多天线系统信道检测中的格基规约预处理技术研究

As the core of 5G technique of communications, multi-antenna linear system is of great value in practical applications. Signal detection speed and bit-error-rate are the two most important indicators for assessing the performance of the system, and accordingly, approximate MIMO detectors and lattice basis reduction play important roles in this field. This is because the approximate detectors can finish the decoding process in polynomial time, while lattice basis reduction can be used as a preprocessor to improve the bit-error-rate of approximate detectors efficiently. However, the LLL algorithm performs weakly when it is applied to ill-conditioned or high dimensional systems. To solve this problem, we introduce several new lattice reduction techniques: 1. new reduction algorithms based on the optimization on the angles between basis vectors; 2. the synchronous reduction algorithms based on the combination of primal-reduction and dual-reduction; 3. the improvement of Seysen's algorithm; 4. detailed theoretical analysis on the error-rate performance for various MIMO detectors preprocessed by the aforementioned reduction algorithms. The error-rate performance of our proposed new reduction algorithms shall outperform the LLL algorithm significantly when applied to ill-conditioned or high-dimensional systems, while the computational complexity of the new reduction algorithms are comparable with the LLL algorithm．

作为5G通讯技术研发的核心，多天线信道系统蕴藏着巨大的应用价值，而信道检测速度和译码误码率是衡量该系统性能的重要指标。近年来，近似译码算法和以LLL算法为代表的格基规约算法已成为该领域的核心技术：前者能在多项式时间内完成信道检测，后者能够作为预处理子有效改善前者的译码误码率水平。但当信道矩阵病态或系统维数较高时，LLL算法往往表现不佳。为克服这一难题，本项目拟研究新型格基规约算法，并将其用作各类信道检测算法的预处理子，以改善其译码误码率。具体研究内容包括：1.基于夹角最优原则的规约算法设计；2.基于原格基及其对偶基同步规约的算法设计；3.对Seysen算法的改进和分析；4.对经以上规约算法预处理的信道检测算法的译码误码率水平作严格理论分析。与LLL算法相比，新算法可在保证计算效率的前提下，极大地改善病态或高维系统的误码率水平，从而有效拓展了传统格基规约算法的适用范围。

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