Signal Shaping for Generalized Spatial Modulation and Generalized Quadrature Spatial Modulation

Abstract
This paper investigates generic signal shaping methods for multiple-data-stream generalized spatial modulation (GenSM) and generalized quadrature spatial modulation (GenQSM). Three cases with different channel state information at the transmitter (CSIT) are considered, including no CSIT, statistical CSIT and perfect CSIT. A unified optimization problem is formulated to find the optimal transmit vector set under size, power and sparsity constraints. We propose an optimization-based signal shaping (OBSS) approach by solving the formulated problem directly and a codebook-based signal shaping (CBSS) approach by finding sub-optimal solutions in discrete space. In the OBSS approach, we reformulate the original problem to optimize the signal constellations used for each transmit antenna combination (TAC). Both the size and entry of all signal constellations are optimized. Specifically, we suggest the use of a recursive design for size optimization. The entry optimization is formulated as a non-convex large-scale quadratically constrained quadratic programming (QCQP) problem and can be solved by existing optimization techniques with rather high complexity. To reduce the complexity, we propose the CBSS approach using a codebook generated by quadrature amplitude modulation (QAM) symbols and a low-complexity selection algorithm to choose the optimal transmit vector set. Simulation results show that the OBSS approach exhibits the optimal performance in comparison with existing benchmarks. However, the OBSS approach is impractical for large-size signal shaping and adaptive signal shaping with instantaneous CSIT due to the demand of high computational complexity. As a low-complexity approach, CBSS shows comparable performance and can be easily implemented in large-size systems.

Citation
Guo, S., Zhang, H., Zhang, P., Dang, S., Liang, C., & Alouini, M.-S. (2019). Signal Shaping for Generalized Spatial Modulation and Generalized Quadrature Spatial Modulation. IEEE Transactions on Wireless Communications, 18(8), 4047–4059. doi:10.1109/twc.2019.2920822

Acknowledgements
The work of S. Guo, S. Dang and M.-S. Alouini were supported by the funding from KAUST. The work of S. Guo and P. Zhang were supported in part by the National Natural Science Foundation of China under Grant 61801266 and 61471269 and by China Postdoctoral Science Foundation under Grant 2017M622202 and by the Shandong Natural Science Foundation under Grant ZR2018BF033. The work of H. Zhang and C. Liang were supported by the National Science Fund of China for Excellent Young Scholars under Grant No. 61622111 National Natural Science Foundation of China under Grant No. 61860206005.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Transactions on Wireless Communications

DOI
10.1109/TWC.2019.2920822

Additional Links
https://ieeexplore.ieee.org/document/8734877/https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8734877

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