Outage Probability Under Channel Distribution Uncertainty
Outage Probability Under Channel Distribution Uncertainty
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DOI：
10.1109/tit.2012.2210190
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发表时间：
2012-11-01
影响因子：
2.5
通讯作者：
Loyka, Sergey
中科院分区：
文献类型：
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作者：
Ioannou, Ioanna;Charalambous, Charalambos D.;Loyka, Sergey
在部分信道分布信息下，研究了一类块衰落MIMO信道的中断概率和容量。具体而言，通道或其分布是未知的，但后者已知属于一类分布，其中每个成员都在标称分布的一定距离（不确定性）内。相对熵被用作分布之间距离的度量。引入并研究了复合中断概率，定义为最小（在发射信号分布上）-最大（在信道分布类上）中断概率。这将标准中断概率推广到部分信道分布信息的情况。复合中断概率的表征（通过1-D凸优化和在一个封闭的形式），它的性质，和近似。它被证明有两个政权的行为：当名义中断概率降低（e。例如，在一个实施例中，通过增加SNR），复合中断首先线性地下降到某一阈值（与相对熵距离相关;这是标称中断主导的状态），然后仅以几何方式（即，非常缓慢;这是不确定性主导的状态），因此不可能有显著的进一步降低。这提出了以下设计准则：通过在第一机制中增加SNR或优化发送信号分布（两者都降低标称中断）以及通过降低信道分布不确定性（e.例如，在一个实施例中，通过更好的估计）在第二个。复合中断仅取决于相对熵距离和标称中断，所有其他细节（标称衰落和噪声分布）是无关的。标称信道分布优化的发射信号分布示出也是最佳的整个类的分布。交换的相对熵分布的影响进行了研究，并建立了错误地板效应。研究了L-p距离约束下的复合中断概率。所得结果具有完全的一般性，即，对于具有任意标称衰落和噪声分布的一般信道模型。
Outage probability and capacity of a class of block-fading MIMO channels are considered under partial channel distribution information. Specifically, the channel or its distribution is not known but the latter is known to belong to a class of distributions where each member is within a certain distance (uncertainty) from a nominal distribution. Relative entropy is used as a measure of distance between distributions. Compound outage probability defined as min (over the transmitted signal distribution) -max (over the channel distribution class) outage probability is introduced and investigated. This generalizes the standard outage probability to the case of partial channel distribution information. Compound outage probability characterization (via 1-D convex optimization and in a closed form), its properties, and approximations are given. It is shown to have two-regime behavior: when the nominal outage probability decreases (e. g., by increasing the SNR), the compound outage first decreases linearly down to a certain threshold (related to the relative entropy distance; this is the nominal outage-dominated regime) and then only logarithmically (i.e., very slowly; this is the uncertainty-dominated regime) so that no significant further decrease is possible. This suggests the following design guideline: the outage probability is decreased by increasing the SNR or optimizing the transmitted signal distribution (both decrease nominal outage) in the first regime and by reducing the channel distribution uncertainty (e. g., via better estimation) in the second one. The compound outage depends on the relative entropy distance and the nominal outage only, all other details (nominal fading and noise distributions) being irrelevant. The transmit signal distribution optimized for the nominal channel distribution is shown to be also optimal for the whole class of distributions. The effect of swapping the distributions in relative entropy is investigated and an error floor effect is established. The compound outage probability under L-p distance constraint is also investigated. The obtained results hold in full generality, i.e., for the general channel model with arbitrary nominal fading and noise distributions.