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 2N
_r
, where N
_r
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 2
ⁿ
N
_r
, n, n ≥ 1, is an integer, and 2
ⁿ
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 2×2
ⁿ
N
_r
, 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 N
_r
> 2. 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 3×10
^-6
, while the 4CS-GSTLD achieves at least 0.7 dB SNR gain compared to the 4CS-Golden code.