411 research outputs found
Compressive Sensing with Optimal Sparsifying Basis and Applications in Spectrum Sensing
We describe a method of integrating Karhunen-Loève Transform (KLT) into compressive sensing, which can as a result improve the compression ratio without affecting the accuracy of decoding. We present two complementary results: 1) by using KLT to find an optimal basis for decoding we can drastically reduce the number of measurements for compressive sensing used in applications such as radio spectrum analysis; 2) by using compressive sensing we can estimate and recover the KLT basis from compressive measurements of an input signal. In particular, we propose CS-KLT, an online estimation algorithm to cope with nonstationarity of wireless channels in reality. We validate our results with empirical data collected from a wideband UHF spectrum and eld experiments to detect multiple radio transmitters, using software-defined radios.Engineering and Applied Science
Modulated Unit-Norm Tight Frames for Compressed Sensing
In this paper, we propose a compressed sensing (CS) framework that consists
of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a
column-wise orthonormal matrix. We prove that this structure satisfies the
restricted isometry property (RIP) with high probability if the number of
measurements for -sparse signals of length
and if the column-wise orthonormal matrix is bounded. Some existing structured
sensing models can be studied under this framework, which then gives tighter
bounds on the required number of measurements to satisfy the RIP. More
importantly, we propose several structured sensing models by appealing to this
unified framework, such as a general sensing model with arbitrary/determinisic
subsamplers, a fast and efficient block compressed sensing scheme, and
structured sensing matrices with deterministic phase modulations, all of which
can lead to improvements on practical applications. In particular, one of the
constructions is applied to simplify the transceiver design of CS-based channel
estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin
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Dynamic Mode Decomposition for Compressive System Identification
Dynamic mode decomposition has emerged as a leading technique to identify
spatiotemporal coherent structures from high-dimensional data, benefiting from
a strong connection to nonlinear dynamical systems via the Koopman operator. In
this work, we integrate and unify two recent innovations that extend DMD to
systems with actuation [Proctor et al., 2016] and systems with heavily
subsampled measurements [Brunton et al., 2015]. When combined, these methods
yield a novel framework for compressive system identification [code is publicly
available at: https://github.com/zhbai/cDMDc]. It is possible to identify a
low-order model from limited input-output data and reconstruct the associated
full-state dynamic modes with compressed sensing, adding interpretability to
the state of the reduced-order model. Moreover, when full-state data is
available, it is possible to dramatically accelerate downstream computations by
first compressing the data. We demonstrate this unified framework on two model
systems, investigating the effects of sensor noise, different types of
measurements (e.g., point sensors, Gaussian random projections, etc.),
compression ratios, and different choices of actuation (e.g., localized,
broadband, etc.). In the first example, we explore this architecture on a test
system with known low-rank dynamics and an artificially inflated state
dimension. The second example consists of a real-world engineering application
given by the fluid flow past a pitching airfoil at low Reynolds number. This
example provides a challenging and realistic test-case for the proposed method,
and results demonstrate that the dominant coherent structures are well
characterized despite actuation and heavily subsampled data
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Scaling network-based spectrum analyzer with constant communication cost
e propose a spectrum analyzer that leverages many networked commodity sensor nodes, each of which sam- ples its portion in a wideband spectrum. The sensors operate in parallel and transmit their measurements over a wireless network without performing any significant computations such as FFT. The measurements are forwarded to the backend of the system where spectrum analysis takes place. In particular, we propose a solution that compresses the raw measurements in a simple random linear projection and combines the compressed measurements from multiple sensors in-network. As a result, we achieve a substantial reduction in the network bandwidth requirement to operate the proposed system. We discover that the overall communication cost can be independent of the number of sensors and is affected only by sparsity of discretized spectrum under analysis. This principle founds the basis for a claim that our network-based spectrum analyzer can scale up the number of sensor nodes to process a very wide spectrum block potentially having a GHz bandwidth. We devise a novel recovery algorithm that systematically undoes compressive encoding and in-network combining done to the raw measurements, incorporating the least squares and l1-minimization decoding used in compressive sensing, and demonstrate that the algorithm can effectively restore an accurate estimate of the original data suitable for fine- rained spectrum analysis. We present mathematical analysis and empirical evaluation of the system with software-defined radios.Engineering and Applied Science
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