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Diversity Analysis of Group Vector Perturbation Precoding

机译：群矢量摄动预编码的多样性分析

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摘要

We study the effect on diversity of using the sphere encoder-based vector perturbation (VP) technique of Peel and the lattice reduction-aided techniques (Babai approximations) of Windpassinger on a subset of the transmitted symbols. For a system with $n$ diversity channels, we prove that the diversity order gap between the maximum diversity of $n$ achieved by the full-size VP and the minimum diversity of 1 provided by linear precoding can be bridged by applying VP to a group of transmitted symbols. In particular, we prove that the diversity order is $n-l$ , where $l$ is the number of symbols that are not vector-perturbed. We show that this result holds true for lattice-reduction with both the rounding-off and nearest plane Babai approximations. The result shows that in terms of diversity, the group of vector-perturbed users counts as a single user. In fact, in a multiple-input and multiple-output Gaussian broadcast channel with $l$ linearly precoded users, we can add up to $n-l$ VP users and the diversity order for all users will decrease only by one, irrespective of how many VP users are added.
机译：我们研究了基于球编码器的Peel向量扰动（VP）技术和Windpassinger的晶格简化辅助技术（Babai近似）对传输符号的子集的多样性的影响。对于具有$ n $分集通道的系统，我们证明通过将VP应用于a可以弥合全尺寸VP实现的$ n $的最大分集与线性预编码提供的最小分集1之间的分集阶差。传输符号组。特别是，我们证明了分集阶次是$ n-l $，其中$ l $是没有向量扰动的符号数。我们证明，对于舍入和最接近的平面Babai近似，此结果对于格约化都是成立的。结果表明，就多样性而言，向量扰动用户组算作单个用户。实际上，在具有线性预编码的$ l $用户的多输入和多输出高斯广播频道中，我们最多可以添加$ nl $ VP用户，并且所有用户的分集阶数只会减少一个，而无论有多少个VP用户已添加。

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