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

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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.