Sampling methods for parametric non-bandlimited signals:extensions and applications

Sampling theory has experienced a strong research revival over the past decade, which led to a generalization of Shannon's original theory and development of more advanced formulations with immediate relevance to signal processing and communications. For example, it was recently shown that it is possible to develop exact sampling schemes for a large class of non-bandlimited signals, namely, certain signals with finite rate of innovation. A common feature of such signals is that they have a parametric representation with a finite number of degrees of freedom and can be perfectly reconstructed from a finite number of samples. The goal of this thesis is to advance the sampling theory for signals of finite rate of innovation and consider its possible extensions and applications. In the first part of the thesis, we revisit the sampling problem for certain classes of such signals, including non-uniform splines and piecewise polynomials, and develop improved schemes that allow for stable and precise reconstruction in the presence of noise. Specifically, we develop a subspace approach to signal reconstruction, which converts a nonlinear estimation problem into the simpler problem of estimating the parameters of a linear model. This provides an elegant and robust framework for solving a large class of sampling problems, while offering more flexibility than the traditional scheme for bandlimited signals. In the second part of the thesis, we focus on applications of our results to certain classes of nonlinear estimation problems encountered in wideband communication systems, most notably ultra-wideband (UWB) systems, where the bandwidth used for transmission is much larger than the bandwidth or rate of information being sent. We develop several frequency domain methods for channel estimation and synchronization in UWB systems, which yield high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. We also propose algorithms that are suitable for identification of more realistic UWB channel models, where a received signal is made up of pulses with different pulse shapes. Finally, we extend our results to multidimensional signals, and develop exact sampling schemes for certain classes of parametric non-bandlimited 2-D signals, such as sets of 2-D Diracs, polygons or signals with polynomial boundaries

Diffraction efficiency of localized holograms in doubly doped LiNbO3 crystals

The diffraction efficiency of M holograms superimposed in the volume of the recording medium is proportional to 1/M^2. We present a method, based on nondestructive localized holograms in a doubly doped LiNbO3 crystal, that allows us to also record M holograms in the same volume without an exposure schedule or a diffraction efficiency that has 1/M dependence. We compare experimentally the final diffraction efficiency obtained with the localized and distributed recording methods

Localized holographic recording in doubly doped lithium niobate

In holographic data storage, pages of information are overlapped in the volume of the recording medium. Due to destructive read-out of holograms in photorefractive crystals such as LiNbO_3:Fe, holograms are recorded with an exposure schedule in order to equalize diffraction efficiency. This leads to a final diffraction efficiency proportional to 1/M^2, where M is the number of exposures. Coherent erasure of a particular page also erases all the other pages stored in the same volume. We believe to have found a technique that does not require an exposure schedule and that can record M holograms with diffraction efficiency following a 1/M dependence. Our technique is based on non-destructive read-out in doubly-doped LiNbO_3. The technique is based on the recording of localized holograms in thin layers across the volume of the crystal

Low-Complexity Subspace Methods for Channel Estimation and Synchronization in Ultra-Wideband Systems

We consider the problem of low-complexity channel estimation in digital ultra-wideband receivers. We extend some of our recent sampling results for certain classes of parametric non-bandlimited signals and develop several methods that take advantage of transform techniques to estimate channel parameters from a low-dimensional subspace of a received signal, that is, by sampling the signal below the Nyquist rate. By lowering the sampling rate we reduce computational requirements compared to current digital solutions, allow for slower A/D converters and potentially significantly reduce power consumption of digital receivers. Our approach is particularly suitable for indoor wireless sensor networks, where low rates and low power consumption are required. One application of our framework to high-resolution acquisition in ultra-wideband localizers is also presented

A sampling theorem for the radon transform of finite complexity objects

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Low-Sampling Rate UWB Channel Characterization and Synchronization

We consider the problem of low-sampling rate high-resolution channel estimation and timing for digital ultra-wideband (UWB) receivers. We extend some of our recent results in sampling of certain classes of parametric non-bandlimited signals and develop a frequency domain method for channel estimation and synchronization in ultra-wideband systems, which uses sub-Nyquist uniform sampling and well-studied computational procedures. In particular, the proposed method can be used for identification of more realistic channel models, where different propagation paths undergo different frequency-selective fading. Moreover, we show that it is possible to obtain high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. Our approach leads to faster acquisition compared to current digital solutions, allows for slower A/D converters, and potentially reduces power consumption of digital UWB receivers significantly

Low-Sampling Rate UWB Channel Characterization and Synchronization

We consider the problem of low-sampling rate high-resolution channel estimation and timing for digital ultra-wideband (UWB) receivers. We extend some of our recent results in sampling of certain classes of parametric nonbandlimited signals and develop a frequency domain method for channel estimation and synchronization in ultra-wideband systems, which uses sub-Nyquist uniform sampling and wellstudied computational procedures. In particular, the proposed method can be used for identification of more realistic channel models, where di#erent propagation paths undergo di#erent frequency-selective fading. Moreover, we show that it is possible to obtain high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. Our approach leads to faster acquisition compared to current digital solutions, allows for slower A/D converters, and potentially reduces power consumption of digital UWB receivers significantly

Sampling With Finite Rate of Innovation: Channel and Timing Estimation for UWB and GPS

Abstract—In this work, we consider the problem of channel estimation by using the recently developed theory for sampling of signals with a finite rate of innovation [1]. We show a framework which allows for lower than Nyquist rate sampling applicable for timing and channel estimation of both narrowband and wideband channels. In certain cases we demonstrate performance exceeding that of algorithms using Nyquist rate sampling while working at lower sampling rates, thus saving power and computational complexity

High-Resolution Acquisition Methods for Wideband Communication Systems

We consider the problem of low-complexity timing synchronization in digital receivers for DS-CDMA and UWB systems operating over channels with single or multiple propagation paths. We extend some of our recent sampling results for certain classes of non-bandlimited signals and develop a method that takes advantage of transform techniques to perform propagation delay estimation from a low-dimensional subspace of a received signal, that is, by sampling below the Nyquist rate. By lowering the sampling rate we reduce computational requirements compared to existing solutions, allow for slower A/D converters and significantly reduce power consumption of digital receivers