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...al-time algorithms have been proposed that can be shown to recover the true sparse vector under appropriate conditions [13]. In our simulations, we use the orthogonal matching pursuit (OMP) algorithm =-=[19, 20]-=-. There have been several other works that employ CS algorithms in the context of radar signal processing such as [21–26]. However, these papers either do not address sample rate reduction and continu...

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...methods, and generally require the measurements to form a consecutive subset of the signal’s Fourier coefficients. An exception is the MUSIC algorithm, which can be applied on any set of coefficients =-=[32]-=-. While these techniques work well at high SNR; their performance deteriorates at low SNR values. In [8] it was suggested to use a nonconsecutive set of Fourier coefficients selected in a distributed ...

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... MF is known to maximize the effective signal-to-noise ratio (SNR). The MF stage is typically carried out digitally, after sampling the detected analog signal. Classic Shannon-Nyquist sampling theory =-=[3]-=- guarantees full recovery of a general bandlimited analog signal from samples taken at twice its baseband bandwidth. However, applying this framework to modern radar systems typically results in extre...

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...al-time algorithms have been proposed that can be shown to recover the true sparse vector under appropriate conditions [13]. In our simulations, we use the orthogonal matching pursuit (OMP) algorithm =-=[19, 20]-=-. There have been several other works that employ CS algorithms in the context of radar signal processing such as [21–26]. However, these papers either do not address sample rate reduction and continu...

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...stricted isometry property (RIP). Selecting the frequency samples uniformly at random, it is known that if K ≥ CL(log N)4, (6) for some positive constant C, then A obeys the RIP with high probability =-=[33]-=-. In contrast, for consecutive frequency selection the RIP is not generally satisfied, unless the cardinality of κ is significantly increased. However, applying random frequency sampling is not practi...

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...n that obtained by Nyquist sampling. Related works [6–8] treat ultrasound signal sampling and are readily adapted to the radar scenario. These methods are based on the finite rate of innovation (FRI) =-=[9]-=- and Xampling [10, 11] approaches. The FRI framework treats sampling and recovery of signals characterized by a finite number of degrees of freedom per unit time and is based on connecting sampling th...

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...fficiently from random frequency samples in the presence of noise providing theoretical justification to our approach. The use of frequency samples for CS of signals sparse in time is also studied in =-=[16]-=-. In order to choose appropriate frequencies to process we connect our problem to that of beampattern design in array processing, and rely on ideas obtained in that context. In particular, it is known...

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...ion III. The remainder of this section is devoted to reviewing algorithmic approaches for solving (3). B. Recovery Algorithm Many mature techniques for solving (3) exist, including matrix pencil (MP) =-=[31]-=-, annihilating filter [9], and others that can be found in [5]. These algorithms arise from spectral analysis methods, and generally require the measurements to form a consecutive subset of the signal...

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...e parametric problem, from a small number of measurements taken after appropriate analog prefiltering. The estimation problem is solved in the frequency domain using known tools from array processing =-=[5]-=-, with the necessary number of measurements typically much smaller than that obtained by Nyquist sampling. Related works [6–8] treat ultrasound signal sampling and are readily adapted to the radar sce...

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...ch is impractical for real-time applications such as radar sensing. Many polynomial-time algorithms have been proposed that can be shown to recover the true sparse vector under appropriate conditions =-=[13]-=-. In our simulations, we use the orthogonal matching pursuit (OMP) algorithm [19, 20]. There have been several other works that employ CS algorithms in the context of radar signal processing such as [...

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...e targets’ location in space and their velocity. Traditional processing methods in both literature and practice involve a preliminary stage, referred to as matched filtering (MF) or pulse compression =-=[1, 2]-=-, in which the transmitted pulse is correlated with the received signal. For the problem of detecting targets in white Gaussian noise, the MF is known to maximize the effective signal-to-noise ratio (...

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...y Nyquist sampling. Related works [6–8] treat ultrasound signal sampling and are readily adapted to the radar scenario. These methods are based on the finite rate of innovation (FRI) [9] and Xampling =-=[10, 11]-=- approaches. The FRI framework treats sampling and recovery of signals characterized by a finite number of degrees of freedom per unit time and is based on connecting sampling theory with array proces...

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...uation of 6.28 dB. The preliminary LPF and the antialiasing LPF have very small insertion loss, and therefore their NFs are negligible. To obtain the total NF of the system, we use the Friis equation =-=[35]-=-, NFsystem = NF1 + N∑ n=2 NFn − 1∏n−1 m=1 Gm (10) where Gn and N Fn are the gain and NF of the nth component in the channel, respectively, and N is the number of total components. Incorporating the fa...

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...veral random groups of coefficients can yield similar performance, while resulting in a simple ADC structure. Our hardware prototype implements a combination of the multichannel topology suggested in =-=[7]-=- and the filtering approach presented in [6], additionally taking into account the practical challenges they impose. In particular, our board consists of 4 channels, each comprising a bandpass crystal...

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...y Nyquist sampling. Related works [6–8] treat ultrasound signal sampling and are readily adapted to the radar scenario. These methods are based on the finite rate of innovation (FRI) [9] and Xampling =-=[10, 11]-=- approaches. The FRI framework treats sampling and recovery of signals characterized by a finite number of degrees of freedom per unit time and is based on connecting sampling theory with array proces...

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...d similar performance, while resulting in a simple ADC structure. Our hardware prototype implements a combination of the multichannel topology suggested in [7] and the filtering approach presented in =-=[6]-=-, additionally taking into account the practical challenges they impose. In particular, our board consists of 4 channels, each comprising a bandpass crystal filter with a random effective carrier freq...

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...rray processing, and rely on ideas obtained in that context. In particular, it is known in the array processing literature that random frequencies spread over a wide aperture lead to good performance =-=[17, 18]-=-. However, in the context of ADC design this choice corresponds to a complicated receiver structure. Instead, we show that choosing several random groups of coefficients can yield similar performance,...

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...wing sampling rates required due to the desire to increase resolution necessitate sophisticated analog front ends and imply higher power consumption and vast memory capacity. Recently, new approaches =-=[4]-=- to radar processing were introduced, which allow practical solution of the parametric problem, from a small number of measurements taken after appropriate analog prefiltering. The estimation problem ...

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...n about the parameters of interest. Our prototype allows to obtain these needed frequency coefficients directly from the analog input using simple analog filters and low rate sampling. The results of =-=[15]-=- establish that a single delay can be found efficiently from random frequency samples in the presence of noise providing theoretical justification to our approach. The use of frequency samples for CS ...

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...practical from a hardware perspective, and therefore a rule for selecting a good constellation of frequency samples is desired. Some practical guidelines for choosing the frequencies are suggested in =-=[34]-=-. The authors consider an equivalent problem to (3), with the roles of frequency and time interchanged. That is, the measurement vector consists of time samples of a signal, described by a spectral li...

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... point targets assumed to be stationary or moving at very slow velocities, so that no Doppler shift is incorporated into the model. We show how to adapt the results to allow for Doppler processing in =-=[30]-=-. The parameters {al, tl}Ll=1 correspond to the estimated pulses’ amplitudes and delays, respectively, and are proportional to the targets’ distance from the receiver and their radar cross section (RC...

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...e targets’ location in space and their velocity. Traditional processing methods in both literature and practice involve a preliminary stage, referred to as matched filtering (MF) or pulse compression =-=[1, 2]-=-, in which the transmitted pulse is correlated with the received signal. For the problem of detecting targets in white Gaussian noise, the MF is known to maximize the effective signal-to-noise ratio (...

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...rray processing, and rely on ideas obtained in that context. In particular, it is known in the array processing literature that random frequencies spread over a wide aperture lead to good performance =-=[17, 18]-=-. However, in the context of ADC design this choice corresponds to a complicated receiver structure. Instead, we show that choosing several random groups of coefficients can yield similar performance,...

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...ficients. An exception is the MUSIC algorithm, which can be applied on any set of coefficients [32]. While these techniques work well at high SNR; their performance deteriorates at low SNR values. In =-=[8]-=- it was suggested to use a nonconsecutive set of Fourier coefficients selected in a distributed manner, as many detection systems (such as ultrasound in [8] and radar in our work) benefit from wide fr...