46 research outputs found
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
Global optimization methods for localization in compressive sensing
The dissertation discusses compressive sensing and its applications to localization in multiple-input multiple-output (MIMO) radars. Compressive sensing is a paradigm at the intersection between signal processing and optimization. It advocates the sensing of “sparse” signals (i.e., represented using just a few terms from a basis expansion) by using a sampling rate much lower than that required by the Nyquist-Shannon sampling theorem (i.e., twice the highest frequency present in the signal of interest). Low-rate sampling reduces implementation’s constraints and translates into cost savings due to fewer measurements required. This is particularly true in localization applications when the number of measurements is commensurate to antenna elements. The theory of compressive sensing provides precise guidance on how the measurements should be acquired, and which optimization algorithm should be used for signal recovery.
The first part of the dissertation addresses the application of compressive sensing for localization in the spatial domain, specifically direction of arrival (DOA), using 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, a bound on the coherence of the resulting measurement matrix is obtained, and conditions under which the measurement matrix satisfies the so-called isotropy property are detailed. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, it is shown 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.
The second part of the dissertation focuses on the sparse recovery problem at the heart of compressive sensing. An algorithm, dubbed Multi-Branch Matching Pursuit (MBMP), is presented which combines three different paradigms: being a greedy method, it performs iterative signal support estimation; as a rank-aware method, it is able to exploit signal subspace information when multiple snapshots are available; and, as its name foretells, it possesses a multi-branch structure which allows it to trade-off performance (e.g., measurements) for computational complexity. A sufficient condition under which MBMP can recover a sparse signal is obtained. This condition, named MB-coherence, is met when the columns of the measurement matrix are sufficiently “incoherent” and when the signal-to-noise ratio is sufficiently high. The condition shows that successful recovery with MBMP is guaranteed for dictionaries which do not satisfy previously known conditions (e.g., coherence, cumulative coherence, or the Hanman relaxed coherence).
Finally, by leveraging the MBMP algorithm, a framework for target detection from a set of compressive sensing radar measurements is established. The proposed framework does not require any prior information about the targets’ scene, and it is competitive with respect to state-of-the-art detection compressive sensing algorithms
Projections Onto Convex Sets (POCS) Based Optimization by Lifting
Two new optimization techniques based on projections onto convex space (POCS)
framework for solving convex and some non-convex optimization problems are
presented. The dimension of the minimization problem is lifted by one and sets
corresponding to the cost function are defined. If the cost function is a
convex function in R^N the corresponding set is a convex set in R^(N+1). The
iterative optimization approach starts with an arbitrary initial estimate in
R^(N+1) and an orthogonal projection is performed onto one of the sets in a
sequential manner at each step of the optimization problem. The method provides
globally optimal solutions in total-variation, filtered variation, l1, and
entropic cost functions. It is also experimentally observed that cost functions
based on lp, p<1 can be handled by using the supporting hyperplane concept
Cognitive Sub-Nyquist Hardware Prototype of a Collocated MIMO Radar
We present the design and hardware implementation of a radar prototype that
demonstrates the principle of a sub-Nyquist collocated multiple-input
multiple-output (MIMO) radar. The setup allows sampling in both spatial and
spectral domains at rates much lower than dictated by the Nyquist sampling
theorem. Our prototype realizes an X-band MIMO radar that can be configured to
have a maximum of 8 transmit and 10 receive antenna elements. We use frequency
division multiplexing (FDM) to achieve the orthogonality of MIMO waveforms and
apply the Xampling framework for signal recovery. The prototype also implements
a cognitive transmission scheme where each transmit waveform is restricted to
those pre-determined subbands of the full signal bandwidth that the receiver
samples and processes. Real-time experiments show reasonable recovery
performance while operating as a 4x5 thinned random array wherein the combined
spatial and spectral sampling factor reduction is 87.5% of that of a filled
8x10 array.Comment: 5 pages, Compressed Sensing Theory and its Applications to Radar,
Sonar and Remote Sensing (CoSeRa) 201
ISAR imaging of space objects using encoded apertures
A major threat to satellites is space debris with their low mass and high
rotational speed. Accordingly, the short observation time of these objects is a
major limitation in space research for appropriate detection and decision. As a
result, these objects do not fully illuminated, leading to their incomplete
images at any snapshot. In this paper, we propose a method to decrease the
number of snapshots in a given observation time and using a limited number of
spot beams per snapshot called the encoded aperture. To recover the space
debris images, an inverse problem is defined based on compressive sensing
methods. Also, we show that for satellite imaging the T V norm is more
appropriate. We develop a procedure to recover space debris and satellites
using L1 and T V norms. Using simulation results, we compare the results with
the well-known SBL and SL0 norm in terms of the number of snapshots, MSE, SNR,
and running time. It is shown that our proposed method can successfully recover
the space objects images using a fewer number of snapshots