Satyabrata Sen

Adaptive OFDM Radar for Target Detection in Multipath Scenarios

We develop methods for detecting a moving target in the presence of multipath reflections, which exist, for example, in urban environments. We take advantage of the multipath propagation that increases the spatial diversity of the radar system and provides different Doppler shifts over different paths. We employ a broadband orthogonal frequency division multiplexing (OFDM) signal to increase the frequency diversity of the system as different scattering centers of a target resonate variably at different frequencies. To overcome the peak-to-average power ratio (PAPR) problem of the conventional OFDM, we also use constant-envelope OFDM (CE-OFDM) signaling scheme. First, we consider a simple scenario in which the radar receives only a finite number of specularly reflected multipath signals. We develop parametric measurement models, for both the OFDM and CE-OFDM signaling methods, under the generalized multivariate analysis of variance (GMANOVA) framework and employ the generalized likelihood ratio (GLR) tests to decide about the presence of a target in a particular range cell. Then, we propose an algorithm to optimally design the parameters of the OFDM transmitting waveform for the next coherent processing interval. In addition, we extend our models to study the aspects of temporal correlations in the measurement noise. We provide a few numerical examples to illustrate the performance characteristics of the proposed detectors and demonstrate the achieved performance improvement due to adaptive OFDM waveform design.

OFDM MIMO Radar With Mutual-Information Waveform Design for Low-Grazing Angle Tracking

We propose an information theoretic waveform design algorithm for target tracking in a low-grazing angle (LGA) scenario. We incorporate realistic physical and statistical effects, such as Earths curvature, vertical refractivity gradient of lower atmosphere, and compound-Gaussian characteristics of sea-clutter, into our model. We employ a co-located multiple-input-multiple-output (MIMO) radar configuration using wideband orthogonal frequency division multiplexing (OFDM) signalling scheme. The frequency diversity of OFDM provides richer information about the target as different scattering centers resonate at different frequencies. Additionally, we use polarization-sensitive transceivers to resolve the multipath signals with small separation angles. Thus, we track the scattering coefficients of the target at different frequencies along with its position and velocity. We apply a sequential Monte Carlo method (particle filter) to track the target. Our tracker works in a closed-loop fashion with an integrated optimal waveform design technique based on mutual information (MI) criterion. We seek the optimal OFDM waveform at the current pulse duration to maximize the MI between the state and measurement vectors at the next pulse duration utilizing all the measurement history up to the current pulse. Our numerical examples demonstrate the importance of realistic physical modeling, effects of frequency diversity through OFDM MIMO configuration, and achieved performance improvements due to adaptive OFDM waveform design.

Multiobjective Optimization of OFDM Radar Waveform for Target Detection

We propose a multiobjective optimization (MOO) technique to design an orthogonal-frequency-division multiplexing (OFDM) radar signal for detecting a moving target in the presence of multipath reflections. We employ an OFDM signal to increase the frequency diversity of the system, as different scattering centers of a target resonate variably at different frequencies. Moreover, the multipath propagation increases the spatial diversity by providing extra “looks” at the target. First, we develop a parametric OFDM radar model by reformulating the target-detection problem as the task of sparse-signal spectrum estimation. At a particular range cell, we exploit the sparsity of multiple paths and the knowledge of the environment to estimate the paths along which the target responses are received. Then, to estimate the sparse vector, we employ a collection of multiple small Dantzig selectors (DS) that utilizes more prior structures of the sparse vector. We use the ℓ1-constrained minimal singular value (ℓ1-CMSV) of the measurement matrix to analytically evaluate the reconstruction performance and demonstrate that our decomposed DS performs better than the standard DS. In addition, we propose a constrained MOO-based algorithm to optimally design the spectral parameters of the OFDM waveform for the next coherent processing interval by simultaneously optimizing two objective functions: minimizing the upper bound on the estimation error to improve the efficiency of sparse-recovery and maximizing the squared Mahalanobis-distance to increase the performance of the underlying detection problem. We provide a few numerical examples to illustrate the performance characteristics of the sparse recovery and demonstrate the achieved performance improvement due to adaptive OFDM waveform design.

Adaptive Design of OFDM Radar Signal With Improved Wideband Ambiguity Function

We propose an adaptive technique to design the spectrum of an orthogonal frequency division multiplexing (OFDM) waveform to improve the radars wideband ambiguity function (WAF). The adaptive OFDM signal yields a better auto-correlation function (ACF) that results into an improved delay (range) resolution for the radar system. First, we develop a mutlicarrier OFDM signal model and the corresponding WAF at the output of the matched filter, emphasizing that the received signal depends on the scattering parameters of the target. Then, we devise an optimization procedure to select the OFDM waveform such that the volume of the corresponding WAF best approximates the volume of a desired ambiguity function. We demonstrate the improvement in the resulting ambiguity function, along with the associated ACF, through numerical examples. We find that the optimization algorithm puts more signal energy at subcarriers in which the target response is weaker.

Target Detection in Clutter Using Adaptive OFDM Radar

We address the problem of detecting a target moving in clutter environment using an orthogonal frequency division multiplexing (OFDM) radar. The broadband OFDM signal provides frequency diversity to improve the performance of the system. First, we develop a parametric model that accounts for the measurements at multiple frequencies including the Doppler shift. Then, we present a statistical detection test and evaluate its performance characteristics. Based on this, we propose an algorithm to adaptively design the parameters for the next transmitting waveform. Numerical examples illustrate our analytical results, demonstrating the achieved performance improvement due to the OFDM signaling method and adaptive waveform design.

OFDM Radar Space-Time Adaptive Processing by Exploiting Spatio-Temporal Sparsity

We propose a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly-moving target using an orthogonal frequency division multiplexing (OFDM) radar. We observe that the target and interference spectra are inherently sparse in the spatio-temporal domain. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data and produces an equivalent performance as the other existing STAP techniques. In addition, the use of an OFDM signal increases the frequency diversity of our system, as different scattering centers of a target resonate at different frequencies, and thus improves the target detectability. First, we formulate a realistic sparse-measurement model for an OFDM radar considering both the clutter and jammer as the interfering sources. Then, we apply a residual sparse-recovery technique based on the LASSO estimator to estimate the target and interference covariance matrices, and subsequently compute the optimal STAP-filter weights. Our numerical results demonstrate a comparative performance analysis of the proposed sparse-STAP algorithm with four other existing STAP methods. Furthermore, we discover that the OFDM-STAP filter-weights are adaptable to the frequency-variabilities of the target and interference responses, in addition to the spatio-temporal variabilities. Hence, by better utilizing the frequency variabilities, we propose an adaptive OFDM-waveform design technique, and consequently gain a significant amount of STAP-performance improvement.

Sparsity-Based Multi-Target Tracking Using OFDM Radar

We propose a sparsity-based approach to track multiple targets in a region of interest using an orthogonal-frequency-division multiplexing (OFDM) radar. We observe that in a particular pulse interval the targets lie at a few points on the delay-Doppler plane and hence we exploit that inherent sparsity to develop a tracking procedure. The use of an OFDM signal not only increases the frequency diversity of our system, as different scattering centers of a target resonate variably at different frequencies, but also decreases the block-coherence measure of the equivalent sparse measurement model. In the tracking filter, we exploit this block-sparsity property in developing a block version of the compressive sampling matching pursuit (CoSaMP) algorithm. We present numerical examples to show the performance of our sparsity-based tracking approach and compare it with a particle filter (PF) based tracking procedure. The sparsity-based tracking algorithm takes much less computational time and provides equivalent and sometimes better, tracking performance than the PF-based tracking.

Adaptive OFDM radar for detecting a moving target in urban scenarios

We address the problem of detecting a moving target in an urban canyon using an orthogonal frequency division multiplexing (OFDM) radar and exploiting the multipath reflections. The multipath propagation increases the spatial diversity of the radar system and provides different Doppler shifts over different path. In addition, the use of broadband OFDM signal provides frequency diversity to the system. We develop a parametric measurement model that accounts for the multipath components at multiple frequencies as well as Doppler shifts. Then, we develop a statistical detection test and evaluate its performance characteristics. Based on this, we propose an algorithm to optimally design the spectral weights for the next transmitting waveform. We present a few numerical examples to illustrate our analytical results. We demonstrate the achieved performance improvement due to the exploitation of multipath propagation, OFDM signalling, and adaptive waveform design.

PAPR-Constrained Pareto-Optimal Waveform Design for OFDM-STAP Radar

We propose a peak-to-average power ratio (PAPR)-constrained Pareto-optimal waveform-design approach for an orthogonal frequency division multiplexing (OFDM) radar signal to detect a target using the space-time adaptive processing (STAP) technique. The use of an OFDM signal does not only increase the frequency diversity of our system but also enable us to adaptively design the OFDM coefficients in order to further improve the system performance. First, we develop a parametric OFDM-STAP measurement model by considering the effects of signal-dependent clutter and colored noise. Then, we observe that the resulting STAP performance can be improved by maximizing the output signal-to-interference-plus-noise ratio (SINR) with respect to the signal parameters. However, in practical scenarios, the computation of output SINR depends on the estimated values of the spatial and temporal frequencies and target-scattering responses. Therefore, we formulate a PAPR-constrained multiobjective-optimization problem to design the OFDM spectral parameters by simultaneously optimizing four objective functions: maximizing the output SINR, minimizing two separate Cramér-Rao bounds (CRBs) on the normalized spatial and temporal frequencies, and minimizing the trace of the CRB matrix on the target-scattering coefficient estimations. We present several numerical examples to demonstrate the achieved performance improvement due to the adaptive waveform design.

Low-Rank Matrix Decomposition and Spatio-Temporal Sparse Recovery for STAP Radar

We develop space-time adaptive processing (STAP) methods by leveraging the advantages of sparse signal processing techniques in order to detect a slowly-moving target. We observe that the inherent sparse characteristics of a STAP problem can be formulated as the low-rankness of clutter covariance matrix when compared to the total adaptive degrees-of-freedom, and also as the sparse interference spectrum on the spatio-temporal domain. By exploiting these sparse properties, we propose two approaches for estimating the interference covariance matrix. In the first approach, we consider a constrained matrix rank minimization problem (RMP) to decompose the sample covariance matrix into a low-rank positive semidefinite and a diagonal matrix. The solution of RMP is obtained by applying the trace minimization technique and the singular value decomposition with matrix shrinkage operator. Our second approach deals with the atomic norm minimization problem to recover the clutter response-vector that has a sparse support on the spatio-temporal plane. We use convex relaxation based standard sparse-recovery techniques to find the solutions. With extensive numerical examples, we demonstrate the performances of proposed STAP approaches with respect to both the ideal and practical scenarios, involving Doppler-ambiguous clutter ridges, spatial and temporal decorrelation effects. The low-rank matrix decomposition based solution requires secondary measurements as many as twice the clutter rank to attain a near-ideal STAP performance; whereas the spatio-temporal sparsity based approach needs a considerably small number of secondary data.