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arXiv 0705.1336cs.ITmath.IT
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大MIMO系统分集复用折衷的渐近分析

Diversity-Multiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems

Sergey Loyka, George Levin

摘要:

分集复用折衷(DMT)提供了一个紧凑的框架,以根据它们提供的两个主要优点(即,高数据率和/或低出错率)来比较各种MIMO系统和信道。对于i.i.d.,该折衷被渐近地表征(SNR->无穷大)。Rayleigh衰落信道[1].渐近DMT高估了有限SNR DMT [2]。在本文中,使用最近的结果上的渐近(在天线的数量)中断容量分布,我们推导和分析有限SNR DMT的广泛的一类信道(不一定是瑞利衰落)。在此基础上,我们给出了渐近DMT由有限信噪比DMT逼近的收敛条件。复用增益的定义示出严重影响的收敛点:当复用增益定义通过平均(遍历)容量,收敛发生在现实的SNR值。此外,在这种情况下,分集增益也可以用来估计中断概率与合理的精度。通过平均容量的高SNR渐近线(如[1])定义的复用增益导致中大型系统的收敛非常缓慢(如1/ln(SNR)^2),因此,渐近DMT不能用于实际的SNR值。对于该定义,高SNR阈值在天线数量和复用增益方面呈指数增加。对于相关锁眼信道,分集增益随信道的相关性和功率不平衡而减小。虽然Zheng和Tse的SNR渐近DMT没有捕捉到这种效应,但尺寸渐近DMT却做到了。

英文摘要:

Diversity-multiplexing tradeoff (DMT) presents a compact framework to compare various MIMO systems and channels in terms of the two main advantages they provide (i.e. high data rate and/or low error rate). This tradeoff was characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The asymptotic DMT overestimates the finite-SNR one [2]. In this paper, using the recent results on the asymptotic (in the number of antennas) outage capacity distribution, we derive and analyze the finite-SNR DMT for a broad class of channels (not necessarily Rayleigh fading). Based on this, we give the convergence conditions for the asymptotic DMT to be approached by the finite-SNR one. The multiplexing gain definition is shown to affect critically the convergence point: when the multiplexing gain is defined via the mean (ergodic) capacity, the convergence takes place at realistic SNR values. Furthermore, in this case the diversity gain can also be used to estimate the outage probability with reasonable accuracy. The multiplexing gain definition via the high-SNR asymptote of the mean capacity (as in [1]) results in very slow convergence for moderate to large systems (as 1/ln(SNR)^2) and, hence, the asymptotic DMT cannot be used at realistic SNR values. For this definition, the high-SNR threshold increases exponentially in the number of antennas and in the multiplexing gain. For correlated keyhole channel, the diversity gain is shown to decrease with correlation and power imbalance of the channel. While the SNR-asymptotic DMT of Zheng and Tse does not capture this effect, the size-asymptotic DMT does.

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