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arXiv 0708.3567cs.ITmath.IT
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MIMO放大转发多跳信道特征谱失真研究

On the Distortion of the Eigenvalue Spectrum in MIMO Amplify-and-Forward Multi-Hop Channels

Joerg Wagner, Armin Wittneben

摘要:

考虑具有n_s个非合作源天线和n_d个完全合作目的天线的无线MIMO多跳信道,以及每个包含k个非合作中继天线的L个簇。源信号在到达目的地之前穿过中继天线的所有L个集群。当相同集群内的中继天线在重传之前以相同常数缩放其接收信号时,将源天线处的输入信号与目的地天线处的输出信号相关联的等效信道矩阵H与信道矩阵H_l,l = 1,.,L +1,对应于各个跳。我们对该信道进行渐近容量分析如下:在第一种情况下,我们取限制n_s-> infty,n_d-> infty和k-> infty,但保持n_s/n_d和k/n_d固定。然后,我们取极限L-> infty和k/n_d-> infty。在H_l满足Marcenko-Pastur定律的条件下,证明了只要k/n_d之比至少在L中线性地变化,则容量在min {n_s,n_d}中线性地变化。此外,我们表明,高达噪声惩罚和前对数因子的点对点MIMO信道的容量接近,当这种缩放比线性稍快。相反,几乎所有的空间自由度小于线性缩放消失。

英文摘要:

Consider a wireless MIMO multi-hop channel with n_s non-cooperating source antennas and n_d fully cooperating destination antennas, as well as L clusters containing k non-cooperating relay antennas each. The source signal traverses all L clusters of relay antennas, before it reaches the destination. When relay antennas within the same cluster scale their received signals by the same constant before the retransmission, the equivalent channel matrix H relating the input signals at the source antennas to the output signals at the destination antennas is proportional to the product of channel matrices H_l, l=1,...,L+1, corresponding to the individual hops. We perform an asymptotic capacity analysis for this channel as follows: In a first instance we take the limits n_s->infty, n_d->infty and k->infty, but keep both n_s/n_d and k/n_d fixed. Then, we take the limits L->infty and k/n_d->infty. Requiring that the H_l's satisfy the conditions needed for the Marcenko-Pastur law, we prove that the capacity scales linearly in min{n_s,n_d}, as long as the ratio k/n_d scales at least linearly in L. Moreover, we show that up to a noise penalty and a pre-log factor the capacity of a point-to-point MIMO channel is approached, when this scaling is slightly faster than linear. Conversely, almost all spatial degrees of freedom vanish for less than linear scaling.

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