Sampling of communications systems with bandwidth expansion

Many communication systems are {\em bandwidth-expanding}: the transmitted signal occupies a bandwidth larger than the {\em symbol rate}. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. shows that in order to represent a bandlimited signal, it is necessary to sample at what is popularly referred to as the Shannon or Nyquist rate. However, in many systems, the required sampling rate is very high and expensive to implement. In this work we show that it is possible to get suboptimal performance by sampling close to the {\em symbol rate} of the signal, using well-studied algorithmic components. This work is based on recent results on sampling for some classes of non-bandlimited signals. In the present paper, we extend these sampling results to the case when there is noise. In our exposition, we use Ultra Wideband (UWB) signals as an example of how our framework can be applied

Sampling signals with finite rate of innovation

Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we showthat they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results. Applications of these new sampling results can be found in signal processing, communications systems, and biological systems

Hardware Development of an Ultra-Wideband System for High Precision Localization Applications

A precise localization system in an indoor environment has been developed. The developed system is based on transmitting and receiving picosecond pulses and carrying out a complete narrow-pulse, signal detection and processing scheme in the time domain. The challenges in developing such a system include: generating ultra wideband (UWB) pulses, pulse dispersion due to antennas, modeling of complex propagation channels with severe multipath effects, need for extremely high sampling rates for digital processing, synchronization between the tag and receivers’ clocks, clock jitter, local oscillator (LO) phase noise, frequency offset between tag and receivers’ LOs, and antenna phase center variation. For such a high precision system with mm or even sub-mm accuracy, all these effects should be accounted for and minimized. In this work, we have successfully addressed many of the above challenges and developed a stand-alone system for positioning both static and dynamic targets with approximately 2 mm and 6 mm of 3-D accuracy, respectively. The results have exceeded the state of the art for any commercially available UWB positioning system and are considered a great milestone in developing such technology. My contributions include the development of a picosecond pulse generator, an extremely wideband omni-directional antenna, a highly directive UWB receiving antenna with low phase center variation, an extremely high data rate sampler, and establishment of a non-synchronized UWB system architecture. The developed low cost sampler, for example, can be easily utilized to sample narrow pulses with up to 1000 GS/s while the developed antennas can cover over 6 GHz bandwidth with minimal pulse distortion. The stand-alone prototype system is based on tracking a target using 4-6 base stations and utilizing a triangulation scheme to find its location in space. Advanced signal processing algorithms based on first peak and leading edge detection have been developed and extensively evaluated to achieve high accuracy 3-D localization. 1D, 2D and 3D experiments have been carried out and validated using an optical reference system which provides better than 0.3 mm 3-D accuracy. Such a high accuracy wireless localization system should have a great impact on the operating room of the future

The Future of the Operating Room: Surgical Preplanning and Navigation using High Accuracy Ultra-Wideband Positioning and Advanced Bone Measurement

This dissertation embodies the diversity and creativity of my research, of which much has been peer-reviewed, published in archival quality journals, and presented nationally and internationally. Portions of the work described herein have been published in the fields of image processing, forensic anthropology, physical anthropology, biomedical engineering, clinical orthopedics, and microwave engineering. The problem studied is primarily that of developing the tools and technologies for a next-generation surgical navigation system. The discussion focuses on the underlying technologies of a novel microwave positioning subsystem and a bone analysis subsystem. The methodologies behind each of these technologies are presented in the context of the overall system with the salient results helping to elucidate the difficult facets of the problem. The microwave positioning system is currently the highest accuracy wireless ultra-wideband positioning system that can be found in the literature. The challenges in producing a system with these capabilities are many, and the research and development in solving these problems should further the art of high accuracy pulse-based positioning