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The Golden code has full-rate and full-diversity. However, its applications are limited because of the very high detection complexity. The complexity of sphere decoding depends on the size of signal set, <inline-formula> <tex-math notation="LaTeX">$M^{2}$ </tex-math></inline-formula>, and the depth of search. Meanwhile, the complexity of fast essentially maximum likelihood (ML) detection is still <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(M^{2})$ </tex-math></inline-formula> for <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary quadrature amplitude modulation (<inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>QAM). In this paper, we propose two reduced complexity detection schemes, fast essentially ML with detection subset and sphere decoding with detection subset. Two theoretical bounds on the average bit error probability for the Golden code with <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>QAM are also formulated in this paper. Simulation results demonstrate that both the fast essentially ML with detection subset and sphere decoding with detection subset agree well with the formulated theoretical bounds and can achieve the error performance of the conventional fast essentially ML detector and sphere decoding.

Reduced Complexity Detection Schemes for Golden Code Systems