Conventional synthetic aperture radar (SAR) systems are limited in their ability to satisfy the increasing requirement for improved spatial resolution and wider coverage. The demand for high resolution requires high sampling rates, while coverage is limited by the pulse repetition frequency. Consequently, sampling rate reduction is of high practical value in SAR imaging. In this paper, we introduce a new algorithm, equivalent to the well-known range-Doppler method, to process SAR data using the Fourier series coefficients of the raw signals. We then demonstrate how to exploit the algorithm features to reduce sampling rate in both range and azimuth axes and process the signals at sub-Nyquist rates, by using compressive sensing (CS) tools. In particular, we demonstrate recovery of an image using only a portion of the received signal’s bandwidth and also while dropping a large percentage of the transmitted pulses. The complementary pulses may be used to capture other scenes within the same coherent processing interval. In addition, we propose exploiting the ability to reconstruct the image from narrow bands in order to dynamically adapt the transmitted waveform energy to vacant spectral bands, paving the way to cognitive SAR. The proposed recovery algorithms form a new CS-SAR imaging method that can be applied to high-resolution SAR data acquired at sub-Nyquist rates in range and azimuth. The performance of our method is assessed using simulated and real data sets. Finally, our approach is implemented in hardware using a previously suggested Xampling radar prototype.
CS theory has shown promising results in the field of sub-Nyquist sampling in radar applications. The use of Fourier series coefficients in pulse-Doppler radar enables practical sub-Nyquist sampling when the illuminated scene consists of moving targets that correspond to a sparse range-Doppler map @cite_25 @cite_31 @cite_23 . CS has also been explored in a wide range of radar imaging applications @cite_39 . In @cite_35 , the authors applied CS on SAR images by separating the processing into two decoupled one-dimensional operations. They showed that CS theory can then be applied in order to reduce the rate in azimuth. However, since RCMC is ignored, this method does not consider system setups with range varying parameters, hence, the quality of some images might be degraded.
@cite_35 @cite_39 @cite_23 @cite_31 @cite_25
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Radar data have already proven to be compressible with no significant losses for most of the applications in which it is used. In the framework of information theory, the compressibility of a signal implies that it can be decomposed onto a reduced set of basic elements. Since the same quantity of information is carried by the original signal and its decomposition, it can be deduced that a certain degree of redundancy exists in the explicit representation. According to the theory of compressive sensing (CS), due to this redundancy, it is possible to infer an accurate representation of an unknown compressible signal through a highly incomplete set of measurements. Based on this assumption, this paper proposes a novel method for the focusing of raw data in the framework of radar imaging. The technique presented is introduced as an alternative option to the traditional matched filtering, and it suggests that the new modes of acquisition of data are more efficient in orbital configurations. In this paper, this method is first tested on 1-D simulated signals, and results are discussed. An experiment with synthetic aperture radar (SAR) raw data is also described. Its purpose is to show the potential of CS applied to SAR systems. In particular, we show that an image can be reconstructed, without the loss of resolution, after dropping a large percentage of the received pulses, which would allow the implementation of wide-swath modes without reducing the azimuth resolution. Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights. Recently, a new approach to sub-Nyquist sampling and processing in pulse-Doppler radar was introduced, based on the Xampling approach to reduced-rate sampling combined with Doppler focusing performed on the low-rate samples. This method imposes no restrictions on the transmitter, reduces both the sam- pling and processing rates and exhibits linear signal-to-noise ratio improvement with the number of pulses. Here we extend previous work on sub-Nyquist pulse-Doppler radar by incorporating a clutter removal algorithm operating on the sub-Nyquist samples, allowing to reject clutter modeled as a colored Gaussian random process. In particular, we show how to adapt standard clutter rejection techniques to work directly on the sub-Nyquist samples, allowing to preserve high detection rates even in the presence of strong clutter, while avoiding the need to first interpolate the samples to the Nyquist grid. Traditional radar sensing typically employs matched filtering between the received signal and the shape of the transmitted pulse. Matched filtering (MF) is conventionally carried out digitally, after sampling the received analog signals. Here, principles from classic sampling theory are generally employed, requiring that the received signals be sampled at twice their baseband bandwidth. The resulting sampling rates necessary for correlation-based radar systems become quite high, as growing demands for target distinction capability and spatial resolution stretch the bandwidth of the transmitted pulse. The large amounts of sampled data also necessitate vast memory capacity. In addition, real-time data processing typically results in high power consumption. Recently, new approaches for radar sensing and estimation were introduced, based on the finite rate of innovation (FRI) and Xampling frameworks. Exploiting the parametric nature of radar signals, these techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's estimation capabilities at sufficiently high signal-to-noise ratios (SNRs). Here we present for the first time a design and implementation of an Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demonstrate by real-time analog experiments that our system is able to maintain reasonable recovery capabilities, while sampling radar signals that require sampling at a rate of about 30 MHz at a total rate of 1 MHz. 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 - 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.