SNR gain compared to the 4CS-Golden code.

Abstract licence: CC BY-NC-ND

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