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Sampling signals with finite rate of innovation
 IEEE Transactions on Signal Processing
, 2002
"... Abstract—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 ..."
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Cited by 350 (67 self)
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Abstract—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 show that 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 finitelength streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinitelength 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 errorcorrection 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. Index Terms—Analogtodigital conversion, annihilating filters, generalized sampling, nonbandlimited signals, nonuniform splines, piecewise polynomials, poisson processes, sampling. I.
LowSampling Rate UWB Channel Characterization and Synchronization
, 2003
"... We consider the problem of lowsampling rate highresolution channel estimation and timing for digital ultrawideband (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 ..."
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Cited by 15 (2 self)
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We consider the problem of lowsampling rate highresolution channel estimation and timing for digital ultrawideband (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 ultrawideband systems, which uses subNyquist 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 frequencyselective fading. Moreover, we show that it is possible to obtain highresolution 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
, 2003
"... 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 w ..."
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Cited by 14 (2 self)
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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. I.
Sampling Signals with Finite Rate of Innovation: The Noisy Case
, 2002
"... In [1] 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 bandlimited signals can be sampled at or above the rate of innovation. In the present paper, we consider the case of such sig ..."
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Cited by 2 (1 self)
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In [1] 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 bandlimited 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 signaltonoise ratio (SNR) is sufficient, several methods are possible to reconstruct the signal while sampling well below the Nyquist rate. We thus explore the tradeoffs 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 [2].
A Flexible Low Power Subsampling UWB Receiver Based on Line Spectrum Estimation Methods
"... Abstract — This paper presents a low power pulsed UWB receiver sampling below Nyquist rate which can accomodate timevarying data rate and qualityofservice requirements for applications communicating via UWB. The performance of pulse amplitude and pulse position modulations is assessed in AWGN and ..."
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Abstract — This paper presents a low power pulsed UWB receiver sampling below Nyquist rate which can accomodate timevarying data rate and qualityofservice requirements for applications communicating via UWB. The performance of pulse amplitude and pulse position modulations is assessed in AWGN and dense multipath environments using the standard IEEE 802.15.3a channel models. The proposed subsampling receiver provides an attractive digital alternative to the classical approach based on analog correlations, and can reach data rates above 100 Mb/s. I.
Performance Analysis of a Flexible Subsampling Receiver for Pulsed UWB Signals
"... Abstract—This paper presents a flexible digital receiver for pulsed UltraWideband (UWB) communications which is sampling below Nyquist rate. This receiver can trade demodulation performance for sampling rate, i.e. power consumption. The bit error rate for pulse amplitude and pulse position modulati ..."
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Abstract—This paper presents a flexible digital receiver for pulsed UltraWideband (UWB) communications which is sampling below Nyquist rate. This receiver can trade demodulation performance for sampling rate, i.e. power consumption. The bit error rate for pulse amplitude and pulse position modulations is evaluated in AWGN and typical UWB channels. The performance of several types of equalizer is compared, taking into account their implementation complexity. A suboptimal but implementation efficient Minimum MeanSquare Error (MMSE) equalizer which reaches performances similar to the ideal MMSE equalizer is proposed. The impact of imperfect knowledge of the propagation channel and signaltonoise ratio, due to the limited number of training symbols, on the performance of the receiver is assessed. Finally, the receiver architecture and implementation cost are discussed. The proposed subsampling receiver provides an attractive alternative to classical architectures based on correlation with a template. Index Terms—Ultra wideband (UWB), subsampling receiver, Nyquist. I.
A BERNOULLIGAUSSIAN APPROACH TO THE RECONSTRUCTION OF NOISY SIGNALS WITH FINITE RATE OF INNOVATION
"... Recently, it was shown that a large class of nonbandlimited signals that have a finite rate of innovation, such as streams of Diracs, nonuniform splines and piecewise polynomials, can be perfectly reconstructed from a uniform set of samples taken at the rate of innovation [1]. While this is true i ..."
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Recently, it was shown that a large class of nonbandlimited signals that have a finite rate of innovation, such as streams of Diracs, nonuniform splines and piecewise polynomials, can be perfectly reconstructed from a uniform set of samples taken at the rate of innovation [1]. While this is true in the noiseless case, in the presence of noise the finite rate of innovation property is lost and exact reconstruction is no longer possible. In this paper we consider the problem of reconstructing such signals when noise is present. We focus on the case when a discretetime signal is made up of a sum of weighted Diracs and we propose a stochastic reconstruction method based on the BernoulliGauss model and on a maximum a posteriori optimization. Our approach is numerically stable and yields precise reconstruction by sampling the signal way below the Nyquist rate, significantly outperforming commonly used subspace methods [2, 3]. Applications of our method can be found in acquisition and processing of signals in wideband communication systems, such as ultrawideband (UWB) systems.
Applications
, 2008
"... I am submitting herewith a dissertation written by Cemin Zhang entitled “Hardware ..."
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I am submitting herewith a dissertation written by Cemin Zhang entitled “Hardware
Orthogonal Multicode Channelization Applied to Subsampling Digital UWB Receiver
"... Abstract — This paper assesses in AWGN and dense multipath environments several equalization alternatives for a digital pulsed UWB receiver sampling below Nyquist rate. A suboptimal but implementation efficient Minimum MeanSquare Error (MMSE) equalizer which reaches performances similar to the idea ..."
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Abstract — This paper assesses in AWGN and dense multipath environments several equalization alternatives for a digital pulsed UWB receiver sampling below Nyquist rate. A suboptimal but implementation efficient Minimum MeanSquare Error (MMSE) equalizer which reaches performances similar to the ideal MMSE equalizer is proposed. By making an efficient use of orthogonal codes, the UWB transceivers have flexible channelization means to accomodate timevarying data rate in the order of magnitude of 100 Mb/s with sampling rates below 1 GHz. The proposed multicode approach takes into account the peculiarities of pulsed UWB signals and avoids high peaktoaverage amplitude ratios. I.