Pawan Setlur

Multipath Model and Exploitation in Through-the-Wall and Urban Radar Sensing

We derive a multipath model for sensing through walls using radars. The model considers propagation through a front wall and specular reflections at interior walls in an enclosed room under surveillance. The model is derived such that additional eigenrays can be easily accommodated. A synthetic aperture radar (SAR) system is considered, and stationary or slowly moving targets are assumed. The focused downrange and crossrange locations of multipath ghosts are established and validated using numerical, as well as experimental data. The multipath model permits an implementation of a multipath exploitation algorithm, which associates, as well as maps, each target ghost back to its corresponding true target location. In doing so, the proposed algorithm improves the radar system performance by aiding in ameliorating the false positives in the original SAR image, as well as increasing the signal-to-clutter ratio at the target locations, culminating in enhanced behind the wall target detection and localization.

Target Localization with a Single Sensor via Multipath Exploitation

In urban sensing and through-the-wall (TTW) radar, the existence of targets inside buildings results in multipath returns. These multipath returns are exploited to achieve target localization with a single sensor. A time-of-arrival (TOA) wall association algorithm is derived to relate multipath returns to their respective walls and targets, followed by a nonlinear least squares (NLS) optimization to localize the targets. Simulations and experimental data are used to validate the proposed algorithms.

Analysis of micro-Doppler signals using linear FM basis decomposition

Micro-Doppler is generated from targets with simple harmonic motions, characterized by a sinusoidal instantaneous frequency in the time-frequency plane. This type of micro-Doppler arises from vibrating or rotating targets, which are commonly present in indoor settings. It is shown that the use of basis functions matched to the sinusoidal micro-Doppler signatures proves effective in identifying the micro-Doppler components in indoor imaging. These functions are optimum in the maximum likelihood (ML) sense. Asymptotic properties of the proposed linear decomposition are derived. The basis decomposition provides enhanced phase and frequency resolutions and is robust to noise. It is strongly dependent on the Bessel function (of the first kind) characteristics. Simulation results are presented to demonstrate the effect of non-orthogonality of the basis functions and the respective frequency and phase resolution properties of the decomposition.

Micro-doppler signal estimation for vibrating and rotating targets

Vibrations or rotations of a target or structures on a target give rise to the micro-Doppler effect of the reflected waveforms. In this paper, we analyze micro- Doppler signals in the joint time-frequency plane using commonly applied distributions and time-frequency transforms. Performance is evaluated based on achieved resolution and reduced artifacts. The latter is significant in microDoppler analysis, as the signals have sinusoidal timefrequency (TF) signatures. This presents a challenge for the already established distributions, as they have to suppress the cross as well as the auto artifacts. We propose a new decomposition of basis functions, given the apriori knowledge of the time varying nature of the radar returns. This approach can be cast as an application of waveform diversity. The new decomposition is free from any artifacts and provides improved estimates of the target micro-Doppler signature.

Through-the-wall target localization using dual-frequency CW radars

A simple through-the-wall radar system for moving target localization is proposed. This scheme is based on trilateration and range estimation from three independent dual-frequency CW radar units. The dual-frequency technique uses phase comparison of the transmitted and received CW signals to provide an estimate of the range-to-motion. The difference in frequency of the two CW carriers determines the maximum unambiguous range of the target. The range estimates from the three independent CW radar units are then combined using trilateration for target localization. The composition and thickness of the wall, its dielectric constant, and the angle of incidence all affect the characteristics of the signal propagating through the wall. The propagating signal slows down, encounters refraction, and is attenuated as it passes through the wall. If unaccounted for, the non-line-of-sight propagation due to refraction and the slowing down of the waves will introduce a bias in the estimated target location. Our scheme takes into account the presence of the wall and corrects for its refraction and speed of propagation effects. Proof of concept is provided using simulated data. The results show that the proposed dual-frequency CW radar system is able to correctly locate and track moving targets behind walls.

Multipath Exploitation in Through-Wall Radar Imaging Via Point Spread Functions

Due to several sources of multipath in through-wall radar sensing, such as walls, floors, and ceilings, there could exist multipath ghosts associated with a few genuine targets in the synthetic aperture beamformed image. The multipath ghosts are false positives and therefore confusable with genuine targets. Here, we develop a multipath exploitation technique using point spread functions, which associate and map back the multipath ghosts to their genuine targets, thereby increasing the effective signal-to-clutter ratio (SCR) at the genuine target locations. To do so, we first develop a multipath model advocating the Householder transformation, which permits modeling multiple reflections at multiple walls, and also allows for unconventional room/building geometries. Second, closed-form solutions of the multipath ghost locations assuming free space propagation are derived. Third, a nonlinear least squares optimization is formulated and initialized with these free space solutions to localize the multipath ghosts in through-wall radar sensing. The exploitation approach is general and does not require a priori assumptions on the number of targets. The free space multipath ghost locations and exploitation technique derived here may be used as is for multipath exploitation in urban canyons via synthetic aperture radar. Analytical expressions quantifying the SCR gain after multipath exploitation are derived. The analysis is validated with experimental EM results using finite-difference time-domain simulations.

Moving Target Localization for Indoor Imaging using Dual Frequency CW Radars

In this paper, we propose a simple method, to determine the unambiguous range of a moving target, using dual frequency continuous wave (CW) radars. The carrier frequencies, and hence the wavelength, determine the maximum unambiguous range of the target. The technique is capable of determining range for an indoor moving target. It uses phase comparison of the Doppler signals to estimate the range, where as the target velocity is directly obtained from the Doppler shift. Simulation results are presented in the presence of noise to validate the technique. Experimental results are also provided showing the effectiveness of the proposed method for indoor range estimation. Specifically, we have performed two experiments, the first experiment is in an indoor laboratory setting with absorbers to mitigate multipath. In the second experiment, the target was behind a one foot thick concrete wall, in an indoor setting without absorbers. For both experiments, we were able to successfully detect the target and estimate its range

Urban target classifications using time-frequency micro-Doppler signatures

Moving target indicators (MTI) find important applications in urban sensing. While motion detection can be achieved using simple CW radars, characterization of moving targets can be provided by estimating the key parameters of the target micro-Doppler signature. For indoor sensing, this signature has underlying instantaneous frequency features, which may depend on the radar viewing angle. This paper considers typical animate and inanimate moving objects and presents time-frequency motion classifiers using quadratic time-frequency distributions. The distinctions between the different target micro-Doppler parameter values and bounds are delineated.

Waveform Design for Radar STAP in Signal Dependent Interference

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms.

Maximum likelihood time delay estimation and Cramér-Rao bounds for multipath exploitation

In this paper, time delay estimation using the maximum likelihood principle is addressed for the multipath exploitation problem, and the corresponding Cramér-Rao bounds are derived. A single wideband radar, and a target in a known reflecting geometry are assumed. If the multipath is indeed detectable and resolvable, it is shown here that multipath exploitation, firstly, permits estimating the angle of arrival (AoA) of the target with a single sensor, and secondly, improves estimation accuracy of the direct path time delay. Both these are possible because the multipaths time delay is a deterministic function of the time delay of the direct path as well as its AoA, as is demonstrated here. The multipath caused from reflections from surfaces yields virtual radar sensors observing the target from different aspects, thereby allowing AoA estimation.