MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Unit Circle Roots Based Sensor Array Signal Processing

As technology continues to rapidly evolve, the presence of sensor arrays and the algorithms processing the data they generate take an ever-increasing role in modern human life. From remote sensing to wireless communications, the importance of sensor signal processing cannot be understated. Capon\u27s pioneering work on minimum variance distortionless response (MVDR) beamforming forms the basis of many modern sensor array signal processing (SASP) algorithms. In 2004, Steinhardt and Guerci proved that the roots of the polynomial corresponding to the optimal MVDR beamformer must lie on the unit circle, but this result was limited to only the MVDR. This dissertation contains a new proof of the unit circle roots property which generalizes to other SASP algorithms. Motivated by this result, a unit circle roots constrained (UCRC) framework for SASP is established and includes MVDR as well as single-input single-output (SISO) and distributed multiple-input multiple-output (MIMO) radar moving target detection. Through extensive simulation examples, it will be shown that the UCRC-based SASP algorithms achieve higher output gains and detection probabilities than their non-UCRC counterparts. Additional robustness to signal contamination and limited secondary data will be shown for the UCRC-based beamforming and target detection applications, respectively

Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case

In \cite{Abramovich04}, it was demonstrated that the likelihood ratio (LR) for multivariate complex Gaussian distribution has the invariance property that can be exploited in many applications. Specifically, the probability density function (p.d.f.) of this LR for the (unknown) actual covariance matrix $\R_{0}$ does not depend on this matrix and is fully specified by the matrix dimension $M$ and the number of independent training samples $T$. Since this p.d.f. could therefore be pre-calculated for any a priori known $(M,T)$, one gets a possibility to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically ``as likely'' as the a priori unknown actual covariance matrix. This ``expected likelihood'' (EL) quality assessment allows for significant improvement of MUSIC DOA estimation performance in the so-called ``threshold area'' \cite{Abramovich04,Abramovich07d}, and for diagonal loading and TVAR model order selection in adaptive detectors \cite{Abramovich07,Abramovich07b}. Recently, a broad class of the so-called complex elliptically symmetric (CES) distributions has been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative of CES, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix \mSigma_{0}. Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario ($T \geq M$) while Part 2 deals with the under-sampled scenario ($T \leq M$)

Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays

Massive MIMO (multiple-input multiple-output) is no longer a "wild" or "promising" concept for future cellular networks - in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequencies - once viewed prohibitively complicated and costly - is well underway. In a few years, Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In this paper, we explain how the first chapter of the Massive MIMO research saga has come to an end, while the story has just begun. The coming wide-scale deployment of BSs with massive antenna arrays opens the door to a brand new world where spatial processing capabilities are omnipresent. In addition to mobile broadband services, the antennas can be used for other communication applications, such as low-power machine-type or ultra-reliable communications, as well as non-communication applications such as radar, sensing and positioning. We outline five new Massive MIMO related research directions: Extremely large aperture arrays, Holographic Massive MIMO, Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive MIMO.Comment: 20 pages, 9 figures, submitted to Digital Signal Processin

Moving Target Parameters Estimation in Non-Coherent MIMO Radar Systems

The problem of estimating the parameters of a moving target in multiple-input multiple-output (MIMO) radar is considered and a new approach for estimating the moving target parameters by making use of the phase information associated with each transmit-receive path is introduced. It is required for this technique that different receive antennas have the same time reference, but no synchronization of initial phases of the receive antennas is needed and, therefore, the estimation process is non-coherent. We model the target motion within a certain processing interval as a polynomial of general order. The first three coefficients of such a polynomial correspond to the initial location, velocity, and acceleration of the target, respectively. A new maximum likelihood (ML) technique for estimating the target motion coefficients is developed. It is shown that the considered ML problem can be interpreted as the classic "overdetermined" nonlinear least-squares problem. The proposed ML estimator requires multi-dimensional search over the unknown polynomial coefficients. The Cram\'er-Rao Bound (CRB) for the proposed parameter estimation problem is derived. The performance of the proposed estimator is validated by simulation results and is shown to achieve the CRB.Comment: 17 pages, 4 figures, Submitted to the IEEE Trans. Signal Processing in Aug. 201

Adaptive OFDM Radar for Target Detection and Tracking

We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing: OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar\u27s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the $ell_1$-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose an tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter

Auto-regressive model based polarimetric adaptive detection scheme part I: Theoretical derivation and performance analysis

This paper deals with the problem of target detection in coherent radar systems exploiting polarimetric diversity. We resort to a parametric approach and we model the disturbance affecting the data as a multi-channel autoregressive (AR) process. Following this model, a new polarimetric adaptive detector is derived, which aims at improving the target detection capability while relaxing the requirements on the training data size and the computational burden with respect to existing solutions. A complete theoretical characterization of the asymptotic performance of the derived detector is provided, using two different target fluctuation models. The effectiveness of the proposed approach is shown against simulated data, in comparison with alternative existing solutions

Subspace Compressive GLRT Detector for MIMO Radar in the Presence of Clutter

The problem of optimising the target detection performance of MIMO radar in the presence of clutter is considered. The increased false alarm rate which is a consequence of the presence of clutter returns is known to seriously degrade the target detection performance of the radar target detector, especially under low SNR conditions. In this paper, a mathematical model is proposed to optimise the target detection performance of a MIMO radar detector in the presence of clutter. The number of samples that are required to be processed by a radar target detector regulates the amount of processing burden while achieving a given detection reliability. While Subspace Compressive GLRT (SSC-GLRT) detector is known to give optimised radar target detection performance with reduced computational complexity, it however suffers a significant deterioration in target detection performance in the presence of clutter. In this paper we provide evidence that the proposed mathematical model for SSC-GLRT detector outperforms the existing detectors in the presence of clutter. The performance analysis of the existing detectors and the proposed SSC-GLRT detector for MIMO radar in the presence of clutter are provided in this paper

Mathematical optimization and game theoretic methods for radar networks

Radar systems are undoubtedly included in the hall of the most momentous discoveries of the previous century. Although radars were initially used for ship and aircraft detection, nowadays these systems are used in highly diverse fields, expanding from civil aviation, marine navigation and air-defence to ocean surveillance, meteorology and medicine. Recent advances in signal processing and the constant development of computational capabilities led to radar systems with impressive surveillance and tracking characteristics but on the other hand the continuous growth of distributed networks made them susceptible to multisource interference. This thesis aims at addressing vulnerabilities of modern radar networks and further improving their characteristics through the design of signal processing algorithms and by utilizing convex optimization and game theoretic methods. In particular, the problems of beamforming, power allocation, jammer avoidance and uncertainty within the context of multiple-input multiple-output (MIMO) radar networks are addressed. In order to improve the beamforming performance of phased-array and MIMO radars employing two-dimensional arrays of antennas, a hybrid two-dimensional Phased-MIMO radar with fully overlapped subarrays is proposed. The work considers both adaptive (convex optimization, CAPON beamformer) and non-adaptive (conventional) beamforming techniques. The transmit, receive and overall beampatterns of the Phased-MIMO model are compared with the respective beampatterns of the phased-array and the MIMO schemes, proving that the hybrid model provides superior capabilities in beamforming. By incorporating game theoretic techniques in the radar field, various vulnerabilities and problems can be investigated. Hence, a game theoretic power allocation scheme is proposed and a Nash equilibrium analysis for a multistatic MIMO network is performed. A network of radars is considered, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since no communication between the clusters is assumed, non-cooperative game theoretic techniques and convex optimization methods are utilized to tackle the power adaptation problem. During the proof of the existence and the uniqueness of the solution, which is also presented, important contributions on the SINR performance and the transmission power of the radars have been derived. Game theory can also been applied to mitigate jammer interference in a radar network. Hence, a competitive power allocation problem for a MIMO radar system in the presence of multiple jammers is investigated. The main objective of the radar network is to minimize the total power emitted by the radars while achieving a specific detection criterion for each of the targets-jammers, while the intelligent jammers have the ability to observe the radar transmission power and consequently decide its jamming power to maximize the interference to the radar system. In this context, convex optimization methods, noncooperative game theoretic techniques and hypothesis testing are incorporated to identify the jammers and to determine the optimal power allocation. Furthermore, a proof of the existence and the uniqueness of the solution is presented. Apart from resource allocation applications, game theory can also address distributed beamforming problems. More specifically, a distributed beamforming and power allocation technique for a radar system in the presence of multiple targets is considered. The primary goal of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Initially, a strategic noncooperative game (SNG) is used, where there is no communication between the various radars of the system. Subsequently, a more coordinated game theoretic approach incorporating a pricing mechanism is adopted. Furthermore, a Stackelberg game is formulated by adding a surveillance radar to the system model, which will play the role of the leader, and thus the remaining radars will be the followers. For each one of these games, a proof of the existence and uniqueness of the solution is presented. In the aforementioned game theoretic applications, the radars are considered to know the exact radar cross section (RCS) parameters of the targets and thus the exact channel gains of all players, which may not be feasible in a real system. Therefore, in the last part of this thesis, uncertainty regarding the channel gains among the radars and the targets is introduced, which originates from the RCS fluctuations of the targets. Bayesian game theory provides a framework to address such problems of incomplete information. Hence, a Bayesian game is proposed, where each radar egotistically maximizes its SINR, under a predefined power constraint