This is a proposal by the Program in Applied and Computational Mathematics 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.
