An Alternative Encoding of the Golden Code and its Low Complexity Detection

The Golden code is a full-rate full-diversity (FRFD) space-time block code. The encoder of the Golden code takes four complex symbols and generates two pairs of Golden codewords. The encoding of each Golden codeword can be regarded as superposition coding with "complex" power allocation. In this paper, we propose an alternative encoding of the Golden code which can be regarded as superposition coding with "real" power allocation. The Golden code with "complex" power allocation or "real" power allocation is hereinafter referred to as the C-Golden code or R-Golden code, respectively. The R-Golden code also preserves the FRFD property. The R-Golden code can be easily implemented in passband modulation using in-phase and quadrature components compared to the C-Golden code. An equivalent received signal model of the R-Golden code system is constructed, then used to derive a closed-form on the lower bound of the average bit error probability. We further propose a low complexity detection scheme, the fast essentially maximum-likelihood detection with adaptive signal detection subset (FE-ML-ASDS) for the R-Golden code. Both simulation and theoretical results show that both the C-Golden code and the R-Golden code achieve the same error performance. Compared to the fast essentially ML detection with signal detection subset (FE-ML-SDS), at high signal-to-noise ratios, the proposed FE-ML-ASDS further reduces detection complexity by at least 68% for the 16QAM or 64QAM R-Golden code with three receive antennas.