Collaborative Research: MSPA-MCS: Back to the Future: The Value of Algebraic Structure in Cross-Layer Design

这是普林斯顿大学应用与计算数学项目和UT达拉斯的电气工程系提出的一项建议，旨在证明代数结构对多天线无线通信系统跨层设计的价值。在网络层，它开发了多路访问（多对一）和广播（一对多）通信技术，其中代数结构可以非常简单地实现。自适应和非相干技术将在物理层用于设计在移动性下稳健的接收器架构，并且其中信号处理的端到端复杂性与单天线系统的端到端复杂性相当。代数结构将使非常有效地整合这些不同的功能成为可能。网络层的重点是通过编码和信号处理方面的创新，将高速率与高可靠性联合收割机结合起来。多路访问将支持使用外来的代数结构，如凯莱数设计新的干扰消除方法。广播应用（固定的和移动的）将通过一种新型的代码来支持，该代码被设计为实现高速率，但是在其中嵌入了更高分集（更低速率）的代码。这背离了标准做法，即牺牲多样性来实现高速率，反之亦然。另一个重要的主题是强调从吞吐量、延迟或应用层的实用性方面衡量物理层创新的价值。本提案中的研究活动引起了电信基础设施公司的强烈兴趣，其中包括在达拉斯地区设有研发设施的一些公司。该提案建立在Calderbank和Al-Dhahir之间的实质性合作基础上，其标准对CDMA和GSM都有影响。强调代数结构对新兴宽带无线标准的价值，为与工业合作伙伴的讨论创造了一种通用语言。熟悉这些标准将有利于研究生申请实习，预计他们将能够进入项目并立即做出贡献。集成信道估计、解码和均衡以及集成应用和物理层创新的价值将在可与工业合作伙伴和学术合作者共享的模拟中得到体现。学生还可以在UT达拉斯的一个新的MIMO无线测试平台上实现为该项目开发的信号处理算法。这些举措将减少采用的障碍，并促进对数学力量的好奇心。跨越传统领域界限的研究将增加欣赏数学力量及其在工程和许多科学中发挥的重要作用的学生人数。它将鼓励跨学科的探索和广度，它将培养学生，使他们能够在与不同学科相关的不同文化中蓬勃发展。连接不同世界的能力是一种对学术和非学术职业成功越来越重要的品质。

This is a proposal by the Program in Applied and ComputationalMathematics at Princeton University and the Electrical Engineering Department at UT Dallas aimed at demonstrating the value of algebraic structure to cross layer design of multiple antenna wireless communication systems. At the network layer it develops techniques for multiple access (many to one) and broadcast (one to many) communication where algebraic structure enables very simple implementation. Adaptive and non-coherent techniques will be used at the physical layer to design receiver architectures that are robust under mobility, and where the end to end complexity of signal processing is comparable to that of single antenna systems. Algebraic structure will make it possible to integrate these different functions very efficiently. The focus at the network layer is to combine high rates with high reliability through innovation in coding and signal processing. Multiple access will be supported by using exotic algebraic structures such as Cayley Numbers to design new methods for interference cancellation. Broadcast applications (fixed and mobile) will be supported through a new type of code that is designed to achieve high rate, but has embedded within it a higher diversity (lower rate) code. This departs from standard practice which is to sacrifice diversity to achieve high rate and vice versa. Another important theme is the emphasis on measuring the value of innovation at the physical layer in terms of throughput, latency, or utility at the application layer. The research activities in this proposal have attracted strong interest from telecommunications infrastructure companies, including some with R&D facilities in the Dallas area. The proposal builds on a substantive collaboration between Calderbank and Al-Dhahir with a history of standards impact on both CDMA and GSM. The emphasis on expressing the value of algebraic structure to emerging broadband wireless standards creates a common language for discussion with industrial partners. Familiarity with these standards will advantage graduate students when they apply for internships and it is expected they will be able to jump into projects and make an immediate contribution. The value of integrating channel estimation, decoding and equalization and of integrating applications and physical layer innovation will be expressed in simulations that can be shared with industrial partners and academic collaborators. Students may also implement signal processing algorithms developed for this project in a new MIMO wireless testbed at UT Dallas. These initiatives will reduce the barrier to adoption and promote curiosity about the power of mathematics. Research across traditional domain boundaries will increase the pool of students who appreciate the power of mathematics and the important role that it plays in engineering and many of the sciences. It will encourage interdisciplinary exploration and breadth, and it will train students so that they can flourish in the different cultures associated with different academic disciplines. The ability to bridge different worlds is a quality that is increasingly important to success in both academic and non-academic careers.