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.

High-Resolution Acquisition Methods for Wideband Communication Systems

Irena Maravic, Martin Vetterli

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.

2003

Sampling signals with finite rate of innovation: the noisy case

Irena Maravic, Andrea Ridolfi, Martin Vetterli

Recently a sampling theorem for a certain class of signals with finite rate of innovation (which includes for example stream of Diracs) has been developed. In essence, such non band-limited signals can be sampled at or above the rate of innovation. In the present paper, we consider the case of such signals when noise is present. Clearly, the finite rate of innovation property is lost, but if the signal-to-noise ratio (SNR) is sufficient, several methods are possible to reconstruct the signal while sampling well below the Nyquist rate. We thus explore the trade-offs between SNR, sampling rate, computational complexity and reconstruction quality. Applications of such methods can be found in acquisition and processing of signals in high bandwidth communications, like ultra wide band communication.

2002

Sampling methods for parametric non-bandlimited signals

Irena Maravic

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.

EPFL2004

Sampling methods for parametric non-bandlimited signals

Irena Maravic

EPFL2004