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arXiv 1612.04797cs.ITmath.IT
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高斯MIMO信道在总功率和天线功率约束下的容量

The Capacity of Gaussian MIMO Channels Under Total and Per-Antenna Power Constraints

S. Loyka

摘要:

固定高斯多输入多输出(MIMO)信道的容量和总功率(TP)约束下的最优传输策略和完整的信道状态信息是众所周知的。这个问题在一般情况下仍然是开放的,在个别的每天线(PA)的功率约束,而一些特殊情况下已经得到解决。这些包括用于MIMO信道的满秩解决方案和用于多输入单输出(MISO)信道的一般解决方案。本文考虑了固定高斯MISO信道,在一般情况下,在总功率和天线功率联合约束下,以封闭形式给出了其容量和最优传输策略。特别地,最优策略是混合的,包括两部分:第一部分是等增益传输,第二部分是最大比传输,它们分别负责PA和TP约束。给出了最优波束形成向量的封闭形式,并提出了一个准确而简单的近似容量。最后,通过建立联合功率约束下衰落MIMO信道的遍历容量,将上述结果推广到MIMO情况,当衰落分布为右酉不变时(其中i.i.d.和半相关瑞利衰落是特殊情况)。与固定的MISO的情况下,最佳的信令示出在这种情况下是各向同性的。

英文摘要:

The capacity of a fixed Gaussian multiple-input multiple-output (MIMO) channel and the optimal transmission strategy under the total power (TP) constraint and full channel state information are well-known. This problem remains open in the general case under individual per-antenna (PA) power constraints, while some special cases have been solved. These include a full-rank solution for the MIMO channel and a general solution for the multiple-input single-output (MISO) channel. In this paper, the fixed Gaussian MISO channel is considered and its capacity as well as optimal transmission strategies are determined in a closed form under the joint total and per-antenna power constraints in the general case. In particular, the optimal strategy is hybrid and includes two parts: first is equal-gain transmission and second is maximum-ratio transmission, which are responsible for the PA and TP constraints respectively. The optimal beamforming vector is given in a closed-form and an accurate yet simple approximation to the capacity is proposed. Finally, the above results are extended to the MIMO case by establishing the ergodic capacity of fading MIMO channels under the joint power constraints when the fading distribution is right unitary-invariant (of which i.i.d. and semi-correlated Rayleigh fading are special cases). Unlike the fixed MISO case, the optimal signaling is shown to be isotropic in this case.

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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