MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods

Secrecy rate optimizations for MIMO communication radar

In this paper, we investigate transmit beampattern optimization techniques for a multiple-input multiple-output (MIMO) radar in the presence of a legitimate communications receiver and an eavesdropping target. The primary objectives of the radar are to satisfy a certain target detection criterion and to simultaneously communicate safely with a legitimate receiver by maximizing the secrecy rate against the eavesdropping target. Therefore, we consider three optimization problems, namely, target return signal to interference plus noise ratio (SINR) maximization, secrecy rate maximization and transmit power minimization. However, these problems are non-convex due to the non-concavity of the secrecy rate function, which appears in all three optimizations either as the objective function or as a constraint. To solve this issue, we use Taylor series approximation of the non-convex elements through an iterative algorithm, which recasts the problem as a convex problem. Two transmit covariance matrices are designed to detect the target and convey the information safely to the communication receiver. Simulation results are presented to validate the efficiency of the aforementioned optimizations

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

Reconfigurable Linear Antenna Arrays for Beam-Pattern Matching in Collocated MIMO Radars

Beam-pattern matching plays an important role in multiple-input multiple-output radars. In the vast majority of research done in this area, the aim is to find the covariance matrix of the waveforms fed into the transmit array. Also, reconfiguring a preset array of antennas (antenna selection), which means turning off some of the antennas in the array, is an effective technique to reach the desired beam patterns, dynamically. In this article, we introduce a novel multistep method to implement this reconfiguration technique to a uniform linear array. In each step, by exploiting the relation between the diagonal elements of a covariance matrix resulted from solving a beam-pattern matching problem and the transmitted power of the antennas, we find the least important antenna of the array and turn it off accordingly. Then, we repeat this process until a predefined number of antennas remains. Our proposed method outperforms its counterparts in the literature in terms of beam-pattern matching as well as computational complexity, which makes it an appropriate method for real-time applications. Simulations are used to show the validity and superiority of the proposed method

Complexity Reduction in Beamforming of Uniform Array Antennas for MIMO Radars

Covariance matrix design and beamforming in multiple-input multiple-output (MIMO) radar systems have always been a time-consuming task with a substantial number of unknown variables in the optimization problem to be solved. Based on the radar and target conditions, beamforming can be a dynamic process and in real-time scenarios, it is critical to have a fast beamforming. In this paper, we propose a beampattern matching design technique that is much faster compared to the well-known traditional semidefinite quadratic programming (SQP) counterpart. We show how to calculate the covariance matrix of the probing transmitted signal to obtain the MIMO radar desired beampattern, using a facilitator library. While the proposed technique inherently satisfies the required practical constraints in covariance matrix design, it significantly reduces the number of unknown variables used in the minimum square error (MSE) optimization problem, and therefore reduces the computational complexity considerably. Simulation results show the superiority of the proposed technique in terms of complexity and speed, compared with existing methods. This superiority is enhanced by increasing the number of antennas

Space-Time Transmit-Receive Design for Colocated MIMO Radar

This chapter deals with the design of multiple input multiple-output (MIMO) radar space-time transmit code (STTC) and space-time receive filter (STRF) to enhance moving targets detection in the presence of signal-dependent interferences, where we assume that some knowledge of target and clutter statistics are available for MIMO radar system according to a cognitive paradigm by using a site-specific (possible dynamic) environment database. Thus, an iterative sequential optimization algorithm with ensuring the convergence is proposed to maximize the signal to interference plus noise ratio (SINR) under the similarity and constant modulus constraints on the probing waveform. In particular, each iteration of the proposed algorithm requires to solve the hidden convex problems. The computational complexity is linear with the number of iterations and polynomial with the sizes of the STTW and the STRF. Finally, the gain and the computation time of the proposed algorithm also compared with the available methods are evaluated

Mathematical optimization techniques for cognitive radar networks

This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise

Robust MIMO Beamforming for Cellular and Radar Coexistence

In this letter, we consider the coexistence and spectrum sharing between downlink multi-user multiple-input-multiple-output (MU-MIMO) communication and an MIMO radar. For a given performance requirement of the downlink communication system, we design the transmit beamforming such that the detection probability of the radar is maximized. While the original optimization problem is non-convex, we exploit the monotonically increasing relationship of the detection probability with the non-centrality parameter of the resulting probability distribution to obtain a convex lower-bound optimization. The proposed beamformer is designed to be robust to imperfect channel state information (CSI). Simulation results verify that the proposed approach facilitates the coexistence between radar and communication links, and illustrates a scalable tradeoff between the two systems' performance