Shaping Multidimensional Signal Spaces-Part I : Optimum Shaping , Shell Mapping
Shaping Multidimensional Signal Spaces-Part I : Optimum Shaping , Shell Mapping
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塑造多维信号空间 - 第一部分：最佳塑造、壳映射
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
P. Kabal
中科院分区：
文献类型：
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作者：
Arnir;K. Kbandani;P. Kabal
在选择用于数据传输的信号星座的边界时，人们试图最小化给定分组中给定数量点的星座的平均能量。由于使用区域Z作为边界而不是超立方体，每二维平均能量的减少被称为L?的整形增益y。整形需要付出的代价包括：1)星座扩展比（CER）的增加，2)峰值平均功率比（PAR）的增加，以及3)寻址复杂性的增加。一般来说，在ys和CER、PAR之间存在权衡。在本工作中，介绍了同时优化这两种权衡的区域结构。在N-d （N维）最优整形区域（N偶）中，二维球面是二维子空间的边界，一个N-d球面是整个空间的边界。导出了最佳权衡曲线的解析表达式。通过将变量的变化表示为壳映射，将最佳整形区域映射到在单纯形内截断的超立方体。这种映射简化了性能计算，也简化了最佳整形区域的寻址。利用壳映射，我们引入了一种低复杂度的寻址方案，以达到最佳权衡曲线上的一个点。为了在选择折衷点时获得更大的灵活性，采用了自由度更大的二次成形方法。在该方法中，一个二维球是二维子空间的边界，一个N ' d球N ' 22是N ' d子空间的边界，一个N ' d球是整个空间的边界。索引tems -最佳形状，壳映射，截断立方体，均匀密度，最佳权衡。
In selecting the boundary of a signal constellation used for data transmission, one tries to minimize the average energy of the constellation for a given number of points from a given packing. The reduction in the average energy per two dimensions due to the use of a region ‘Z as the boundary instead of a hypercube is called the shaping gain y, of L?‘. The price to be paid for shaping involves: 1) an increase in the factor constellation-expansion ratio (CER,), 2) an increase in the factor peak-to-average-power ratio (PAR), and 3) an increase in the addressing complexity. In general, there exists a tradeoff between ys and CER,, PAR. In this work, the structure of the region which simultaneously optimizes both of these tradeoffs is introduced. In an N-D (N-dimensional) optimum shaping region (N even), a 2-D sphere is the boundary of the 2-D subspaces and an N-D sphere is the boundary of the whole space. Analytical expressions are derived for the optimum tradeoff curves. By applying a change of variable denoted as shell mapping, the optimum shaping region is mapped to a hypercube truncated within a simplex. This mapping facilitates the performance computation, and also the addressing of the optimum shaping region. Using shell mapping, we introduce an addressing scheme with low complexity to achieve a point on the optimum tradeoff curves. To obtain more flexibility in selecting the tradeoff point, a second shaping method with more degrees of freedom is used. In this method, a 2-D sphere is the boundary of the 2-D subspaces, an N’-D sphere, N’ 2 2, is the boundary of the N’-D subspaces, and an N-D sphere is the boundary of the whole space. Index Temts-Optimum shaping, shell mapping, truncated cube, uniform density, optimum tradeoff.