标题： 多用户系统中具有拟模体容量区域的公平性 显示英文标题

标题： Fairness in Multiuser Systems with Polymatroid Capacity Region

摘要： 对于广泛的一类多用户系统，包含角点和总容量面的容量区域的一个子集具有称为超模体的特殊结构。具有固定输入分布的多址信道和多天线广播信道是此类系统的例子。总容量面上的任何内部点都可以通过在角点之间进行时间共享或通过一种称为速率分割的替代方法来实现。本文的主要目的是找到一个满足活跃用户之间公平性概念的总容量面上的点。这个问题分为两种情况处理：(i) 实现内部点的复杂度不可行时，以及(ii) 实现内部点的复杂度可行时。对于第一种情况，需要选择一个使活跃用户最低速率最大化的角点（最大最小角点）进行信号传输。引入了一种简单的贪心算法来找到最优的最大最小角点。对于第二种情况，利用超模体的性质，在总容量面上定位一个最优公平的速率向量，使得所有用户中的最低速率最大（最大最小速率）。当某些用户的速率不能再增加（达到最大最小值）时，该算法递归地最大化其余用户的最低速率。证明了推导时间共享系数或速率分割方案的问题可以通过将问题分解为一些低维子问题来解决。此外，提出了一种快速算法来计算时间共享系数，以达到总容量面上的任意一点。 显示英文摘要

摘要： For a wide class of multi-user systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Multiaccess channels with fixed input distributions and multiple-antenna broadcast channels are examples of such systems. Any interior point of the sum-capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum-capacity facet which satisfies a notion of fairness among active users. This problem is addressed in two cases: (i) where the complexity of achieving interior points is not feasible, and (ii) where the complexity of achieving interior points is feasible. For the first case, the corner point for which the minimum rate of the active users is maximized (max-min corner point) is desired for signaling. A simple greedy algorithm is introduced to find the optimum max-min corner point. For the second case, the polymatroid properties are exploited to locate a rate-vector on the sum-capacity facet which is optimally fair in the sense that the minimum rate among all users is maximized (max-min rate). In the case that the rate of some users can not increase further (attain the max-min value), the algorithm recursively maximizes the minimum rate among the rest of the users. It is shown that the problems of deriving the time-sharing coefficients or rate-spitting scheme can be solved by decomposing the problem to some lower-dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum-capacity facet is proposed.