Zero-forcing precoding and generalized inverses
Zero-forcing precoding and generalized inverses
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DOI：
10.1109/tsp.2008.924638
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发表时间：
2008-09-01
影响因子：
5.4
通讯作者：
Shamai (Shitz), Shlomo
中科院分区：
文献类型：
--
作者：
Wiesel, Ami;Eldar, Yonina C.;Shamai (Shitz), Shlomo
我们考虑了线性逼零预编码设计问题，并讨论了它与线性代数中广义逆理论的关系。对一种称为伪逆的特殊广义逆给予了特别的关注。我们从总功率约束下的标准设计入手，证明了在这种情况下，基于伪逆的预编码器在广义逆中是最优的。然后，我们继续检查每个天线的单个功率限制。在这种情况下，伪逆不一定是最优逆。事实上，寻找最优矩阵并不是一件容易的事，而且取决于具体的性能指标。我们讨论了两个常见的准则，公平性和吞吐量，并证明了使用标准的凸优化方法可以找到最优的广义逆。我们使用计算机模拟演示了我们的方法所提供的改进的性能。
We consider the problem of linear zero-forcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudo-inverse. We begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo-inverse are optimal among the generalized inverses in this setting. Then, we proceed to examine individual per-antenna power constraints. In this case, the pseudo-inverse is not necessarily the optimal inverse. In fact, finding the optimal matrix is nontrivial and depends on the specific performance measure. We address two common criteria, fairness and throughput, and show that the optimal generalized inverses may be found using standard convex optimization methods. We demonstrate the improved performance offered by our approach using computer simulations.