Results 1 -
9 of
9
Sub-Nyquist radar via Doppler focusing
- IEEE Transactions on Signal Processing
"... Abstract—We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets sparsely populated in the radar’s unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem but either do not address sample rate ..."
Abstract
-
Cited by 10 (5 self)
- Add to MetaCart
(Show Context)
Abstract—We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets sparsely populated in the radar’s unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or per-form poorly in noisy conditions. Here, we describe a sub-Nyquist sampling and recovery approach called Doppler focusing, which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size, which does not increase with increasing number of pulses. Furthermore, in the presence of noise, Doppler focusing enjoys a signal-to-noise ratio (SNR) improvement, which scales linearly with, obtaining good detec-tion performance even at SNR as low as 25 dB. The recovery is based on the Xampling framework, which allows reduction of the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling radar prototype. Index Terms—Compressed sensing, rate of innovation, radar, sparse recovery, sub-Nyquist sampling, delay-Doppler estimation. I.
Spatial compressive sensing for MIMO radar
- IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2014
"... 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. Th ..."
Abstract
-
Cited by 7 (0 self)
- Add to MetaCart
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, (which is also the number of degrees of freedom), scales with, where is the number of targets and is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product scales linearly with, the logarithmic dependence on 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.
Fourier domain beamforming: The path to compressed ultrasound imaging
- IEEE Trans. Ultrason., Ferroelectr., Freq. Control
"... ar ..."
(Show Context)
COMPRESSIVE SHIFT RETRIEVAL
"... The classical shift retrieval problem considers two signals in vector form that are related by a cyclic shift. In this paper, we develop a compressive variant where the measurement of the signals is undersampled. While the standard procedure to shift retrieval is to maximize the real part of their d ..."
Abstract
-
Cited by 1 (0 self)
- Add to MetaCart
(Show Context)
The classical shift retrieval problem considers two signals in vector form that are related by a cyclic shift. In this paper, we develop a compressive variant where the measurement of the signals is undersampled. While the standard procedure to shift retrieval is to maximize the real part of their dot product, we show that the shift can be exactly recovered from the corresponding compressed measurements if the sensing matrix satisfies certain conditions. A special case is the partial Fourier matrix. In this setting we show that the true shift can be found by as low as two measurements. We further show that the shift can often be recovered when the measurements are perturbed by noise. Index Terms — Compressed sensing, shift retrieval, signal reconstruction, signal registration. 1.
1Sub-Nyquist Radar via Doppler Focusing
"... Abstract—We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets, sparsely populated in the radar’s unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample ra ..."
Abstract
- Add to MetaCart
Abstract—We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets, sparsely populated in the radar’s unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here we describe a sub-Nyquist sampling and recovery approach called Doppler focusing which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys a signal-to-noise ratio (SNR) improvement which scales linearly with P, obtaining good detection performance even at SNR as low as-25dB. The recovery is based on the Xampling framework, which allows reducing the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling radar prototype. Index Terms—compressed sensing, rate of innovation, radar, sparse recovery, sub-Nyquist sampling, delay-Doppler estimation. I.
1Spatial Compressive Sensing for MIMO Radar
"... Abstract—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 ra ..."
Abstract
- Add to MetaCart
Abstract—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 es-tablish 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 (logG)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. Index Terms—Compressive sensing, MIMO radar, random arrays, direction of arrival estimation. I.
Detection Performance from Compressed Measurements
"... Abstract—This work uses two performance metrics, target detection and scene reconstruction performance, to compare various estimation techniques that operate on compressed measurements. Specifically we compare the performance of the compressed matched filter, ℓ1-regularized least squares, and comple ..."
Abstract
- Add to MetaCart
(Show Context)
Abstract—This work uses two performance metrics, target detection and scene reconstruction performance, to compare various estimation techniques that operate on compressed measurements. Specifically we compare the performance of the compressed matched filter, ℓ1-regularized least squares, and complex approximate message passing (CAMP), as well as a sparsified matched filter estimate. We show that the compressed matched filter provides the same or similar detection performance as the other, more computationally expensive techniques, but at the expense of poorer signal reconstruction error. However, by sparsifying the matched filter estimate using a soft-thresholding function, this estimate can achieve high reconstruction performance as well, and at much lower computational cost. Index Terms—Target Detection; Compressed Sensing I.
Pulse-Doppler Signal Processing With Quadrature Compressive Sampling
"... Quadrature compressive sampling (QuadCS) is a recently introduced sub-Nyquist sampling scheme for effective acquisition of inphase and quadrature (I/Q) components of sparse radio frequency signals. In applications to pulse-Doppler radars, the QuadCS outputs can be arranged into a two-dimensional dat ..."
Abstract
- Add to MetaCart
Quadrature compressive sampling (QuadCS) is a recently introduced sub-Nyquist sampling scheme for effective acquisition of inphase and quadrature (I/Q) components of sparse radio frequency signals. In applications to pulse-Doppler radars, the QuadCS outputs can be arranged into a two-dimensional data format, in terms of slow time and virtual fast time, similar to that by Nyquist sampling. This paper develops a compressive sampling pulse-Doppler (CoSaPD) processing scheme which performs Doppler estimation/detection and range estimation from the sub-Nyquist data without recovering the Nyquist samples. The Doppler estimation is realized through a spectrum analyzer as in classical processing, whereas the detection is performed using the Doppler bin data. The range estimation is performed using sparse recovery algorithms only for the detected targets to reduce the computational load. A low detection threshold is used to improve the detection probability and the introduced false
Global Testing Against Sparse Alternatives in Time-Frequency Analysis
"... In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the number and magnitude of the complex sinusoids hidden in the serie ..."
Abstract
- Add to MetaCart
(Show Context)
In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the number and magnitude of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram over-sampled by O(logN) is proven universally optimal in global testing for periodicities under a mild minimum separation condition. Connections to the problem of detecting a stream of pulses from frequency measurements in signal processing is also discussed.
