Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

A new class of Space Time Block Codes (STBCs) known as block orthogonal STBCs (BOSTBCs) was recently presented by Ren et al., which could be exploited by a QR decomposition decoder with M paths (QRDM decoder) to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed, was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including codes formed as the sum of Clifford Unitary Weight Designs (CUWDs). We also show that, construction methods from Coordinate Interleaved Orthogonal Designs (CIODs), Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs) can lead to BOSTBCs. In addition, we show that the block orthogonal STBCs offer a reduced decoding complexity when used in tandem with a fast sphere decoder using a depth first search approach. Simulation results involving decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.