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arXiv 2005.07515cs.ITmath.IT
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干扰约束下高斯MIMO信道的容量(完整版)

On The Capacity of Gaussian MIMO Channels Under Interference Constraints (full version)

Sergey Loyka

摘要:

研究了在总发射功率和多干扰功率约束下的高斯MIMO信道。在一般情况下(直到对偶变量),得到其最优发射协方差矩阵的封闭形式的解决方案。在一些特殊情况下,获得了许多更显式的封闭形式的解决方案,包括满秩和秩1(波束成形)解决方案,其与众所周知的注水解决方案显著不同(例如,信道本征模式上的信令不再是最佳的,并且对于非零发射功率,容量可以为零)。白化滤波器被证明是干扰约束下的最优预编码的重要组成部分。容量缩放与发射功率的研究:它的定性行为是由自然的线性代数结构引起的MIMO信道的多个用户。给出了一个简单的秩条件来描述频谱共享的可能性。TPC和IPC之间的相互作用进行了研究,包括从功率限制到干扰限制制度的过渡。指出了IPC下最优协方差矩阵的一些不寻常的性质,并建立了其秩的界。在自适应天线阵列文献中已知的部分零形成被证明是最佳的,从信息理论的角度来看,以及在某些情况下。

英文摘要:

Gaussian MIMO channel under total transmit and multiple interference power constraints (TPC and IPCs) is considered. A closed-form solution for its optimal transmit covariance matrix is obtained in the general case (up to dual variables). A number of more explicit closed-form solutions are obtained in some special cases, including full-rank and rank-1 (beamforming) solutions, which differ significantly from the well-known water-filling solutions (e.g. signaling on the channel eigenmodes is not optimal anymore and the capacity can be zero for non-zero transmit power). A whitening filter is shown to be an important part of optimal precoding under interference constraints. Capacity scaling with transmit power is studied: its qualitative behaviour is determined by a natural linear-algebraic structure induced by MIMO channels of multiple users. A simple rank condition is given to characterize the cases where spectrum sharing is possible. An interplay between the TPC and IPCs is investigated, including the transition from power-limited to interference-limited regimes. A number of unusual properties of an optimal covariance matrix under IPCs are pointed out and a bound on its rank is established. Partial null forming known in the adaptive antenna array literature is shown to be optimal from the information-theoretic perspective as well in some cases.

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