Low Complexity Decoding of the 4×4 Perfect Space-time Block Code

The 4x4 perfect space-time block code (STBC) is one type in a family of perfect STBCs that have full rate, full diversity, a non- vanishing constant minimum determinant that improves spectral efficiency, uniform average transmitted energy per antenna, and good shaping. These codes suffer very high complexity maximum likelihood (ML) decoding. The exhaustive ML decoding of the 4x4 perfect STBC for instance has complexity of O(N16), with N being the size of the underlying QAM constellation. This paper suggests a fast decoding algorithm for the 4x4 perfect STBC that reduces decoding complexity from O(N16) to O(N8). The algorithm is based on conditional minimization of the ML decision metric with respect to one subset of symbols given another. This low complexity decoding approach is essentially ML because it suffers no loss in symbol error rate (SER) performance when compared to the exhaustive ML decoding.