3,547 research outputs found
The Cognitive Compressive Sensing Problem
In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR)
seeks to optimize the reward obtained by sensing an underlying dimensional
random vector, by collecting at most arbitrary projections of it. The
components of the latent vector represent sub-channels states, that change
dynamically from "busy" to "idle" and vice versa, as a Markov chain that is
biased towards producing sparse vectors. To identify the optimal strategy we
formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem,
generalizing the popular Cognitive Spectrum Sensing model, in which the CR can
sense out of the sub-channels, as well as the typical static setting of
Compressive Sensing, in which the CR observes linear combinations of the
dimensional sparse vector. The CR opportunistic choice of the sensing
matrix should balance the desire of revealing the state of as many dimensions
of the latent vector as possible, while not exceeding the limits beyond which
the vector support is no longer uniquely identifiable.Comment: 8 pages, 2 figure
Analysis of Sparse MIMO Radar
We consider a multiple-input-multiple-output radar system and derive a
theoretical framework for the recoverability of targets in the azimuth-range
domain and the azimuth-range-Doppler domain via sparse approximation
algorithms. Using tools developed in the area of compressive sensing, we prove
bounds on the number of detectable targets and the achievable resolution in the
presence of additive noise. Our theoretical findings are validated by numerical
simulations
Accurate detection of moving targets via random sensor arrays and Kerdock codes
The detection and parameter estimation of moving targets is one of the most
important tasks in radar. Arrays of randomly distributed antennas have been
popular for this purpose for about half a century. Yet, surprisingly little
rigorous mathematical theory exists for random arrays that addresses
fundamental question such as how many targets can be recovered, at what
resolution, at which noise level, and with which algorithm. In a different line
of research in radar, mathematicians and engineers have invested significant
effort into the design of radar transmission waveforms which satisfy various
desirable properties. In this paper we bring these two seemingly unrelated
areas together. Using tools from compressive sensing we derive a theoretical
framework for the recovery of targets in the azimuth-range-Doppler domain via
random antennas arrays. In one manifestation of our theory we use Kerdock codes
as transmission waveforms and exploit some of their peculiar properties in our
analysis. Our paper provides two main contributions: (i) We derive the first
rigorous mathematical theory for the detection of moving targets using random
sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties
that are very desirable and important from a practical viewpoint. Thus our
approach does not just lead to useful theoretical insights, but is also of
practical importance. Various extensions of our results are derived and
numerical simulations confirming our theory are presented
Spectral Compressive Sensing with Model Selection
The performance of existing approaches to the recovery of frequency-sparse
signals from compressed measurements is limited by the coherence of required
sparsity dictionaries and the discretization of frequency parameter space. In
this paper, we adopt a parametric joint recovery-estimation method based on
model selection in spectral compressive sensing. Numerical experiments show
that our approach outperforms most state-of-the-art spectral CS recovery
approaches in fidelity, tolerance to noise and computation efficiency.Comment: 5 pages, 2 figures, 1 table, published in ICASSP 201
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