We consider sequences $(B_{k})_{k=0}^{\infty}$
 of points obtained by projecting a given point B=B
 0 back and forth between two manifolds $\mathcal{M}_{1}$
 and $\mathcal{M}_{2}$
 , and give conditions guaranteeing that the sequence converges to a limit $B_{\infty}\in\mathcal{M}_{1}\cap\mathcal{M}_{2}$
 . Our motivation is the study of algorithms based on finding the limit of such sequences, which have proved useful in a number of areas. The intersection is typically a set with desirable properties but for which there is no efficient method for finding the closest point B
 opt
 in $\mathcal{M}_{1}\cap\mathcal{M}_{2}$
 . Under appropriate conditions, we prove not only that the sequence of alternating projections converges, but that the limit point is fairly close to B
 opt
 , in a manner relative to the distance ∥B
 0−B
 opt
 ∥, thereby significantly improving earlier results in the field.

/pdf/alternating-projections-on-nontangential-manifolds-1f3ufnrcln.pdf

Alternating Projections on Nontangential Manifolds

The exact time-of-arrival (TOA) information of the multi-path signals is crucial for optimal channel estimation in vehicular OFDM systems. Super-resolution algorithms such as ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique) have been applied to retrieve this information from embedded pilots in the received OFDM symbols. These algorithms have high applicability for vehicular wireless environs characterized by high Doppler frequencies which leads to faster auto-correlation averaging. In this paper, we propose to improve upon the classical ESPRIT algorithm by incorporating the iterative reduced rank Hankel approximation (RRHA) technique. We show that this allows achieving of a lower MSE (mean square error) compared to the classical ESPRIT algorithm. Further, we portray that the degree of improvement brought forth increases with the increased number of RRHA-iterations.

An Improved ESPRIT Based Time-of-Arrival Estimation Algorithm for Vehicular OFDM Systems

This paper proposes a novel approach to estimate the fundamental frequency, harmonic and interharmonic phasors in power networks. The proposed method is based on the Matrix Pencil Method (MPM) and Principle Component Analysis (PCA). It estimates parameters of the Prony model that represents the measured signal under noisy conditions. The frequency decomposition feature of the MPM allows concurrent estimation of all frequency components (including all harmonics) of the signal without an additional computational cost. The performance of the proposed method is evaluated with respect to all the requirements defined in the IEEE Std. C37.118 for both M- and P-class phasor measurement units (PMUs). It is shown that the method is compliant with the operating conditions of both PMU classes and at the same time, is able to provide accurate harmonic phasor estimation.

Harmonic and Interharmonic Phasor Estimation Using Matrix Pencil Method for Phasor Measurement Units

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states (cMPS), a complete set of variational states grasping states in one-dimensional quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomized cMPS from their correlation data and study the robustness of the reconstruction for different noise models. Furthermore, we apply the method to data generated by simulations based on cMPS and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as those encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input–output formalism in quantum optics, it also allows for studying open quantum systems.

https://iopscience.iop.org/article/10.1088/1367-2630/16/12/123010/pdf

Quantum field tomography

Channel shortening filters have been used in acoustics to reduce reverberation, in error control decoding to reduce complexity, and in communication systems to reduce inter-symbol interference. The cascade of a channel and a channel shortening filter would produce an overall impulse response that has more of the energy in the channel impulse response compacted into fewer adjacent samples. Once designed, channel shortening filters operate on a per-sample basis. In this paper, we evaluate sparse FIR filters, which use more design complexity and less per-sample processing complexity, for channel shortening. Our contributions include (1) proposing a new sparse FIR filter design method for channel shortening, and (2) evaluating design tradeoffs in energy compaction vs. implementation complexity for sparse and non-sparse FIR filters. Our simulation results for ADSL channels show that sparse designs could achieve the same energy compaction with half as many coefficients than non-sparse FIR filters for low filter orders.

https://users.ece.utexas.edu/~bevans/papers/2010/sparseFilters/sparseTEQsICASSP2010PaperDraft.pdf

Design of sparse filters for channel shortening

We study the problem of estimating signal parameters from a noisy data sequence containing superimposed damped sinusoids. We propose three novel methods by combining the reduced-rank Hankel approximation and the matrix pencil method. We demonstrate that two of the proposed methods significantly outperform both the original matrix pencil method and the modified Kumaresan-Tufts (1982) method, especially at low signal-to-noise ratio.

/pdf/improved-matrix-pencil-methods-4ewqx15pdm.pdf

Improved matrix pencil methods

Commonly used time domain equalizer (TEQ) design methods have been recently unified as an optimization problem involving an objective function in the form of a Rayleigh quotient. The direct generalized eigenvalue solution relies on matrix decompositions. To reduce implementation complexity, we propose an iterative refinement approach in which the TEQ length starts at two taps and increases by one tap at each iteration. Each iteration involves matrix-vector multiplications and vector additions with 2 × 2 matrices and two-element vectors. At each iteration, the optimization of the objective function either improves or the approach terminates. The iterative refinement approach provides a range of communication performance versus implementation complexity tradeoffs for any TEQ method that fits the Rayleigh quotient framework. We apply the proposed approach to three such TEQ design methods: maximum shortening signal-to-noise ratio, minimum intersymbol interference, and minimum delay spread.

/pdf/iterative-refinement-methods-for-time-domain-equalizer-3ptff6btlm.pdf

Biao Lu

Papers

Improved matrix pencil methods

Iterative refinement methods for time-domain equalizer design