Dirty Paper Coding (DPC) is considered as the optimal precoding which achieves capacity for the Gaussian Multiple-Input Multiple-Output (MIMO) broadcast channel (BC). However, to find the optimal precoding order, it needs to repeat N! times for N users as there are N! possible precoding orders. This extremely high complexity limits its practical use in modern wireless networks. In this paper, we show the equivalence of DPC and the recently proposed Higher Order Mercer's Theorem (HOGMT) precoding[1][2] in 2-D (spatial) case, which provides an alternate implementation for DPC. Furthermore, we show that the proposed implementation method is linear over the permutation operator when permuting over multi-user channels. Therefore, we present a low complexity algorithm that optimizes the precoding order for DPC with beamforming, eliminating repeated computation of DPC for each precoding order. Simulations show that our method can achieve the same result as conventional DPC with about 20 dB lower complexity for N = 5 users.
翻译:摘要:Dirty Paper Coding(DPC)被认为是实现高斯多输入多输出(MIMO)广播通道(BC)容量的最佳预编码。然而,为了找到最佳预编码顺序,需要重复N!次,因为有N!种可能的预编码顺序。这种极高的复杂性限制了它在现代无线网络中的实际使用。本文展示了DPC和最近提出的Higher Order Mercer's Theorem(HOGMT)预编码[1][2]在二维(空间)情况下的等效性,这提供了DPC的替代实现方法。此外,我们展示了当在多用户信道上进行置换时,所提出的实施方法在置换运算符上是线性的。因此,我们提出了一个低复杂度算法,用于优化带有波束形成的DPC的预编码顺序,消除了每个预编码顺序计算DPC的重复计算。模拟结果表明,我们的方法可以在N = 5用户时以约20 dB较低的复杂度达到与传统DPC相同的结果。