Sampling with finite rate of innovation: channel and timing estimation for UWB and GPS

Kusuma, Julius; Maravic, Irena; Vetterli, Martin

doi:10.1109/icc.2003.1204112

Cited by 40 publications

(39 citation statements)

References 10 publications

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“…Ref. [7] proposed a finite rate of innovation approach which projects a signal into lower dimensional subspace. Unfortunately, due to the closely spaced path arrivals inherent in UWB-IR, the solution to rate of innovation is often ill-conditioned.…”

Section: Introductionmentioning

confidence: 99%

Compressed Sensing Maximum Likelihood Channel Estimation for Ultra-Wideband Impulse Radio

Liu

Dong

2009

2009 IEEE International Conference on Communications

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Abstract-One of the most attractive features of ultrawideband impulse radio is the collection of rich multipath with the transmission of ultra-short pulses. Exploiting the rich multipath diversity with channel estimating Rake receivers enables significant energy capture, higher performance and flexibility than suboptimal receivers. Although data-aided (DA) maximum likelihood (ML) channel estimator shows a promising performance, its implementation is restricted by the Nyquist sampling criterion. The emerging theory of compressed sensing (CS) describes a novel framework to jointly compress and detect a sparse signal with fewer samples than the traditional Nyquist criterion. In this paper, we propose a CS-ML channel estimator which combines the compression framework of CS for sampling rate reduction while retaining the noise statistics formulation of ML to achieve a reliable performance. Simulation assessment indicates that, with far fewer measurements, the performance of our proposed scheme supersedes that of the 1-norm minimization estimator of CS and can be as close as the ML, but with a reduction in complexity.

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Section: Introductionmentioning

confidence: 99%

Compressed Sensing Maximum Likelihood Channel Estimation for Ultra-Wideband Impulse Radio

Liu

Dong

2009

2009 IEEE International Conference on Communications

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“…One way to extend this process is to model each action potential with a small number of Fourier series coefficients [9]. This capability will be useful to support more powerful spike sorting, and potentially to perform other unforeseen analyses.…”

Section: Extension To Full Action Potential Recoverymentioning

confidence: 99%

“…For example, the rate of innovation K in a sequence of pulses is given by the average number of pulses per unit time multiplied by the number of parameters that characterize each pulse. In prior work [8], [9], a class of parametric methods were developed to exploit the rate of innovation in a canonical set of FRI signals to achieve sampling rates of M = O(K). This theory allows for temporal resolution that far exceeds the sampling rate but degrades with signalto-noise ratio (SNR).…”

Section: Introductionmentioning

confidence: 99%

Acquisition of action potentials with ultra-low sampling rates

Srinivasan

Varshney²,

Kusuma

2010

2010 Annual International Conference of the IEEE Engineering in Medicine and Biology

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Abstract-We introduce finite rate of innovation (FRI) based spike acquisition, a new approach to the sampling of action potentials. Drawing from emerging theory on sampling FRI signals, our process aims to acquire the precise shape and timing of spikes from electrodes with single or multiunit spiking activity using sampling rates of 1000 Hz or less. The key insight is that action potentials are essentially stereotyped pulses that are generated by neurons at a rate limited by an absolute refractory period. We use this insight to push sampling below the Nyquist rate. Our process is a parametric method distinct from compressed sensing (CS). In its full implementation, this process could improve spike-based devices for neuroscience and medicine by reducing energy consumption, computational complexity, and hardware demands.

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“…Let the noisy estimate of the received signal be defined as (15) and the error in estimating the true signal from this estimate be defined as (16) with denoting the variance of each of its elements. If the above mentioned heuristics are true, then the variance of the elements of the error vector can be tracked by the following state evolution (SE) method for every iteration (17) where the function is defined as (18) where is a vector of zero-mean standard i.i.d. Gaussian random variables, i.e., and we have considered under Assumption 1.…”

Section: A Reconstruction Based Detectors 1) Signal Reconstruction Amentioning

confidence: 99%

“…The symbol decision is determined by the pulse position that contains most of the energy. Note that different works on CS in combination with UWB signals have appeared recently, e.g., in [15] for coherent receivers, in [16] for symbol-rate sampling but requiring pre-identification of the channel which was then extended to [17] for channel and timing estimation, in [18] for a GLRT based detector which was then extended to [19] with an effective measurement matrix design but both requiring the transmission of pilot symbols, in [20] for joint time of arrival estimation and data decoding which requires channel estimation, in [21] and [22] to account for narrow-band interference, in [23] and [24] for UWB channel estimation, in [25] for time-delay estimation and in [26] for differential detection of UWB signals. In contrast to previous methods, we present noncoherent UWB detectors.…”

mentioning

confidence: 99%

Compressive Sampling Based Energy Detection of Ultra-Wideband Pulse Position Modulation

Gishkori

Leus

2013

IEEE Trans. Signal Process.

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Abstract-Compressive sampling (CS) based energy detectors are developed for ultra-wideband (UWB) pulse position modulation (PPM), in multipath fading environments so as to reduce the sampling complexity at the receiver side. Due to sub-Nyquist rate sampling, the CS process outputs a compressed version of the received signal such that the original signal can be recovered from this low dimensional representation. Using the principles of generalized maximum likelihood (GML), we propose two types of energy detectors for such signals. The first type of detectors involves the reconstruction of the received signal followed by a detection stage. Statistical properties of the reconstruction error have been used for the realization of such kind of detectors. The second type of detectors does not rely on reconstruction and carries out the detection operation directly on the compressed signal, thereby offering a further reduction in the implementation complexity. The performance of the proposed detectors is independent of the spreading factor. We analyze the bit error performance of the proposed energy detectors for two scenarios of the propagation channel: when the channel is deterministic, and when it is Gaussian distributed. We provide exact bit error probability (BEP) expressions of the CS based energy detectors for each scenario of the channel. The BEP expressions obtained for the detectors working on the compressed signal directly can naturally be extended to BEP expressions for the related energy detectors working on the Nyquist-rate sampled signal. Simulation results validate the accuracy of these BEP expressions.

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Sampling with finite rate of innovation: channel and timing estimation for UWB and GPS

Cited by 40 publications

References 10 publications

Compressed Sensing Maximum Likelihood Channel Estimation for Ultra-Wideband Impulse Radio

Compressed Sensing Maximum Likelihood Channel Estimation for Ultra-Wideband Impulse Radio

Acquisition of action potentials with ultra-low sampling rates

Compressive Sampling Based Energy Detection of Ultra-Wideband Pulse Position Modulation

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