Secure Degrees of Freedom of MIMO Rayleigh Block Fading Wiretap Channels With No CSI Anywhere
Secure Degrees of Freedom of MIMO Rayleigh Block Fading Wiretap Channels With No CSI Anywhere
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安全的 MIMO 瑞利自由度可阻止衰落窃听通道，无需任何 CSI
DOI：
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发表时间：
2015
影响因子：
10.4
通讯作者：
Y. Hong
中科院分区：
文献类型：
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作者：
Ta;P. Mukherjee;S. Ulukus;Shih;Y. Hong
我们考虑块瑞利衰落多输入多输出 (MIMO) 窃听信道，任何终端都没有可用的先前信道状态信息 (CSI)。信道增益在T个符号的相干间隔内保持恒定，然后在下一个相干间隔改变到另一个独立的实现。发射机、合法接收机和窃听者分别拥有 nt、nr 和 ne 个天线。当 T ≥ 2min(nt,nr) 时，我们确定该系统的精确安全自由度 (s.d.o.f.)。我们证明，在这种情况下，s.d.o.f.完全等于 (min(nt,nr)-ne)+(T -min(nt,nr))/T。该表达式中的第一项可以解释为窃听者使用 ne 个天线从发射机和合法接收机上拿走 ne 个天线。第二项可以解释为 s.d.o.f 的一部分。由于合法接收方缺少 CSI 而丢失。特别是，损失分数 min(nt,nr)/T 可以解释为专用于训练合法接收器以使其学习自己的 CSI 的信道使用的分数。我们证明这个 s.d.o.f.可以通过采用恒定范数信道输入来实现，这可以被视为离散信令到多个维度的推广。
We consider the block Rayleigh fading multiple-input multiple-output (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant within a coherence interval of T symbols, and then change to another independent realization in the next coherence interval. The transmitter, the legitimate receiver, and the eavesdropper have nt, nr, and ne antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2min(nt,nr). We show that, in this case, the s.d.o.f. is exactly equal to (min(nt,nr)-ne)+(T -min(nt,nr))/T. The first term in this expression can be interpreted as the eavesdropper with ne antennas taking away ne antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of the s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(nt,nr)/T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions.