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

Transmit Signal Design for MIMO Radar and Massive MIMO Channel Estimation

The widespread availability of antenna arrays and the capability to independently control signal emissions from each antenna make transmit signal design increasingly important for radar and wireless communication systems. In the rst part of this work, we develop the framework for a MIMO radar transmit scheme which trades o waveform diversity for beampattern directivity. Time-division beamforming consists of a linear precoder that provides direct control of the transmit beampattern and is able to form multiple transmit beams in a single pulse. The MIMO receive ambiguity function, which incorporates the receiver structure, reveals a space and delay-Doppler separability that emphasizes the importance of the transmit-receive beampattern and single-input single-output (SISO) ambiguity function. The second part of this work focuses on channel estimation for massive MIMO systems. As the size of arrays increase, conventional channel estimation techniques no longer remain practical. In current systems, training sequences probe wireless channels in orthogonal directions to obtain channel state information for block fading channels. The training overhead becomes signicant as the number of transmit antennas increases, thereby creating a need for alternative channel estimation techniques. In this work, we relax the orthogonal restriction on the sounding vectors and introduce a feedback channel to enable closed-loop sounding vector design. A probability of misalignment framework is introduced, which provides a measure to sequentially design sounding vectors

Beamforming Design for the Distributed RISs-aided THz Communications with Double-Layer True Time Delays

In this paper, we investigate the reconfigurable intelligent surface (RIS)-aided terahertz (THz) communication system with the sparse radio frequency chains antenna structure at the base station (BS). To overcome the beam split of the BS, different from the conventional single-layer true-time-delay (TTD) scheme, we propose a double-layer TTD scheme that can effectively reduce the number of large-range delay devices, which involve additional insertion loss and amplification circuitry. Next, we analyze the system performance under the proposed double-layer TTD scheme. To relieve the beam split of the RIS, we consider multiple distributed RISs to replace an ultra-large size RIS. Based on this, we formulate an achievable rate maximization problem for the distributed RISs-aided THz communications via jointly optimizing the hybrid analog/digital beamforming, time delays of the double-layer TTD network and reflection coefficients of RISs. Considering the practical hardware limitation, the finite-resolution phase shift, time delay and reflection phase are constrained. To solve the formulated problem, we first design an analog beamforming scheme including optimizing phase shift and time delay based on the RISs' locations. Then, an alternatively optimization algorithm is proposed to obtain the digital beamforming and reflection coefficients based on the minimum mean square error and coordinate update techniques. Finally, simulation results show the effectiveness of the proposed scheme

Adaptive Illumination Patterns for Radar Applications

The fundamental goal of Fully Adaptive Radar (FAR) involves full exploitation of the joint, synergistic adaptivity of the radar\u27s transmitter and receiver. Little work has been done to exploit the joint space time Degrees-of-Freedom (DOF) available via an Active Electronically Steered Array (AESA) during the radar\u27s transmit illumination cycle. This research introduces Adaptive Illumination Patterns (AIP) as a means for exploiting this previously untapped transmit DOF. This research investigates ways to mitigate clutter interference effects by adapting the illumination pattern on transmit. Two types of illumination pattern adaptivity were explored, termed Space Time Illumination Patterns (STIP) and Scene Adaptive Illumination Patterns (SAIP). Using clairvoyant knowledge, STIP demonstrates the ability to remove sidelobe clutter at user specified Doppler frequencies, resulting in optimum receiver performance using a non-adaptive receive processor. Using available database knowledge, SAIP demonstrated the ability to reduce training data heterogeneity in dense target environments, thereby greatly improving the minimum discernable velocity achieved through STAP processing

Three-Dimensional Target Localization and Cramér-Rao Bound for Two-Dimensional OFDM-MIMO Radar

Target localization using a frequency diversity multiple-input multiple-output (MIMO) system is one of the hottest research directions in the radar society. In this paper, three-dimensional (3D) target localization is considered for two-dimensional MIMO radar with orthogonal frequency division multiplexing linear frequency modulated (OFDM-LFM) waveforms. To realize joint estimation for range and angle in azimuth and elevation, the range-angle-dependent beam pattern with high range resolution is produced by the OFDM-LFM waveform. Then, the 3D target localization proposal is presented and the corresponding closed-form expressions of Cramér-Rao bound (CRB) are derived. Furthermore, for mitigating the coupling of angle and range and further improving the estimation precision, a CRB optimization method is proposed. Different from the existing methods of FDA-based radar, the proposed method can provide higher range estimation because of multiple transmitted frequency bands. Numerical simulation results are provided to demonstrate the effectiveness of the proposed approach and its improved performance of target localization

Applying Deep Learning for Phase-Array Antenna Design

Master of Engineering (Electrical Engineering), 2021Hybrid beamforming (HBF) can provide rapid data transmission rates while reducing the complexity and cost of massive multiple-input multiple-output (MIMO) systems. However, channel state information (CSI) is imperfect in realistic downlink channels, introducing challenges to hybrid beamforming (HBF) design. For HBF designs, we had a hard time finding the proper labels. If we use the optimized output based on the traditional algorithm as the label, the neural network can only be trained to approximate the traditional algorithm, but not better than the traditional algorithm. This thesis proposes a hybrid beamforming neural network based on unsupervised deep learning (USDNN) to prevent the labeling overhead of supervised learning and improve the achievable sum rate based on imperfect CSI. Compared with the traditional HBF method, the unsupervised learning-based method can avoid the labeling overhead as well as obtain better performance than the traditional algorithm. The network consists of 5 dense layers, 4 batch normalization (BN) layers and 5 activation functions. After training, the optimized beamformer can be obtained, and the optimized beamforming vector can be directly output. The simulation results show that our proposed method is 74% better than manifold optimization (MO) and 120% better than orthogonal match pursuit (OMP) systems. Furthermore, our proposed USDNN can achieve near-optimal performance