Multiple-input multiple-output (MIMO) radar employs orthogonal or partially correlated transmit signals to achieve performance benefits over its phased-array counterpart. It has been shown that MIMO radar can achieve greater spatial resolution, improved signal-to-noise ratio (SNR) and target localization, and greater clutter resolution using space-time adaptive processing (STAP). This thesis explores various methods to improve the signal-to-interference-plus-noise ratio (SINR) via transmit and receive beamforming. In MIMO radar settings, it is often desirable to transmit power only to a given location or set of locations defined by a beampattern. Current methods involve a two- step process of designing the transmit covariance matrix R via iterative solutions and then using R to generate waveforms that fulfill practical constraints such as having a constant-envelope or drawing from a finite alphabet. In this document, a closed- form method to design R is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniform elemental power constraint and provides performance similar to that of iterative methods, which require a much greater computation time. Next, a transmit architecture is presented 
that exploits the orthogonality of frequencies at discrete DFT values to transmit a sum of orthogonal signals from each antenna. The resulting waveforms provide a lower mean-square error than current methods at a much lower computational cost, and a simulated detection scenario demonstrates the performance advantages achieved. It is also desirable to receive signal power only from a given set of directions defined by a beampattern. In a later chapter of this document, the problem of receive beampattern matching is formulated and three solutions to this problem are demonstrated. We show that partitioning the received data vector into subvectors and then multiplying each subvector with its corresponding weight vector can improve performance and reduce the length of the data vector. Simulation results show that all methods are capable of matching a desired beampattern. Signal-to-interference- plus-noise ratio (SINR) calculations demonstrate a significant improvement over the unaltered MIMO case.

Multiple Input Multiple Output (MIMO) radar systems has attracted lately a lot of attention thanks to its advantage over the classical phased array radar systems. We site among these advantages the improvement of parametric identifiability, achievement of higher spatial resolution and design of complex beampatterns. In colocated multiple-input multiple-output radar systems, it is usually desirable to steer transmitted power in the region-of-interest in order to increase the Signal to Noise Ratio (SNR) and reduce any undesired signal and thus improve the detection process. This problem is also known as transmit beampattern design. To achieve this goal, conventional methods optimize the waveform covariance matrix, R, for the desired beampattern, which is then used to generate the actual transmitted waveforms. Both steps require constrained optimization. Most of the existing methods use iterative algorithms to solve these problems, therefore their computational complexity is very high which makes them hard to use in practice especially for real time radar applications. In this paper, we provide a closed-form solution to design the covariance matrix for a given beampattern in the three dimensional space using planar arrays, which is then used to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope waveforms. The proposed algorithm exploits the two-dimensional discrete Fourier transform which is implemented using fast Fourier transform algorithm. Consequently, the computational complexity of the proposed beampattern solution is very low allowing it to be used for large arrays to change the beampattern in real time. We also show that the number of required snapshots in each waveform depends on the beampattern and that it is less than the total number of transmit antennas. In addition, we show that the proposed waveform design method can be used with non symmetric beampatterns. The performance of our proposed algorithm compares favorably with the existing iterative methods in terms of mean square error.

Multiple-input multiple-output (MIMO) radar has been receiving increasing attention in recent years due to the dramatic advantages offered by MIMO systems in communications. The amount of energy reflected from a common radar target varies considerably with the observation angle, and these scintillations may cause signal fading which severely degrades the performance of conventional radars. MIMO radar with widely spaced antennas is able to view several aspects of a target simultaneously, which realizes a spatial diversity gain to overcome the target scintillation problem, leading to significantly enhanced system performance. Building on the initial studies presented in the literature, MIMO radar is investigated in detail in this thesis. First of all, a finite scatterers model is proposed, based on which the target detection performance of a MIMO radar system with arbitrary array-target configurations is evaluated and analyzed. A MIMO radar involving a realistic target is also set up, whose simulation results corroborate the conclusions drawn based on theoretical target models, validating in a practical setting the improvements in detection performance brought in by the MIMO radar configuration. Next, a hybrid bistatic radar is introduced, which combines the phased-array and MIMO radar configurations to take advantage of both coherent processing gain and spatial diversity gain simultaneously. The target detection performance is first assessed, followed by the evaluation of the direction finding performance, i.e., performance of estimating angle of arrival as well as angel of departure. The presented theoretical expressions can be used to select the best architecture for a radar system, particularly when the total number of antennas is fixed. Finally, a novel two phase radar scheme involving signal retransmission is studied. It is based on the time-reversal (TR) detection and is investigated to improve the detection performance of a wideband MIMO radar or sonar system. Three detectors demanding various amounts of a priori information are developed, whose performance is evaluated and compared. Three schemes are proposed to design the retransmitted waveform with constraints on the transmitted signal power, further enhancing the detection performance with respect to the TR approach.

La localisation active et passive par un réseau de capteurs distribués est un problème rencontré dans différents domaines d’application. En localisation active, telle que la localisation par radar MIMO (Multiple Input Multiple Output), les émetteurs transmettent des signaux qui sont réfléchis par les cibles visées, puis captés par les antennes réceptrices, alors qu’en localisation passive, les capteurs reçoivent des signaux transmis par les cibles elles-mêmes. L’objectif de cette thèse est d’étudier différentes techniques d’optimisation pour la localisation active et passive de haute précision. Dans la première partie de la thèse, on s’intéresse à la localisation active, où de multiples émetteurs illuminent les cibles depuis différentes directions. Les signaux peuvent être émis avec des puissances ou des largeurs de bande différentes. Ces différentes ressources, par nature en général fortement limitées, sont souvent, par défaut, réparties de façon uniforme entre les différents émetteurs. Or, la précision de la localisation dépend de la position des émetteurs, ainsi que des paramètres (les gains notamment) des différents canaux existant entre émetteurs, cibles, et capteurs. En utilisant comme critère d’optimisation la borne de Cramér-Rao sur la précision de la localisation de cibles multiples, nous proposons une méthode fournissant des solutions approchées aux problèmes d’allocation optimale de puissances seules, de largeurs de bande seules, ou au problème d’allocation conjointe de puissances et de largeurs de bande. Ces solutions sont obtenues en minimisant une suite de problèmes convexes. La qualité de ces solutions approchées est évaluée au travers de nombreuses simulations numériques, mais également par la comparaison avec une borne inférieure définie comme la solution d’un problème d’optimisation avec contraintes relaxées, cette borne pouvant être calculée de façon exacte (numériquement). Cette comparaison permet de constater la proximité de la solution approchée fournie par l’algorithme proposé par rapport à la solution théorique. D’autre part, les simulations ont montré que l’allocation de bande joue un rôle plus important dans les performances de localisation que l’allocation de puissance. Dans la seconde partie de la thèse, on considère le cas de la localisation passive de sources multiples dans un environnement multi-trajet. Ce problème se rencontre notamment dans le cadre de la géolocalisation indoor ou outdoor. Dans ce cas de figure, les approches généralement proposées dans la littérature sont basées sur une méthode ad-hoc de réduction d’interférence couplée à une localisation indirecte obtenue par une estimation de paramètres comme les temps d’arrivée des signaux ou les différences de temps d’arrivée, ou la puissance des signaux reçus. Cependant, les performances de ces approches sont limitées, notamment par le fait que la localisation indirecte d’une cible donnée ne prend pas en compte le fait que les signaux reçus par les différents capteurs émanent d’une seule et même source. Dans cette thèse, nous proposons une modélisation parcimonieuse des signaux reçus. Cette modélisation nous permet, en supposant les formes d’onde connues mais les canaux multi-trajets totalement inconnus, de développer une méthode de localisation directe de l’ensemble des cibles. Cette approche exploite certaines propriétés des canaux, qui permettent de séparer les trajets directs des trajets indirects. Un algorithme d’optimisation conique de second ordre est développé afin d’obtenir une décomposition dite atomique optimale, qui permet d’obtenir une localisation de très bonne précision dans des conditions de propagation difficiles, présentant un phénomène de multi-trajet important et/ou une absence de trajets directs. / Active and passive localization employing widely distributed sensors is a problem of interest in various fields. In active localization, such as in MIMO radar, transmitters emit signals that are reflected by the targets and collected by the receive sensors, whereas, in passive localization the sensors collect the signals emitted by the sources themselves. This dissertation studies optimization methods for high precision active and passive localization. In the case of active localization, multiple transmit elements illuminate the targets from different directions. The signals emitted by the transmitters may differ in power and bandwidth. Such resources are often limited and distributed uniformly among the transmitters. However, previous studies based on the well known Crámer-Rao lower bound have shown that the localization accuracy depends on the locations of the transmitters as well as the individual channel gains between different transmitters, targets and receivers. Thus, it is natural to ask whether localization accuracy may be improved by judiciously allocating such limited resources among the transmitters. Using the Crámer-Rao lower bound for target localization of multiple targets as a figure of merit, approximate solutions are proposed to the problems of optimal power, optimal bandwidth and optimal joint power and bandwidth allocation. These solutions are computed by minimizing a sequence of convex problems. The quality of these solutions is assessed through extensive numerical simulations and with the help of a lower-bound that certifies their optimality. Simulation results reveal that bandwidth allocation policies have a stronger impact on performance than power. Passive localization of radio frequency sources over multipath channels is a difficult problem arising in applications such as outdoor or indoor geolocation. Common approaches that combine ad-hoc methods for multipath mitigation with indirect localization relying on intermediary parameters such as time-of-arrivals, time difference of arrivals or received signal strengths, are unsatisfactory. This dissertation models the localization of known waveforms over unknown multipath channels in a sparse framework, and develops a direct approach in which multiple sources are localized jointly, directly from observations obtained at distributed sources. The proposed approach exploits channel properties that enable to distinguish line-of-sight (LOS) from non-LOS signal paths. Theoretical guarantees are established for correct recovery of the sources’ locations by atomic norm minimization. A second-order-cone-based algorithm is developed to produce the optimal atomic decomposition, and it is shown to produce high accuracy location estimates over complex scenes, in which sources are subject to diverse multipath conditions, including lack of LOS.

The topic of multiple input multiple output (MIMO) radar recently gained considerable interest because it can transmit partially correlated or fully independent waveforms. The inherited waveform diversity helps MIMO radars identify more targets and adds flexibility to the beampattern design. The realized advantages come at the expense of enhanced processing requirements and increased system complexity. In this regards, a closed-form method is derived to generate practical finite-alphabet waveforms with specific correlation properties to match the desired beampattern. Next, the performance of adaptive estimation techniques is examined. Indeed, target localization or reflection coefficient estimation usually involves optimizing a given cost-function over a grid of points. The estimation performance is directly affected by the grid resolution. In this work, the cost function of Capon and amplitude and phase estimation (APES) adaptive beamformers are reformulated. The new cost functions can be evaluated using the two-dimensional fast-Fourier-transform (2D-FFT) which reduces the estimation runtime. Generalized expressions of the Cram´er-Rao lower bound are computed to assess the performance of our estimators. Afterward, a novel estimation algorithm based on the monopulse technique is proposed. In comparison with adaptive methods, monopulse requires less number of received pulses. Hence, it is widely used for fast target localization and tracking purposes. This work suggests an approach that localizes two point targets present in the hemisphere using one set of four antennas. To separate targets sharing the same elevation or azimuth angles, a second set of antennas is required. Two solutions are suggested to combine the outputs from the antenna sets and improve the overall detection performance. The last part of the dissertation focuses on the application and implementation side of radars rather than the theoretical aspects. It describes the realized hardware and software design of a compact portable 24 GHz frequency-modulated-continuous-wave (FMCW) radar. The prototype can assist the visually impaired during their outdoor journeys and prevents collisions with their surrounding environment. Moreover, the device performs diverse tasks such as range-direction mapping, velocity estimation, presence detection, and vital sign monitoring. The experimental result section demonstrates the device’s capabilities in different use-cases.

Radio frequency spectrum is a scarce natural resource that is utilized for many services including surveillance, navigation, communication, and broadcasting. Recent years have seen tremendous growth in use of spectrum especially by commercial cellular operators. As a result, cellular operators are experiencing a shortage of radio spectrum to meet bandwidth demands of users. Spectrum sharing is a promising approach to solve the problem of spectrum congestion as it allows cellular operators access to more spectrum in order to satisfy the ever growing bandwidth demands of commercial users. The US spectrum regulatory bodies are working on an initiative to share 150 MHz of spectrum, held by federal agencies, in the 3.5 GHz band with commercial wireless operators. This band is primarily used by radar systems that are critical to national defense. Field tests have shown that spectrum sharing between radars and communication systems require large separation distance in order to protect them from harmful interference. Thus, novel methods are required to ensure spectrum sharing between the two systems without the need of large protection distances. In order to efficiently share spectrum between radars and communication systems at the same time and in the same geographical area, a novel method is proposed that transforms radar signal in such a way that it does not interfere with communication systems. This is accomplished by projecting the radar signal onto null space of the wireless channel between radar and communication system. In order to understand the effects of the proposed sharing mechanism -- in urban, sub-urban, and littoral areas -- new channel models, specifically, two- and three-dimensional channel models are designed that capture azimuth and elevation angles of communication systems and helps in placing accurate nulls. In addition, interference coming from communication systems into radar receivers is analyzed and radar performance is accessed. Using this information, resource allocation schemes are designed for communication systems that take advantage of the carrier aggregation feature of the LTE-Advanced systems. This further helps in dynamic sharing of spectrum between radars and communication systems. The proposed signal projection approach not only meets radar objectives but also meets spectrum sharing objectives. However, there is a trade-off as signal projection results in some performance degradation for radars. Performance metrics such as probability of target detection, Cramer Rao bound and maximum likelihood estimate of target's angle of arrival, and beampattern of radar are studied for performance degradation. The results show minimal degradation in radar performance and reduction in exclusion zones, thus, showing the efficacy of the proposed approach. / Ph. D.

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