Optimum sparse subarray design for multitask receivers

The problem of optimum sparse array configuration to maximize the beamformer output signal-to-interference plus noise ratio (MaxSINR) in the presence of multiple sources of interest (SOI) has been recently addressed in the literature. In this paper, we consider a shared aperture system where optimum sparse subarrays are allocated to individual SOIs and collectively span the entire full array receiver aperture. Each subarray may have its own antenna type and can comprise a different number of antennas. The optimum joint sparse subarray design for shared aperture based on maximizing the sum of the subarray beamformer SINRs is considered with and without SINR threshold constraints. We utilize Taylor series approximation and sequential convex programming (SCP) techniques to render the initial non-convex optimization a convex problem. The simulation results validate the shared aperture design solutions for MaxSINR for both cases where the number of sparse subarray antennas is predefined or left to comstitute an optimization variable

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

Source enumeration in non-white noise and small sample size via subspace averaging

This paper addresses the problem of source enumeration by an array of sensors in the challenging conditions of: i) large uniform arrays with few snapshots, and ii) non-white or spatially correlated noises with arbitrary correlation. To solve this problem, we combine a subspace averaging (SA) technique, recently proposed for the case of independent and identically distributed (i.i.d.) noises, with a majority vote approach. The number of sources is detected for increasing dimensions of the SA technique and then a majority vote is applied to determine the final estimate. As illustrated by some simulation examples, this simple modification makes SA a very robust method of enumerating sources in these challenging scenarios.This work was supported by the Ministerio de Economía y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2016-75067-C4-4-R (CARMEN) and BES-2017-080542

Multi-Step Knowledge-Aided Iterative ESPRIT for Direction Finding

In this work, we propose a subspace-based algorithm for DOA estimation which iteratively reduces the disturbance factors of the estimated data covariance matrix and incorporates prior knowledge which is gradually obtained on line. An analysis of the MSE of the reshaped data covariance matrix is carried out along with comparisons between computational complexities of the proposed and existing algorithms. Simulations focusing on closely-spaced sources, where they are uncorrelated and correlated, illustrate the improvements achieved.Comment: 7 figures. arXiv admin note: text overlap with arXiv:1703.1052

Subspace-based order estimation techniques in massive MIMO

Order estimation, also known as source enumeration, is a classical problem in array signal processing which consists in estimating the number of signals received by an array of sensors. In the last decades, numerous approaches to this problem have been proposed. However, the need of working with large-scale arrays (like in massive MIMO systems), low signal-to-noise- ratios, and poor sample regime scenarios, introduce new challenges to order estimation problems. For instance, most of the classical approaches are based on information theoretic criteria, which usually require a large sample size, typically several times larger than the number of sensors. Obtaining a number of samples several times larger than the number of sensors is not always possible with large-scale arrays. In addition, most of the methods found in literature assume that the noise is spatially white, which is very restrictive for many practical scenarios. This dissertation deals with the problem of source enumeration for large-scale arrays, and proposes solutions that work robustly in the small sample regime under various noise models. The first part of the dissertation solves the problem by applying the idea of subspace averaging. The input data are modelled as subspaces, and an average or central subspace is computed. The source enumeration problem can be seen as an estimation of the dimension of the central subspace. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. The proposed SA criterion is especially effective in high-dimensional scenarios with low sample support for uniform linear arrays in the presence of white noise. Further, the proposed SA method is extended for: i) non-white noises, and ii) non-uniform linear arrays. The SA criterion is sensitive with the chosen dimension of extracted subspaces. To solve this problem, we combine the SA technique with a majority vote approach. The number of sources is detected for increasing dimensions of the SA technique and then a majority vote is applied to determine the final estimate. Further, to extend SA for arrays with arbitrary geometries, the SA is combined with a sparse reconstruction (SR) step. In the first step, each received snapshot is approximated by a sparse linear combination of the rest of snapshots. The SR problem is regularized by the logarithm-based surrogate of the l-0 norm and solved using a majorization-minimization approach. Based on the SR solution, a sampling mechanism is proposed in the second step to generate a collection of subspaces, all of which approximately span the same signal subspace. Finally, the dimension of the average of this collection of subspaces provides a robust estimate for the number of sources. The second half of the dissertation introduces a completely different approach to the order estimation for uniform linear arrays, which is based on matrix completion algorithms. This part first discusses the problem of order estimation in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. The proposed method performs robustly for both small and large-scale arrays with few snapshots. Finally, an approach to work with a reduced number of radio–frequency (RF) chains is proposed. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low- rank structure of the signal subspace, but also the shift-invariance property of uniform linear arrays, which results in a better estimation of the signal subspace. In addition, the effect of MC on DOA estimation is discussed under the perturbation theory framework. Further, this approach is extended to devise a novel order estimation criterion for missing data scenario. The proposed source enumeration criterion is based on the chordal subspace distance between two sub-matrices extracted from the reconstructed matrix after using MC for increasing rank values. We show that the proposed order estimation criterion performs consistently with a very few available entries in the data matrix.This work was supported by the Ministerio de Ciencia e Innovación (MICINN) of Spain, under grants TEC2016-75067-C4-4-R (CARMEN) and BES-2017-080542