Laura Anitori

Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)

Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex-valued. We study the popular recovery method of l1-regularized least squares or LASSO. While several studies have shown that LASSO provides desirable solutions under certain conditions, the precise asymptotic performance of this algorithm in the complex setting is not yet known. In this paper, we extend the approximate message passing (AMP) algorithm to solve the complex-valued LASSO problem and obtain the complex approximate message passing algorithm (CAMP). We then generalize the state evolution framework recently introduced for the analysis of AMP to the complex setting. Using the state evolution, we derive accurate formulas for the phase transition and noise sensitivity of both LASSO and CAMP. Our theoretical results are concerned with the case of i.i.d. Gaussian sensing matrices. Simulations confirm that our results hold for a larger class of random matrices.

Design and Analysis of Compressed Sensing Radar Detectors

We consider the problem of target detection from a set of Compressed Sensing (CS) radar measurements corrupted by additive white Gaussian noise. We propose two novel architectures and compare their performance by means of Receiver Operating Characteristic (ROC) curves. Using asymptotic arguments and the Complex Approximate Message Passing (CAMP) algorithm, we characterize the statistics of the ℓ1-norm reconstruction error and derive closed form expressions for both the detection and false alarm probabilities of both schemes. Of the two architectures, we demonstrate that the best performing one consists of a reconstruction stage based on CAMP followed by a detector. This architecture, which outperforms the ℓ1-based detector in the ideal case of known background noise, can also be made fully adaptive by combining it with a conventional Constant False Alarm Rate (CFAR) processor. Using the state evolution framework of CAMP, we also derive Signal to Noise Ratio (SNR) maps that, together with the ROC curves, can be used to design a CS-based CFAR radar detector. Our theoretical findings are confirmed by means of both Monte Carlo simulations and experimental results.

FMCW radar for life-sign detection

In this paper we investigate the use of Frequency Modulated Continuous Wave (FMCW) radars for detecting life-sign of people, i.e. breathing and heartbeat. An optimum frequency has been selected to observe life-sign, taking into consideration also design factors, such as bandwidth availability and interference with other systems. A new compact X-band FMCW radar has been built at TNO laboratories and experimental results are presented here, which demonstrate the ability of this new system to detect life-sign.

Compressive CFAR radar detection

In this paper we develop the first Compressive Sensing (CS) adaptive radar detector. We propose three novel architectures and demonstrate how a classical Constant False Alarm Rate (CFAR) detector can be combined with l1-norm minimization. Using asymptotic arguments and the Complex Approximate Message Passing (CAMP) algorithm we characterize the statistics of the l1-norm reconstruction error and derive closed form expressions for both the detection and false alarm probabilities. We support our theoretical findings with a range of experiments that show that our theoretical conclusions hold even in non-asymptotic setting. We also report on the results from a radar measurement campaign, where we designed ad hoc transmitted waveforms to obtain a set of CS frequency measurements. We compare the performance of our new detection schemes using Receiver Operating Characteristic (ROC) curves.

Light weight digital array SAR

A light weight SAR has been designed, suitable for short range tactical UAVs, consisting of a fully digital receive array, and a very compact active transmit antenna. The weight of the complete RF front is expected to be below 3 kg, with a power consumption below 30 W. This X-band system can provide image resolution down to 10 cm at up to 5 km range. The system makes use of FMCW technology and digital beam forming in the horizontal direction, with 24 receive channels. A switchable transmit antenna is designed, to allow wide coverage with sufficient antenna gain. RF electronics for the receive panels have been realized and tested, as well as a low phase noise transmitter. Detailed antenna design has been performed, and critical issues such as bandwidth and transmit-receive isolation have been assessed by simulation.

Detection performance of Compressive Sensing applied to radar

In this paper some results are presented on detection performance of radar using Compressive Sensing. Compressive sensing is a recently developed theory which allows reconstruction of sparse signals with a number of measurements much lower than implied by the Nyquist rate. In this work the behavior of detection and false alarm performance of a CS based radar using a stepped frequency waveform is analyzed. The results are obtained via simulations with known noise levels for several different scenarios (e.g. single and multiple targets, varying compression factors and Signal to Noise Ratios (SNR). Performance of CS reconstruction and detection are analyzed by means of Receiver Operating Characteristic (ROC) curves and compared to conventional Matched Filtering

False alarm probability estimation for Compressive Sensing radar

In this paper false alarm probability (FAP) estimation of a radar using Compressive Sensing (CS) in the frequency domain is investigated. Compressive Sensing is a recently proposed technique which allows reconstruction of sparse signal from sub-Nyquist rate measurements. The estimation of the FAP is based on an empirical model derived from simulations of the probability density function (pdf) of the noise samples reconstructed using the basis pursuit denoising (BPDN) algorithm. During simulations noise levels were assumed to be known; in practice noise or clutter power is not known a priori, and must be estimated from the radar data. As in radar applications it is desirable to have a Constant False Alarm Rate (CFAR), the aim here is to understand the statistical behavior of noise after CS reconstruction for designing CFAR radar detection schemes.

Detection and classification of landmines using AR modeling of GPR data

In this paper we present some results on detection and classification of low metal content anti personnel (AP) landmines using a modified version of the Auto Regressive (AR) modeling algorithm presented in. A statistical distance is computed between the AR coefficients of the measured GPR time signal and the AR coefficients of a reference database (containing the AR models of the mines of interest) and a detection is declared if this distance is below a given threshold.

Array aperture extrapolation using sparse reconstruction

In this paper we present some preliminary results on antenna array extrapolation for Direction Of Arrival (DOA) estimation using Sparse Reconstruction (SR). The objective of this study is to establish wether it is possible to achieve with an array of a given physical length the performance (in terms of accuracy, resolution and sidelobe level) of an equivalent larger array by using SR. The difference between our work and previous publications on DOA estimation using SR lies in the fact that we do not use SR as a beamformer, but instead we use the sparse solution for aperture extrapolation. We adopt an approach similar to the one of Swingler and Walker in [1], where the extrapolated sensor data are first tapered and then beamformed to suppress sidelobes of strong interfering targets, resulting in improved detection of weak targets.

Performance of low-rank STAP detectors

In this paper the STAP detector based on the low-rank approximation of the normalized adaptive matched filter (LRNAMF) is investigated for its false alarm probability (FAP) performance. An exact formula for the FAP of the LRNAMF detector is derived using the g-method estimator [4]. The non-CFAR behavior of this detector is shown via simulations using different models for the clutter-plus-noise covariance matrix. The detection probability is also evaluated, and the LRNAMF detector exhibits robustness in the presence of inhomogeneities consisting of interferers in the training data, for both non-fluctuating as well as fluctuating target models.