On Optimal Quasi-Orthogonal Space–Time Block Codes With Minimum Decoding Complexity
On Optimal Quasi-Orthogonal Space–Time Block Codes With Minimum Decoding Complexity
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DOI：
10.1109/tit.2008.2011521
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发表时间：
2009-03
影响因子：
2.5
通讯作者：
Haiquan Wang;Dong Wang;X. Xia
中科院分区：
文献类型：
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作者：
Haiquan Wang;Dong Wang;X. Xia
基于正交设计的正交空时分组码（OSTBC）具有符号级最大似然（ML）译码和全分集的优点。然而，它们的符号速率的上限为3/4，用于复杂符号的两个以上的天线。为了提高符号速率，它们在文献中被推广到准正交空时分组码（QOSTBC），但是分集阶数减少了一半，并且复符号ML解码显著增加到复符号成对（复符号对）ML解码。QOSTBC已经通过旋转复符号的一半来进行修改，以实现全分集，同时保持复符号成对ML解码。Su-Xia已经找到了位于正方形格和等文字三角形格上的任何有限符号的任何信号星座的最佳旋转角，其中最优性意味着最佳分集积（或乘积距离）。Yuen-Guan-Tjhung还通过以另一种方式旋转信息符号来修改QOSTBC，使得其具有完全分集，同时具有真实的符号成对ML解码（复杂度与复杂的逐符号解码相同）和正方形和矩形QAM星座的最佳旋转角。我们系统地研究了用于QOSTBC的信息符号的一般线性变换，以具有全分集和真实的符号成对ML解码。我们提出了最佳的变换矩阵（在所有可能的线性变换，不一定是符号旋转）的信息符号的QOSTBC与真实的符号成对ML解码，使最佳的分集产品是实现一般的平方QAM和一般的矩形QAM信号星座。此外，我们新提出的QOSTBC的最佳线性变换也适用于一般的QAM星座，在这个意义上，QOSTBC具有良好的分集积属性和真实的符号成对ML解码的全分集。有趣的是，本文所得到的基于信息符号最优线性变换的平方QAM星座的最优分集积与Yuen-Guan-Tjhung利用最优旋转得到的最优分集积一致。然而，最佳的分集产品（非正方形）矩形QAM星座的信息符号的最佳线性变换，本文发现优于Yuen-Guan-Tjhung通过使用他们的最佳旋转。在本文中，我们还提出了最佳的转换坐标交织正交设计（CIOD）提出的Khan-Rajan矩形QAM星座。
Orthogonal space-time block codes (OSTBC) from orthogonal designs have both advantages of complex symbol-wise maximum-likelihood (ML) decoding and full diversity. However, their symbol rates are upper bounded by 3/4 for more than two antennas for complex symbols. To increase the symbol rates, they have been generalized to quasi-orthogonal space-time block codes (QOSTBC) in the literature but the diversity order is reduced by half and the complex symbol-wise ML decoding is significantly increased to complex symbol pair-wise (pair of complex symbols) ML decoding. The QOSTBC has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair-wise ML decoding. The optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal-literal triangular lattices have been found by Su-Xia, where the optimality means the optimal diversity product (or product distance). QOSTBC has also been modified by Yuen-Guan-Tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair-wise ML decoding (the same complexity as complex symbol-wise decoding) and the optimal rotation angle for square and rectangular QAM constellations has been found. In this paper, we systematically study general linear transformations of information symbols for QOSTBC to have both full diversity and real symbol pair-wise ML decoding. We present the optimal transformation matrices (among all possible linear transformations not necessarily symbol rotations) of information symbols for QOSTBC with real symbol pair-wise ML decoding such that the optimal diversity product is achieved for both general square QAM and general rectangular QAM signal constellations. Furthermore, our newly proposed optimal linear transformations for QOSTBC also work for general QAM constellations in the sense that QOSTBC have full diversity with good diversity product property and real symbol pair-wise ML decoding. Interestingly, the optimal diversity products for square QAM constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. However, the optimal diversity products for (nonsquare) rectangular QAM constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. In this paper, we also present the optimal transformations for the co-ordinate interleaved orthogonal designs (CIOD) proposed by Khan-Rajan for rectangular QAM constellations.