基于最大化接收信号的最小欧氏距离准则，提出一种适用于传输三路数据流的多输入多输出预编码新算法. 该算法利用实参数旋转矩阵约束，从几何角度将非凸预编码优化问题的求解转化为离线计算和在线计算两步实施，并获得表征最小欧氏距离的闭合表达式，其中离线计算部分通过搜索三维空间中依特定条件膨胀的二次曲面并获得所有可行曲面，而在线计算部分则根据信道条件选择可行曲面，从而构造出相应的预编码矩阵. 仿真实验结果和分析表明，该算法相比于其他同类算法不仅具有较低的计算复杂度，而且随着正交幅度调制星座图的增大可以获得超过3 dB 的误比特率性能增益.
A new MIMO precoding method is proposed based on maximizing the minimum Euclidean distance between points in the received signal space for triple-stream transmission. Under a real-valued rotation matrix constraint, the proposed algorithm solves the non-convex optimization problem with two steps from
the geometric viewpoint, named offline step and online step, respectively. In the offline step, all feasible surfaces are collected by expanding quadric surfaces within 3-dimensional space. In the online step, the precoder matrix is constructed with respect to the unique feasible surface chosen by particular channel implementation. Meanwhile, a closed-form expression of the minimum distance is also provided in this paper. Simulation results validate that the proposed method not only outperforms existing schemes with low computational complexity, but also has superior performance of more than 3 dB in terms of bit-error-rate (BER) with increase of the quadrature amplitude modulation (QAM) constellations.
[1] Palomar D P, Jiang Y. MIMO transceiver design via majorization theory [J]. Foundations and Trends in Communications and Information Theory, 2006, 3(4): 331-551.
[2] Xiao C, Zheng Y R, Ding Z. Globally optimal linear precoders for finite alphabet signals over complex vector Gaussian channels [J]. IEEE Transactions on Signal Processing, 2011, 59(7): 3301-3314.
[3] Sampath H, Stoica P, Paulraj A. Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion [J]. IEEE Transactions on Communications, 2001, 49(12): 2198-2206.
[4] 武大伟，何晨，蒋铃鸽. 鲁棒的基于几何均值分解的矢量预编码算法 [J]. 上海交通大学学报：自然版, 2011, 45(07): 1046-1049.
Wu Dawei, He Chen, Jiang Lingge . Research on robust GMD-based vector precoding [J]. Journal of shanghai Jiaotong University: Science, 2011, 45(07): 1046-1049.
[5] Jiang, Y, Li J, Hager W W. Joint transceiver design for MIMO communications using geometric mean decomposition [J]. IEEE Transactions on Signal Processing, 2005, 53(10): 3791-3803.
[6] 高献坤，崔岩，傅洪亮. 连续迭代优化SLNR准则的下行多用户MIMO预编码 [J]. 应用科学学报，2011, 29(3): 251-255.
Gao Xiankun, Cui Yan, Fu Hongliang. Downlink pre-coding for multi-user MIMO system with successive iterative optimal SLNR [J]. Journal of Applied Sciences - Electronics and Information Engineering, 2011, 29(3): 251-255. (in Chinese)
[7] Collin L, Berder O, Rostaing P, Burel G. Optimal minimum distance-based precoder for MIMO spatial multiplexing systems [J]. IEEE Transactions on Signal Processing, 2004, 52: 617-627.
[8] Ngo Q T, Berder O, Vrigneau B, Sentieys O. Minimum distance based precoder for MIMO-OFDM systems using a 16-QAM modulation [C]// 2009 IEEE International Conference on Communications, Dresden, 2009: 1-5.
[9] Vrigneau B, Letessier J, Rostaing P, Collin L, BUREL G. Extension of the MIMO precoder based on the minimum Euclidean distance: a cross-form matrix [J]. IEEE Journal of elected Topics in Signal Processing, 2008, 2(2): 135-146.
[10] Srinath K P, Rajan B S. A low ML-decoding complexity, full-diversity, full-rate MIMO precoder [J]. IEEE Transactions on Signal Processing, 2011, 59(11): 5485-5498.
[11] Ngo Q T, Berder O, Scalart P. 3-D minimum Euclidean distance based sub-optimal precoder for MIMO spatial multiplexing systems [C]//2010 IEEE International Conference on Communications, Cape Town, 2010: 1-5.
[12] Rusek F, Kapetanovic D. Design of close to optimal Euclidean distance MIMO-precoders [C]//2009 IEEE International Symposium on Information Theory, Seoul, 2009: 1268-1272.
[13] Scaglione A, Stoica P, Barbarossa S, Giannakis G B, Sampath H. Optimal designs for space-time linear precoders and decoders [J]. IEEE Transactions on Signal Processing, 2002, 50(5): 1051-1064.
[14] Telatar E. Capacity of multi-antenna gaussian channels [J]. European Transactions on Telecommunications, 1999, 10(6): 585-595.
[15] Payaro M, Palomar D P. On optimal precoding in linear vector Gaussian channels with arbitrary input distribution [C]//2009 IEEE International Symposium on Information Theory, Seoul, 2009: 1085-1089.
