论文标题
广义二次矩阵编程：使用任意输入分布的线性预编码的统一框架
Generalized Quadratic Matrix Programming: A Unified Framework for Linear Precoding With Arbitrary Input Distributions
论文作者
论文摘要
本文研究了一类新的非凸优化，该类别为具有任意输入分布的单个/多用户多输入多输出（MIMO）通道提供了一个统一的框架。新的优化称为广义二次矩阵编程（GQMP）。由于不确定的多项式时间（NP） - GQMP问题的掌握性，而不是寻求全球最佳解决方案，因此我们提出了一种有效的算法，该算法保证可以收敛到Karush-Kuhn-tucker（KKT）点。该算法背后的想法是为非凸物目标和约束函数构造明确的凹面下限，然后解决一系列凹面最大化问题的序列，直到收敛为止。在应用方面，我们考虑了一个下行链路底层安全认知无线电（CR）网络，每个节点都有多个天线。我们设计线性预码器，以最大化发射机处的有限词组输入和统计通道状态信息（CSI）最大化平均保密率（SUM）速率。在安全的多播/广播方案下的预编码问题是GQMP问题，因此可以通过我们提出的算法有效地解决它们。提供了几个数值示例，以显示我们算法的功效。
This paper investigates a new class of non-convex optimization, which provides a unified framework for linear precoding in single/multi-user multiple-input multiple-output (MIMO) channels with arbitrary input distributions. The new optimization is called generalized quadratic matrix programming (GQMP). Due to the nondeterministic polynomial time (NP)-hardness of GQMP problems, instead of seeking globally optimal solutions, we propose an efficient algorithm which is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. The idea behind this algorithm is to construct explicit concave lower bounds for non-convex objective and constraint functions, and then solve a sequence of concave maximization problems until convergence. In terms of application, we consider a downlink underlay secure cognitive radio (CR) network, where each node has multiple antennas. We design linear precoders to maximize the average secrecy (sum) rate with finite-alphabet inputs and statistical channel state information (CSI) at the transmitter. The precoding problems under secure multicast/broadcast scenarios are GQMP problems, and thus they can be solved efficiently by our proposed algorithm. Several numerical examples are provided to show the efficacy of our algorithm.
