1,291 research outputs found
Measurement Matrix Design for Compressive Sensing Based MIMO Radar
In colocated multiple-input multiple-output (MIMO) radar using compressive
sensing (CS), a receive node compresses its received signal via a linear
transformation, referred to as measurement matrix. The samples are subsequently
forwarded to a fusion center, where an L1-optimization problem is formulated
and solved for target information. CS-based MIMO radar exploits the target
sparsity in the angle-Doppler-range space and thus achieves the high
localization performance of traditional MIMO radar but with many fewer
measurements. The measurement matrix is vital for CS recovery performance. This
paper considers the design of measurement matrices that achieve an optimality
criterion that depends on the coherence of the sensing matrix (CSM) and/or
signal-to-interference ratio (SIR). The first approach minimizes a performance
penalty that is a linear combination of CSM and the inverse SIR. The second one
imposes a structure on the measurement matrix and determines the parameters
involved so that the SIR is enhanced. Depending on the transmit waveforms, the
second approach can significantly improve SIR, while maintaining CSM comparable
to that of the Gaussian random measurement matrix (GRMM). Simulations indicate
that the proposed measurement matrices can improve detection accuracy as
compared to a GRMM
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
Spatial Compressive Sensing for MIMO Radar
We study compressive sensing in the spatial domain to achieve target
localization, specifically direction of arrival (DOA), using multiple-input
multiple-output (MIMO) radar. A sparse localization framework is proposed for a
MIMO array in which transmit and receive elements are placed at random. This
allows for a dramatic reduction in the number of elements needed, while still
attaining performance comparable to that of a filled (Nyquist) array. By
leveraging properties of structured random matrices, we develop a bound on the
coherence of the resulting measurement matrix, and obtain conditions under
which the measurement matrix satisfies the so-called isotropy property. The
coherence and isotropy concepts are used to establish uniform and non-uniform
recovery guarantees within the proposed spatial compressive sensing framework.
In particular, we show that non-uniform recovery is guaranteed if the product
of the number of transmit and receive elements, MN (which is also the number of
degrees of freedom), scales with K(log(G))^2, where K is the number of targets
and G is proportional to the array aperture and determines the angle
resolution. In contrast with a filled virtual MIMO array where the product MN
scales linearly with G, the logarithmic dependence on G in the proposed
framework supports the high-resolution provided by the virtual array aperture
while using a small number of MIMO radar elements. In the numerical results we
show that, in the proposed framework, compressive sensing recovery algorithms
are capable of better performance than classical methods, such as beamforming
and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin
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