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Sparse Sensing In Colocated MIMO Radar: A Matrix Completion Approach
"... Abstract-In this paper, we investigate a novel networked colocated MIMO radar approach that relies on sparse sensing and matrix completion, and enables significant reduction of the volume of data required for accurate target detection and estimation. More specifically, the receive antennas sample th ..."
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Abstract-In this paper, we investigate a novel networked colocated MIMO radar approach that relies on sparse sensing and matrix completion, and enables significant reduction of the volume of data required for accurate target detection and estimation. More specifically, the receive antennas sample the target returns via two sparse sensing schemes, and forward the obtained samples to a fusion center. Based on the data from multiple antennas, the fusion center can formulate and solve a low rank matrix completion problem, which allows for the recovery of all information needed for target parameters estimation. Both the cases of uniform linear and general 2D arrays are considered. The effectiveness of the proposed approach is justified both theoretically and through numerical simulations.
On the applicability of matrix completion on MIMO radars
- in 48th Annual Asilomar Conference on Signals, Systems, and Computers
"... Abstract—It was recently shown that networked MIMO radars with sparse sensing and matrix completion (MC) can significantly reduce the volume of data required for accurate target detection and estimation. Based on the target returns, forwarded by the receive antennas to a fusion center, a matrix can ..."
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Abstract—It was recently shown that networked MIMO radars with sparse sensing and matrix completion (MC) can significantly reduce the volume of data required for accurate target detection and estimation. Based on the target returns, forwarded by the receive antennas to a fusion center, a matrix can be formulated and used in standard array processing methods to estimate the target parameters. For a small number of targets, the aforemen-tioned matrix is low-rank and thus can be recovered from a small subset of its elements using MC. This allows for sparse sensing at the receive antennas, and subsequently populating the data matrix in a uniformly sparse fashion. This paper studies the applicability of MC theory on the data matrices that arise in colocated MIMO radars using uniform linear arrays. It is shown that the coherence is directly related to transmit waveforms, and that when the waveforms are orthogonal the optimum choice is for them to be spatial white noise-type functions in all snapshots. I.
On Waveform Design for MIMO Radar with Matrix Completion
"... Abstract—In matrix completion based MIMO radars, the data matrix coherence, and consequently the performance of matrix completion depend on the transmit waveforms. It was recently shown that for uniform linear arrays and orthogonal waveforms, the optimal choice for waveforms are white-noise type fun ..."
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Abstract—In matrix completion based MIMO radars, the data matrix coherence, and consequently the performance of matrix completion depend on the transmit waveforms. It was recently shown that for uniform linear arrays and orthogonal waveforms, the optimal choice for waveforms are white-noise type functions. This paper deals with the design of optimal transmit waveforms. The design is formulated as an optimization problem on the complex Stiefel manifold, which is a non-convex set, and the optimal waveforms are found via a steepest descent algorithm with nonmonotone line search methods. Numerical results show that for large dimensional data matrices and for a large number of antennas, the objective function converges to its global minimum and the matrix coherence corresponding to the optimal waveforms is asymptotically optimal, thus resulting in very good target estimation performance. Index Terms—MIMO radar, matrix completion, waveform design, optimization on manifolds, orthogonal constraints
Spectrum sharing between matrix completion based MIMO radars and a MIMO communication system
- in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing
, 2015
"... Recently proposed multiple input multiple output radars based on matrix completion (MIMO-MC) employ sparse sampling to reduce the amount of data forwarded to the radar fusion center, and as such enable savings in communication power and bandwidth. This pa-per proposes designs that optimize the shari ..."
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Recently proposed multiple input multiple output radars based on matrix completion (MIMO-MC) employ sparse sampling to reduce the amount of data forwarded to the radar fusion center, and as such enable savings in communication power and bandwidth. This pa-per proposes designs that optimize the sharing of spectrum between MIMO-MC radars and MIMO communication systems, so that the latter interferes minimally with the former. First, the communication system transmit covariance matrix is designed to minimize the effec-tive interference power (EIP) at the radar receiver, while maintaining certain average capacity and transmit power for the communication system. Two approaches are proposed, namely a noncooperative and a cooperative approach, with the latter being applicable when the radar sampling scheme is known at the communication system. Sec-ond, a joint design of the communication transmit covariance ma-trix and the MIMO-MC radar sampling scheme is proposed, which achieves even further EIP reduction. Index Terms — Collocated MIMO radar, matrix completion, spectrum sharing 1.
Performance Guarantees for Schatten-p Quasi-Norm Minimization in Recovery of Low-Rank Matrices
, 2014
"... We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0, 1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measuring operator, we provide a sufficient condition for exact recovery of low-rank matrices. T ..."
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We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0, 1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measuring operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaranteed by nuclear norm minimization. Secondly, this sufficient condition leads to a theorem proving that all restricted isometry property (RIP) based sufficient conditions for `p quasi-norm minimization generalize to Schatten-p quasi-norm minimization. Based on this theorem, we provide a few RIP based recovery conditions.
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"... While contributory group key agreement is a promising solution to achieve access control in collaborative and dynamic group applications, the existing schemes have not achieved the performance lower bound in terms of time, communication and computation cost. In this paper we propose a contributory g ..."
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While contributory group key agreement is a promising solution to achieve access control in collaborative and dynamic group applications, the existing schemes have not achieved the performance lower bound in terms of time, communication and computation cost. In this paper we propose a contributory group key agreement that achieves the performance lower bound by utilizing a novel logical key tree structure, called PFMH, and the concept of phantom user position. In particular, the proposed scheme only needs O(1) rounds of two-party DH upon any single user join event and O(log n) rounds of two-party DH upon any single user leave event. Both theoretical bound analysis and simulation show that the proposed scheme achieves lower rekeying cost than the existing tree-based contributory group key agreement schemes.
MC-MIMO Radar: Recoverability and Performance Bounds
"... Abstract—It was recently shown that low rank matrix com-pletion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target detection and estimation. This paper focuses on t ..."
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Abstract—It was recently shown that low rank matrix com-pletion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target detection and estimation. This paper focuses on the performance of matrix completion in colocated MIMO radar systems equipped with Uniform Linear Arrays (ULAs). Exploiting the particular structure of the received data matrix, we present novel theoretical results showing that its coherence is both asymptotically and approximately optimal with respect to the number of antennas of the arrays involved and further, that the data matrix is recoverable using a subset of its entries with minimal cardinality.
RADAR PRECODING FOR SPECTRUM SHARING BETWEEN MATRIX COMPLETION BASED MIMO RADARS AND A MIMO COMMUNICATION SYSTEM
"... The paper investigates a new framework for spectrum sharing be-tween a MIMO-MC radar (MIMO radar using matrix completion) and a MIMO communication system, based on radar transmit pre-coding. The radar transmit precoder is jointly designed with the communication codewords so that the SINR at the rada ..."
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The paper investigates a new framework for spectrum sharing be-tween a MIMO-MC radar (MIMO radar using matrix completion) and a MIMO communication system, based on radar transmit pre-coding. The radar transmit precoder is jointly designed with the communication codewords so that the SINR at the radar receiver is maximized while meeting certain rate and power constraints at the communication system. By shaping the transmit beam, the proposed approach results in enhanced SINR at the receive antennas. Unlike prior works, there is no need for sharing the transmit waveforms with the communication system; only the precoding matrix needs to be shared. Therefore, the proposed scheme is less vulnerable to ad-versaries. Simulation results demonstrate that the proposed method improves the radar SINR and the matrix completion accuracy over previous approaches. Index Terms — MIMO radar, matrix completion, spectrum sharing, precoding, alternating optimization 1.
MIMO-MC Radar: A MIMO Radar Approach Based on Matrix Completion
, 2015
"... In a typical multiple-input and multiple-output (MIMO) radar scenario, the receive nodes transmit to a fusion center either samples of the target returns, or the results of matched filtering with the transmit waveforms. Based on the data it receives from multiple antennas, the fusion center formulat ..."
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In a typical multiple-input and multiple-output (MIMO) radar scenario, the receive nodes transmit to a fusion center either samples of the target returns, or the results of matched filtering with the transmit waveforms. Based on the data it receives from multiple antennas, the fusion center formulates a matrix, referred to as the data matrix, which, via standard array processing schemes leads to target detection and parameter estimation. In this paper, it is shown that under certain conditions, the data matrix is low rank and thus can be recovered based on knowledge of a small subset of its entries via matrix completion (MC) techniques. Leveraging the low-rank property of the data matrix, we propose a new MIMO radar approach, termed, MIMO-MC radar, in which each receive node either performs matched filtering with a small number of randomly selected dictionary waveforms or obtains sub-Nyquist samples of the target returns at random sampling instants, and forwards the results to a fusion center. Based on the received samples, and with knowledge of the sampling scheme, the fusion center partially fills the data matrix and subsequently applies MC techniques to estimate the full matrix. MIMO-MC radars share the advantages of MIMO radars with compressive sensing, (MIMO-CS), i.e., high resolution with reduced amounts of data, but unlike MIMO-CS radars do not require grid discretization. The MIMO-MC radar concept is illustrated through a uniform linear array configuration, and its target estimation performance is demonstrated via simulations.
