Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems
Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems
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DOI：
10.1109/tsp.2012.2208635
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发表时间：
2012-02
影响因子：
5.4
通讯作者：
Arash Khabbazibasmenj;F. Roemer;S. Vorobyov;M. Haardt
中科院分区：
文献类型：
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作者：
Arash Khabbazibasmenj;F. Roemer;S. Vorobyov;M. Haardt
双向放大转发（AF）多输入多输出（MIMO）中继中的和速率最大化问题属于一类凸函数差分（DC）规划问题。DC编程问题也发生在其他信号处理应用中，并且通常使用分支定界方法的不同修改来解决，然而，该方法不具有任何多项式时间复杂度保证。在本文中，我们开发了两个有效的多项式时间算法的和速率最大化双向AF MIMO中继。第一个算法保证找到至少一个Karush-Kuhn-Tucker（KKT）解决方案。然而，有强有力的证据表明，这样的解决方案实际上是全局最优的。基于广义特征向量的第二种算法与第一种算法性能相同，但计算复杂度有所降低。该问题的目标函数表示为二次分数比的乘积，并参数化，使得其凸部分（相对于凹部分）仅包含一个（或两个）优化变量。其中一种算法被称为多项式时间DC（POTDC），它基于半定规划（SDP）松弛、线性化和单个参数上的迭代牛顿型搜索。另一种算法被称为速率最大化通过广义特征向量（RAGES），是基于广义特征向量方法和迭代搜索两个（或一个，在其近似版本）优化变量。我们推导出相应的优化问题的最优值的上限，并通过模拟表明，这两种算法都实现了这个上限。它提供了一个证据，该算法找到一个全局最优。所提出的方法也优于其他国家的最先进的算法上级。
Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. The objective function of the problem is represented as a product of quadratic fractional ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed methods are also superior to other state-of-the-art algorithms.