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arXiv 1601.05784cs.ITmath.IT
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高斯MIMO信道中天线选择的一个注记:容量保证和界

A Note on Antenna Selection in Gaussian MIMO Channels: Capacity Guarantees and Bounds

Yahya H. Ezzeldin, Ayan Sengupta, Christina Fragouli

摘要:

研究了在具有$n_t \times n_r$天线的高斯MIMO信道中选择$k_t \times k_r$天线的问题,其中$k_t \leq n_t$和$k_r \leq n_r$ .我们证明了以下两个结果普遍成立,在这个意义上,他们不依赖于信道系数:(i)最好的$k_t \times k_r$子信道的容量总是下界的一部分$\frac{k_t k_r}{n_t n_r}$的全容量(与$n_t \times n_r$天线)。当信道系数在幅度上减小时,该界限是紧的。(ii)总是存在$k_t \times k_r$天线(包括最佳天线)的选择,其在独立于信道矩阵中的系数的附加常数内实现大于全容量的$\frac{\min(k_t ,k_r)}{\min(n_t,n_r)}$的分数。关键的数学思想,使我们能够得出这些普遍的界限是直接关系到主子矩阵的厄米特矩阵的行列式的整个矩阵的行列式。

英文摘要:

We consider the problem of selecting $k_t \times k_r$ antennas from a Gaussian MIMO channel with $n_t \times n_r$ antennas, where $k_t \leq n_t$ and $k_r \leq n_r$. We prove the following two results that hold universally, in the sense that they do not depend on the channel coefficients: (i) The capacity of the best $k_t \times k_r$ subchannel is always lower bounded by a fraction $\frac{k_t k_r}{n_t n_r}$ of the full capacity (with $n_t \times n_r$ antennas). This bound is tight as the channel coefficients diminish in magnitude. (ii) There always exists a selection of $k_t \times k_r$ antennas (including the best) that achieves a fraction greater than $\frac{\min(k_t ,k_r)}{\min(n_t,n_r)}$ of the full capacity within an additive constant that is independent of the coefficients in the channel matrix. The key mathematical idea that allows us to derive these universal bounds is to directly relate the determinants of principle sub-matrices of a Hermitian matrix to the determinant of the entire matrix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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