From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

By Moshe Mishali, Yonina C. Eldar. IEEE Journal on Selected Topics in Signal Processing, 2009

1,201 citations recorded by the source corpus.

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/1cef8d73918665a441827eae81741711c369e71f

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Citations in the corpus

Compressive sensing: From theory to applications, a survey (2013, background): “Recent works propose a converter whose three main components are multiplication of analog signal with bank of periodic waveforms, low pass ﬁltering and uniform sampling at uniform sampling at low rate [83].”
Spectrum Sensing for Cognitive Radio : State-of-the-Art and Recent Advances (2012, background): “It is interesting to observe that this MMV set-up is very closely related to spectrum-blind sampling, in which the goal is to enable minimum-rate sampling and reconstruction given that the spectrum is sparse yet unknown [46].”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, neutral): “MWC was proposed by Mishali and Eldar [21], in 2010.”
Spectrum sensing in cognitive radio (2016, methodology): “In [66], the modulated wideband converter (MWC) [67] is used to obtain the SC from sub-Nyquist samples to then apply cyclostationarity detection.”
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery (2009, methodology): “Furthermore, it was shown in [14], [15] that the block-sparsity model can be used to treat the problem of sampling signals that lie in a union of subspaces [24], [25], [14], [26], [13], [16], [17].”
Structured Compressed Sensing: From Theory to Applications (2011, methodology): “Similar ideas were also developed in the context of array processing [21], [103], [104], equalization of sparse communication channels [105], [106], and more recently cognitive radio and multiband communications [9], [86], [107]–[109].”
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals (2009, background): “Very recently, it has been shown that a bank of random demodulators can be used for blind acquisition of multiband signals [49], [50].”
Robust Recovery of Signals From a Structured Union of Subspaces (2008, methodology): “By formulating this problem within the framework of CS, explic it sub-Nyquist sampling and reconstruction schemes were developed in [15], [16] that ensure perfect-recovery a t the minimal possible rate.”
Spectral compressive sensing (2013, methodology): “Additionally, several alternative frameworks to CS have been proposed for the modeling and acquisition of frequency-sparse signals from a small number of samples, including finite rate of innovation (FROI) sampling [29] [30] [31] [32] and Xampling [9] [10] [33].”
Xampling: Analog to digital at sub-Nyquist rates (2009, methodology): “In [18], we used simulations to show that the reconstruction performance is hardly affected when generating several pi(t) from a single shift register (SR) of length M by using different taps.”
Rank Awareness in Joint Sparse Recovery (2010, background): “These ideas have also been recently expanded to include sub-Nyquist sampling of structured ana log signals [19], [20], [21], [22], [23].”