We present a wide bandwidth, compressed sensing based nonuniform sampling (NUS) system with a custom sample-and-hold chip designed to take advantage of a low average sampling rate. By sampling signals nonuniformly, the average sample rate can be more than a magnitude lower than the Nyquist rate, provided that these signals have a relatively low information content as measured by the sparsity of their spectrum. The hardware design combines a wideband Indium-Phosphide heterojunction bipolar transistor sample-and-hold with a commercial off-the-shelf analog-to-digital converter to digitize an 800 MHz to 2 GHz band (having 100 MHz of noncontiguous spectral content) at an average sample rate of 236 Ms/s. Signal reconstruction is performed via a nonlinear compressed sensing algorithm, and the challenges of developing an efficient implementation are discussed. The NUS system is a general purpose digital receiver. As an example of its real signal capabilities, measured bit-error-rate data for a GSM channel is presented, and comparisons to a conventional wideband 4.4 Gs/s ADC are made.

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A Nonuniform Sampler for Wideband Spectrally-Sparse Environments

We present BigBand, a technology that can capture GHz of spectrum in realtime without sampling the signal at GS/s -i.e., without high speed ADCs. Further, it is simple and can be implemented on commodity low-power radios. Our approach builds on recent advances in the area of sparse Fourier transforms, which show that it is possible to reconstruct a sparse signal without sampling it at the Nyquist rate. To demonstrate our design, we implement it using 3 software radios, each sampling the spectrum at 50 MS/s, producing a device that captures 0.9 GHz — i.e., 6× larger digital bandwidth than the three software radios combined. Finally, an extension of BigBand can perform GHz spectrum sensing even in scenarios where the spectrum is not sparse.

/pdf/ghz-wide-sensing-and-decoding-using-the-sparse-fourier-2r5cpjcrko.pdf

GHz-Wide Sensing and Decoding Using the Sparse Fourier Transform

Traditional radar sensing typically employs matched filtering between the received signal and the shape of the transmitted pulse. Matched filtering (MF) is conventionally carried out digitally, after sampling the received analog signals. Here, principles from classic sampling theory are generally employed, requiring that the received signals be sampled at twice their baseband bandwidth. The resulting sampling rates necessary for correlation-based radar systems become quite high, as growing demands for target distinction capability and spatial resolution stretch the bandwidth of the transmitted pulse. The large amounts of sampled data also necessitate vast memory capacity. In addition, real-time data processing typically results in high power consumption. Recently, new approaches for radar sensing and estimation were introduced, based on the finite rate of innovation (FRI) and Xampling frameworks. Exploiting the parametric nature of radar signals, these techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's estimation capabilities at sufficiently high signal-to-noise ratios (SNRs). Here we present for the first time a design and implementation of an Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demonstrate by real-time analog experiments that our system is able to maintain reasonable recovery capabilities, while sampling radar signals that require sampling at a rate of about 30 MHz at a total rate of 1 MHz.

Sub-Nyquist radar prototype: Hardware and algorithm

In structural health monitoring (SHM) systems
for civil structures, massive amounts of data are often
generated that need data compression techniques to
reduce the cost of signal transfer and storage, meanwhile
offering a simple sensing system. Compressive sensing
(CS) is a novel data acquisition method whereby the
compression is done in a sensor simultaneously with
the sampling. If the original sensed signal is sufficiently
sparse in terms of some orthogonal basis (e.g., a sufficient
number of wavelet coefficients are zero or negligibly
small), the decompression can be done essentially
perfectly up to some critical compression ratio; otherwise
there is a trade-off between the reconstruction error
and how much compression occurs. In this article,
a Bayesian compressive sensing (BCS) method is investigated
that uses sparse Bayesian learning to reconstruct
signals from a compressive sensor. By explicitly quantifying
the uncertainty in the reconstructed signal from
compressed data, the BCS technique exhibits an obvious
benefit over existing regularized norm-minimization
CS methods that provide a single signal estimate. However,
current BCS algorithms suffer from a robustness
problem: sometimes the reconstruction errors are very
large when the number of measurements K are a lot
less than the number of signal degrees of freedom N that are needed to capture the signal accurately in a directly
sampled form. In this article, we present improvements
to the BCS reconstruction method to enhance its
robustness so that even higher compression ratios N/K
can be used and we examine the trade-off between efficiently
compressing data and accurately decompressing
it. Synthetic data and actual acceleration data collected
from a bridge SHM system are used as examples.
Compared with the state-of-the-art BCS reconstruction
algorithms, the improved BCS algorithm demonstrates
superior performance. With the same acceptable error
rate based on a specified threshold of reconstruction error,
the proposed BCS algorithm works with relatively
large compression ratios and it can achieve perfect loss-less
compression performance with quite high compression
ratios. Furthermore, the error bars for the signal reconstruction
are also quantified effectively.

Robust Bayesian Compressive Sensing for Signals in Structural Health Monitoring

Traditional radar sensing typically involves matched filtering between the received signal and the shape of the transmitted pulse. Under the confinement of classic sampling theorem this requires that the received signals must first be sampled at twice the baseband bandwidth, in order to avoid aliasing. The growing demands for target distinction capability and spatial resolution imply significant growth in the bandwidth of the transmitted pulse. Thus, correlation based radar systems require high sampling rates, and with the large amounts of data sampled also necessitate vast memory capacity. In addition, real-time processing of the data typically results in high power consumption. Recently, new approaches for radar sensing and detection were introduced, based on the Finite Rate of Innovation and Xampling frameworks. These techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's detection capabilities at high enough SNR. Here we present for the first time a design and implementation of a Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demostrate by real-time analog experiments that our system is able to maintain reasonable detection capabilities, while sampling radar signals that require sampling at a rate of about 30MHz at a total rate of 1Mhz.

A Sub-Nyquist Radar Prototype: Hardware and Algorithms

In this paper we present a complete (hardware/ software) sub-Nyquist rate (× 13) wideband signal acquisition chain capable of acquiring radar pulse parameters in an instantaneous bandwidth spanning 100 MHz-2.5 GHz with the equivalent of 8 effective number of bits (ENOB) digitizing performance. The approach is based on the alternative sensing-paradigm of compressed sensing (CS). The hardware platform features a fully-integrated CS receiver architecture named the random-modulation preintegrator (RMPI) fabricated in Northrop Grumman's 450 nm InP HBT bipolar technology. The software back-end consists of a novel CS parameter recovery algorithm which extracts information about the signal without performing full time-domain signal reconstruction. This approach significantly reduces the computational overhead involved in retrieving desired information which demonstrates an avenue toward employing CS techniques in power-constrained real-time applications. The developed techniques are validated on CS samples physically measured by the fabricated RMPI and measurement results are presented. The parameter estimation algorithms are described in detail and a complete description of the physical hardware is given.

/pdf/a-compressed-sensing-parameter-extraction-platform-for-radar-4r4qqt3umg.pdf

C. Turnes

Papers

A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition