Career: Bilinear Shape-Constrained Regression in Blind Source Separation/Equalization, and Signal Processing for Chromatographic Analysis

无线通信的爆炸式增长产生了实现无缝集成个人通信服务承诺的竞争压力。 满足无线高级多媒体服务的服务质量限制是一个重要的挑战。 无线信道变化迅速、速率有限，并且由于传播和多用户干扰而导致严重的性能下降。这引发了人们对盲信号分离技术的极大兴趣，该技术能够在不了解信道的情况下分离和估计用户信号。有趣的是，数学上类似的问题出现在化学计量学中的色谱分析（CA）和流动注射分析（FIA）中，并应用于联邦战略领域的制造质量控制。 该计划的研究部分涉及盲信号分离问题的研究，该问题被视为双线性回归（系统），并受到以下约束：（i）因式分解约束； (ii) 对某些因子列的单模态或寡模态、凸性或支持约束（这些利用天线阵列提供的到达方向（DOA）分集，而不需要 DOA 估计；单模态在 CA/FIA 的背景下是有充分动机的，因子分布的平滑性也是如此）； (iii) 调制引起的（例如，有限字母表）约束。重点是相关优化算法的开发和性能分析及其在通信和化学计量学中的应用。两个应用领域之间的交叉融合是该计划的一个整体目标。该计划的教育部分包括：（i）为面向信号处理/通信的本科生和研究生开发优化理论和算法的入门和高级课程； (ii) 开发一套用于实验室/网络教学的 MATLAB 例程； (iii) 创造本科信号处理研究和教育机会； (iv) 通过适当利用多媒体工具来补充传统教学模式，更加重视创新教学。

The explosive growth of wireless communications has generated competitive pressure to fulfill the promise of seamlessly integrated personal communication services. Meeting quality-of-service constraints for advanced multimedia services over wireless is an important challenge. Wireless channels are rapidly-varying, rate-limited, and subject to severe degradation due to propagation and multiuser interference. This has sparked considerable interest in blind signal separation techniques, capable of separating and estimating the users' signals without assuming knowledge of the channel. Interestingly, mathematically similar problems appear in chromatographic analysis (CA) and flow injection analysis (FIA) in chemometrics, with applications in quality control for manufacturing, a Federal Strategic Area. The research component of this program involves the study of blind signal separation problems, posed as a (system of) bilinear regression(s) subject to: (i) factorization constraints; (ii) uni- or oligo-modality, convexity, or support constraints on the columns of certain factors (these exploit direction-of-arrival (DOA) diversity afforded by antenna arrays, without requiring DOA estimation; unimodality is well-motivated in the context of CA/FIA, and so is smoothness of factor profiles); and (iii) modulation-induced (e.g., finite-alphabet) constraints. The emphasis is on the development and performance analysis of associated optimization algorithms, and applications thereof in communications and chemometrics. Cross-fertilization between the two application domains is an integral goal of this program. The educational component of this program includes: (i) the development of introductory and advanced courses on optimization theory and algorithms for signal processing/communications -oriented undergraduate and graduate students; (ii) the development of a suite of MATLAB routines for laboratory/Web instruction; (iii) the creation of undergraduate signal processing research and education opportunities; and (iv) greater emphasis on innovative instruction through proper utilization of multimedia tools to complement traditional modes of instruction.