The Schur-Kronecker Rematch --- Courtesy of Time-Reversal

We present a computationally-efficient and numerically-robust matrix-vector expression for the solution of a matrix linear least squares problem that arises in multistatic antenna array processing. Our derivation relies on an explicit new relation between Kronecker, Khatri-Rao and Schur-Hadamard matrix products, which involves a selection matrix (i.e., a subset of the columns of a permutation matrix). Moreover, we show that the same selection matrix also relates the vectorization-by-columns operator to the diagonal extraction operator, which plays a central role in our computationally-efficient solution. Brief concluding remarks on Schur's contributions to signal processing and linear algebra are also provided.

A Beamforming Method for Blind Calibration of Time-Interleaved A/D Converters

In this presentation, a blind calibration method is described for timing mismatches in a multichannel time-interleaved analog to digital converter (ADC). The proposed method requires that the input signal should be slightly oversampled. This ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the N ADC subchannels contain only N-1 alias components. Then the matrix power spectral density (PSD) of the ADC subchannels is rank deficient over this frequency band. Accordingly, when the timing offsets are known, we can construct a filter bank that nulls the vector signal at the ADC outputs. We employ a parametrization of this filter bank to develop an adaptive null steering algorithm for estimating the ADC timing offsets. The null steering filter bank employs $2N-1$ fixed FIR filters and $N-1$ unknown timing offset parameters which are estimated by using an adaptive stochastic gradient technique. A convergence analysis is presented for the blind calibration method. Numerical simulations for a bandlimited white noise input and for inputs containing several sinusoidal components demonstrate the effectiveness of the proposed technique.

Joint work with Steven Huang.

On Network Routing and Coding for Generalized Multicasting

In practical networks such as the internet, end-to-end information delivery is done by having routers store and forward packets. Recently, network coding emerged as a promising generalization of routing by allowing information to be "mixed" on the network. This informal presentation will highlight our recent findings on network coding, as a result of collaboration between Princeton University, Microsoft Research, and Texas A&M University, etc. We shall treat network coding from the following theoretical and application perspectives: including

1. Graph theoretical perspective (e.g., cut and path structures, algebraic characterizations)
2. Distributed optimization perspective (e.g., minimum energy multicasting)
3. Information theoretical perspective (e.g., coding for a generalization of Slepian-Wolf Theorem in a network setting).

The Next Big Thing in Signal Processing and Communications

Research in signal processing and communications is constantly changing as new theories and applications are developed. As these changes occur, research is constantly evolving as problems are confronted and promising ideas are pursued. This panel discussion will discuss the current status of and the problems facing the field and consider where current trends are leading. In particular, the panel will discuss how current results will influence future technology and potential new areas whose exploration is just beginning. In addition to discussing current research topics such as ultra wideband (UWB), sensor networks, and multi-user and network information theory, the discussion will also consider interdisciplinary topics such as bio-informatics and the interaction between industry and academic research. The panel will consist of several questions from the moderators as well as an opportunity for questions from the audience.