Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

TL;DR

This paper analytically proves the block orthogonal structure of various STBCs, introduces new constructions, and demonstrates a 30% reduction in decoding complexity using sphere decoding techniques.

Contribution

It provides analytical proofs for block orthogonal properties, introduces new code constructions from algebraic structures, and shows practical complexity reduction in decoding.

Findings

Analytical proof of block orthogonal structure in existing codes

New constructions of block orthogonal codes from algebraic methods

30% reduction in sphere decoding complexity with BOSTBCs

Abstract

Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders 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 the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the 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.