Quadrature Spatial Modulation With the Fourth Order Transmit Diversity and Low-Complexity Sphere Decoding for Large-Scale MIMO Systems

Abstract

A quadrature spatial modulation with the fourth order transmit diversity (FO-QSM) scheme is presented in this paper. In this scheme, two dispersion-matrix (DM) sets are assigned at the transmitter, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> out of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> DMs are activated in each set to extend the real and imaginary parts of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> QSM signals respectively, to large number of transmit antennas. The two DM sets are constructed by performing Kronecker product between two simple extension matrices and the DMs of Sezginer-Sari-Biglieri (SSB) code. The framework designs of FO-QSM and the two DM sets make FO-QSM possess the properties: 1) it guarantees the fourth order transmit diversity without requiring any parameter optimization; 2) it has higher spectral efficiency than the newly proposed generalized space-time block coded spatial modulation (GSTBC-SM) scheme. Furthermore, a repeated computation reduced sphere decoding (RCR-SD) is proposed. RCR-SD is very suitable for the schemes constructed by a large number of DMs, including FO-QSM. By sorting the index vectors, the RCR-SD detector can efficiently reduce the repeated computations in the SD searching, which significantly reduces the decoding complexity without sacrificing optimal decoding performance. Simulation results show that FO-QSM has obvious better bit error rate (BER) performance than GSTBC-SM.