Cramer-Rao Bound for Target Localization for Widely Separated MIMO Radar

In this paper, we derive the Cramer-Rao Bounds (CRBs) for the 2-dimensional (2D) target localization and velocity estimations for widely separated Multiple-Input Multiple-Output (MIMO) radar. The transmitters emit signals with different frequencies and the receivers receive these signals with amplitude fluctuations and with Doppler shifts due to the target motion. The received signal model is constructed using the Swerling target fluctuations to take into account the undesired effects of target amplitude and phase fluctuations. Moreover, the time delays and the Doppler frequencies are included in the signal model to get a more realistic model. Then, the Cramer-Rao Bounds are derived for the proposed signal model for the target position and velocity estimations. Contrary to known models of CRBs, we derived the CRBs jointly and using the Swerling target fluctuations

Target localization in MIMO radar systems

MIMO (Multiple-Input Multiple-Output) radar systems employ multiple antennas to transmit multiple waveforms and engage in joint processing of the received echoes from the target. MIMO radar has been receiving increasing attention in recent years from researchers, practitioners, and funding agencies. Elements of MIMO radar have the ability to transmit diverse waveforms ranging from independent to fully correlated. MIMO radar offers a new paradigm for signal processing research. In this dissertation, target localization accuracy performance, attainable by the use of MIMO radar systems, configured with multiple transmit and receive sensors, widely distributed over an area, are studied. The Cramer-Rao lower bound (CRLB) for target localization accuracy is developed for both coherent and noncoherent processing. The CRLB is shown to be inversely proportional to the signal effective bandwidth in the noncoherent case, but is approximately inversely proportional to the carrier frequency in the coherent case. It is shown that optimization over the sensors\u27 positions lowers the CRLB by a factor equal to the product of the number of transmitting and receiving sensors. The best linear unbiased estimator (BLUE) is derived for the MIMO target localization problem. The BLUE\u27s utility is in providing a closed-form localization estimate that facilitates the analysis of the relations between sensors locations, target location, and localization accuracy. Geometric dilution of precision (GDOP) contours are used to map the relative performance accuracy for a given layout of radars over a given geographic area. Coherent processing advantage for target localization relies on time and phase synchronization between transmitting and receiving radars. An analysis of the sensitivity of the localization performance with respect to the variance of phase synchronization error is provided by deriving the hybrid CRLB. The single target case is extended to the evaluation of multiple target localization performance. Thus far, the analysis assumes a stationary target. Study of moving target tracking capabilities is offered through the use of the Bayesian CRLB for the estimation of both target location and velocity. Centralized and decentralized tracking algorithms, inherit to distributed MIMO radar architecture, are proposed and evaluated. It is shown that communication requirements and processing load may be reduced at a relatively low performance cost

Some contributions on MIMO radar

Motivated by recent advances in Multiple Input Multiple Output (MIMO) wireless communications, this dissertation aims at exploring the potential of MIMO approaches in the radar context. In communications, MIMO systems combat the fading effects of the multi-path channel with spatial diversity. Further, the scattering environment can be used by such systems to achieve spatial multiplexing. In radar, a complex target consisting of several scatterers takes the place of the multi-path channel of the communication problem. A target\u27s radar cross section (RCS), which determines the amount of returned power, greatly varies with the considered aspect. Those variations significantly impair the detection and estimation performance of conventional radar employing closely spaced arrays on transmit and receive sides. In contrast, by widely separating the transmit and receive elements, MIMO radar systems observe a target simultaneously from different aspects resulting in spatial diversity. This diversity overcomes the fluctuations in received power. Similar to the multiplexing gain in communications, the simultaneous observation of a target from several perspectives enables resolving its features with an accuracy beyond the one supported by the bandwidth. The dissertation studies the MIMO concept in radar in the following manner. First, angle of arrival estimation is explored for a system applying transmit diversity on the transmit side. Due to the target\u27s RCS fluctuations, the notion of ergodic and outage Cramer Rao bounds is introduced. Both bounds are compared with simulation results revealing the diversity potentials of MIMO radar. Afterwards, the detection of targets in white Gaussian noise is discussed including geometric considerations due to the wide separation between the system elements. The detection performance of MIMO radar is then compared to the one achieved by conventional phased array radar systems. The discussion is extended to include returns from homogeneous clutter. A Doppler processing based moving target detector for MIMO radar is developed in this context. Based on this detector, the moving target detection capabilities of MIMO radar are evaluated and compared to the ones of phased array and multi-static radar systems. It is shown, that MIMO radar is capable of reliably detecting targets moving in an arbitrary direction. The advantage of using several transmitters is illustrated and the constant false alarm rate (CFAR) property of adaptive MIMO moving target detectors is demonstrated. Finally, the high resolution capabilities of MIMO radar are explored. As noted above, the several individual scatterers constituting a target result in its fluctuating RCS. The high resolution mode is aimed at resolving those scatterers. With Cramer Rao bounds and simulation results, it is explored how observing a single isotropic scatterer from several aspects enhances the accuracy of estimating the location of this scatterer. In this context a new, two-dimensional ambiguity function is introduced. This ambiguity function is used to illustrate that several scatterers can be resolved within a conventional resolution cell defined by the bandwidth. The effect of different system parameters on this ambiguity function is discussed

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

Multiple-input Multiple-output Radar Waveform Design Methodologies

Multiple-input multiple-output (MIMO) radar is currently an active area of research. The MIMO techniques have been well studied for communications applications where they offer benefits in multipath fading environments. Partly inspired by these benefits, MIMO techniques are applied to radar and they offer a number of advantages such as improved resolution and sensitivity. It allows the use of transmitting multiple simultaneous waveforms from different phase centers. The employed radar waveform plays a key role in determining the accuracy, resolution, and ambiguity in performing tasks such as determining the target range, velocity, shape, and so on. The excellent performance promised by MIMO radar can be unleashed only by proper waveform design. In this article, a survey on MIMO radar waveform design is presented. The goal of this paper is to elucidate the key concepts of waveform design to encourage further research on this emerging technology.Defence Science Journal, 2013, 63(4), pp.393-401, DOI:http://dx.doi.org/10.14429/dsj.63.253

Target localization in passive and active systems : performance bonds

The main goal of this dissertation is to improve the understanding and to develop ways to predict the performance of localization techniques as a function of signal-to-noise ratio (SNR) and of system parameters. To this end, lower bounds on the maximum likelihood estimator (MLE) performance are studied. The Cramer-Rao lower bound (CRLB) for coherent passive localization of a near-field source is derived. It is shown through the Cramer-Rao bound that, the coherent localization systems can provide high accuracies in localization, to the order of carrier frequency of the observed signal. High accuracies come to a price of having a highly multimodal estimation metric which can lead to sidelobes competing with the mainlobe and engendering ambiguity in the selection of the correct peak. The effect of the sidelobes over the estimator performance at different SNR levels is analyzed and predicted with the use of Ziv-Zakai lower bound (ZZB). Through simulations it is shown that ZZB is tight to the MLEs performance over the whole SNR range. Moreover, the ZZB is a convenient tool to assess the coherent localization performance as a function of various system parameters. The ZZB was also used to derive a lower bound on the MSE of estimating the range and the range rate of a target in active systems. From the expression of the derived lower bound it was noted that, the ZZB is determined by SNR and by the ambiguity function (AF). Thus, the ZZB can serve as an alternative to the ambiguity function (AF) as a tool for radar design. Furthermore, the derivation is extended to the problem of estimating target’s location and velocity in a distributed multiple input multiple output (MIMO) radar system. The derived bound is determined by SNR, by the product between the number of transmitting antennas and the number of receiving antennas from the radar system, and by all the ambiguity functions and the cross-ambiguity functions corresponding to all pairs transmitter-target-receiver. Similar to the coherent localization, the ZZB can be applied to study the performance of the estimator as a function of different system parameters. Comparison between the ZZB and the MSE of the MLE obtained through simulations demonstrate that the bound is tight in all SNR regions

Impairments in ground moving target indicator (GMTI) radar

Radars on multiple distributed airborne or ground based moving platforms are of increasing interest, since they can be deployed in close proximity to the event under investigation and thus offer remarkable sensing opportunities. Ground moving target indicator (GMTI) detects and localizes moving targets in the presence of ground clutter and other interference sources. Space-time adaptive processing (STAP) implemented with antenna arrays has been a classical approach to clutter cancellation in airborne radar. One of the challenges with STAP is that the minimum detectable velocity (MDV) of targets is a function of the baseline of the antenna array: the larger the baseline (i.e., the narrower the beam), the lower the MDV. Unfortunately, increasing the baseline of a uniform linear array (ULA) entails a commensurate increase in the number of elements. An alternative approach to increasing the resolution of a radar, is to use a large, but sparse, random array. The proliferation of relatively inexpensive autonomous sensing vehicles, such as unmanned airborne systems, raises the question whether is it possible to carry out GMTI by distributed airborne platforms. A major obstacle to implementing distributed GMTI is the synchronization of autonomous moving sensors. For range processing, GMTI processing relies on synchronized sampling of the signals received at the array, while STAP processing requires time, frequency and phase synchronization for beamforming and interference cancellation. Distributed sensors have independent oscillators, which are naturally not synchronized and are each subject to different stochastic phase drift. Each sensor has its own local oscillator, unlike a traditional array in which all sensors are connected to the same local oscillator. Even when tuned to the same frequency, phase errors between the sensors will develop over time, due to phase instabilities. These phase errors affect a distributed STAP system. In this dissertation, a distributed STAP application in which sensors are moving autonomously is envisioned. The problems of tracking, detection for our proposed architecture are of important. The first part focuses on developing a direct tracking approach to multiple targets by distributed radar sensors. A challenging scenario of a distributed multi-input multi-output (MIMO) radar system (as shown above), in which relatively simple moving sensors send observations to a fusion center where most of the baseband processing is performed, is presented. The sensors are assumed to maintain time synchronization, but are not phase synchronized. The conventional approach to localization by distributed sensors is to estimate intermediate parameters from the received signals, for example time delay or the angle of arrival. Subsequently, these parameters are used to deduce the location and velocity of the target(s). These classical localization techniques are referred to as indirect localization. Recently, new techniques have been developed capable of estimating target location directly from signal measurements, without an intermediate estimation step. The objective is to develop a direct tracking algorithm for multiple moving targets. It is aimed to develop a direct tracking algorithm of targets state parameters using widely distributed moving sensors for multiple moving targets. Potential candidate for the tracker include Extended Kalman Filter. In the second part of the dissertation,the effect of phase noise on space-time adaptive processing in general, and spatial processing in particular is studied. A power law model is assumed for the phase noise. It is shown that a composite model with several terms is required to properly model the phase noise. It is further shown that the phase noise has almost linear trajectories. The effect of phase noise on spatial processing is analyzed. Simulation results illustrate the effect of phase noise on degrading the performance in terms of beam pattern and receiver operating characteristics. A STAP application, in which spatial processing is performed (together with Doppler processing) over a coherent processing interval, is envisioned