Deep Learning of Sparse Array Configurations —— 从理论到完整复现第一章 理论根基与问题形式化1.3 传统优化方法基准线(Baseline Met

Deep Learning of Sparse Array Configurations —— 从理论到完整复现

第一章 理论根基与问题形式化

1.3 传统优化方法基准线(Baseline Methods)

1.3.1 凸松弛方法家族

1.3.1.1 半定松弛(SDR):将QCQP转化为SDP的升维技巧

半定松弛(Semidefinite Relaxation, SDR)技术代表了处理非凸二次约束二次规划(Quadratically Constrained Quadratic Program, QCQP)问题的经典升维策略。在稀疏阵列配置场景中,核心目标是从N 个候选阵元位置中选择P 个最优位置,使得输出信干噪比(Signal-to-Interference-plus-Noise Ratio, SINR)最大化。

原始优化问题可表述为寻找波束形成权向量w∈CN ,使得在二次约束条件下实现SINR最大化。该问题天然具有NP-hard特性,源于布尔选择变量的组合本质。SDR的核心思想是将原始向量优化问题提升至矩阵空间,通过引入半正定矩阵变量W=wwH 来松弛非凸的秩一约束。

具体而言,原始QCQP形式可重写为:

W∈CN×Nminimize​subject to​Tr(Rxx​W)+μTr(BiW~)Tr(Ra​W)≥1,W~≥∣W∣,W⪰0,Rank(W)=1.​

其中Rxx​ 表示接收数据相关矩阵,Ra​ 为期望信号相关矩阵,Bi 为重加权矩阵,μ

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深度学习工具包Deprecation notice.-----This toolbox is outdated and no longer maintained.There are much better tools available for deep learning than this toolbox, e.g. [Theano](http://deeplearning.net/software/theano/), [torch](http://torch.ch/) or [tensorflow](http://www.tensorflow.org/)I would suggest you use one of the tools mentioned above rather than use this toolbox.Best, Rasmus.DeepLearnToolbox================A Matlab toolbox for Deep Learning.Deep Learning is a new subfield of machine learning that focuses on learning deep hierarchical models of data.It is inspired by the human brain&#39;s apparent deep (layered, hierarchical) architecture.A good overview of the theory of Deep Learning theory is[Learning Deep Architectures for AI](http://www.iro.umontreal.ca/~bengioy/papers/ftml_book.pdf)For a more informal introduction, see the following videos by Geoffrey Hinton and Andrew Ng.* [The Next Generation of Neural Networks](http://www.youtube.com/watch?v=AyzOUbkUf3M) (Hinton, 2007)* [Recent Developments in Deep Learning](http://www.youtube.com/watch?v=VdIURAu1-aU) (Hinton, 2010)* [Unsupervised Feature Learning and Deep Learning](http://www.youtube.com/watch?v=ZmNOAtZIgIk) (Ng, 2011)If you use this toolbox in your research please cite [Prediction as a candidate for learning deep hierarchical models of data](http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=6284)```@MASTERSTHESIS\{IMM2012-06284, author = "R. 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上一篇: 【Deep Learning of Sparse Array Configurations】 —— 从理论到完整复现 第一章 理论根基与问题形式化 1.1 稀疏阵列信号处理基础
下一篇: 【Deep Learning of Sparse Array Configurations】 —— 从理论到完整复现 第二章 深度学习架构与数据工程2.1 问题重构:从优化到多标签分类
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