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When uncorrelated signals are incident on a uniform linear array, the array covariance matrix is of the Toeplitz form. An adaptive beamforming method is proposed based on the signal-plus-interference (SI) subspace via the Toeplitz rectification of the sample matrix. The rectified matrix is shown to be more accurate in a norm sense than the modified matrix according to the centro-Hermitian property. Since the former also is centro-Hermitian we can efficiently obtain its eigen-decomposition from a real matrix and then the weight vector in the estimated SI subspace. The proposed method, showing robustness to pointing errors, is not only computationally efficient but also very quickly converges to the optimum performance as demonstrated in the simulation.

In this article, the problem of Bayesian detecting rank-one distributed targets under subspace interference and compound Gaussian clutter with inverse Gaussian texture is investigated. Due to the clutter heterogeneity, the training data may be insufficient. To tackle this problem, the clutter speckle covariance matrix (CM) is assumed to obey the complex inverse Wishart distribution, and the Bayesian theory is utilized to obtain an effective estimation. Moreover, the target echo is assumed to be with a known steering vector and unknown amplitudes across range cells. The interference is regarded as a steering matrix that is linearly independent of the target steering vector. By utilizing the generalized likelihood ratio test (GLRT), a Bayesian interference-canceling detector that can work in the absence of training data is derived. Moreover, five interference-cancelling detectors based on the maximum a posteriori (MAP) estimate of the speckle CM are proposed with the two-step GLRT, the Rao, Wald, Gradient, and Durbin tests. Experiments with simulated and measured sea clutter data indicate that the Bayesian interference-canceling detectors show better performance than the competitor in scenarios with limited training data.

The conventional Wiener–Hopf beamformer is subject to substantial performance degradation in the presence of steering vector pointing errors. By removing the effects of the desired signal, the modified Wiener–Hopf beamformer avoids this problem but allows cochannel interferences to pass through in order to maximise the signal-to-noise ratio. In this study, a novel array beamformer is proposed, which not only reduces the effect of pointing errors, but also asymptotically provides complete interference rejection. In particular, the proposed beamformer utilises a vector space projection method and employs a one-step computation for the desired signal power. Using this, the effects of the desired signal can be extracted to form the desired-signal-absent covariance matrix. Thus, a weight vector orthogonal with the interference subspace can be constructed. Numerical results demonstrate the superior performance of the proposed beamformer in the presence of pointing errors relative to other existing approaches such as ‘diagonal loading’, ‘robust Capon’ and ‘signal subspace projection’ beamformers.

This paper studies adaptive radar detection of a subspace signal embedded in two disturbance sources. The former is thermal noise with known power. The latter is a Gaussian subspace interference with zero mean and unknown covariance matrix (CM). It is assumed that the signal and interference subspaces are known and partially related. As customary, several secondary data containing only interference and thermal noise are used to estimate this interference CM. This paper derives the generalized likelihood ratio test (GLRT), and theoretically deduces the probabilities of false alarm (PFA) and detection of the new detector. This PFA shows that the new detector has the constant false alarm rate (CFAR) property against the interference CM. Several numerical experiments are performed to evaluate the detection performance of the new detector. The results show that the performance of the new detector is better than the natural counterparts in some scenarios.

When the training snapshots are contaminated by the desired signal, the performance of the orthogonal projection (OP) approach degrades significantly. Therefore, an improved OP adaptive beamforming is proposed by reconstructing interference covariance matrix to eliminate the desired signal cancellation effect. In the proposed method, by integrating the Capon spatial spectrum over a region separated from the desired signal direction, the interference-plus-noise covariance matrix is reconstructed first to remove the desired signal component from the sample covariance matrix. Subsequently, the interference subspace is estimated by eigenvalue decomposition, and then the adaptive weight vector is calculated using the OP algorithm to eliminate the noise perturbation. Simulation results show that the performance of the proposed algorithm is almost the same as the optimum beamforming.

Adaptive detection of distributed radar targets in homogeneous Gaussian noise plus subspace interference is addressed. It is assumed that the actual steering vectors lie along a fixed and unknown direction of a preassigned and known subspace, while interfering signals are supposed to belong to an unknown subspace, with directions possibly varying from one resolution cell to another. The resulting detection problem is formulated in the framework of statistical hypothesis testing and solved using an ad hoc algorithm strongly related to the generalised likelihood ratio test. A performance analysis, carried out also in comparison to natural benchmarks, is presented.

The performance of location-based services provided by global navigation satellite systems is compromised by interference and multipath propagations. Although time/frequency interference suppression methods have been widely studied in the literature, they fail to cope with wideband interference signals. Instead, techniques utilising several antenna elements can be employed to mitigate both narrowband and broadband interference signals. However, the performance of beamforming techniques utilising antenna arrays severely degrades in dealing with correlated and coherent multipath components which cause signal cancellation phenomenon and temporal correlation matrix rank deficiency. This study proposes a two-stage beamformer to jointly deal with interference and multipath signals. In the first stage, before the despreading process, by applying the subspace method, the interference subspace is estimated and used as a constraint for the optimisation problem in the next stage. In the second stage, a modified version of the minimum power distortionless response beamformer employing several overlapping sub-arrays called the minimum difference output power method is utilised to mitigate the correlated multipath components. The proposed beamformer can deal with the signal cancellation phenomenon and temporal correlation matrix rank deficiency. Several simulation examples and a real data test are provided to illustrate the effectiveness of the proposed beamformer. Results show that the proposed method is able to put deep nulls in the direction of the narrowband and wideband interference signals, and significantly reduces the multipath-induced time of the arrival error.

In this study, the authors propose a novel blind adaptive minor subspace tracking interference alignment (BAMST-IA) scheme for slowly fading two-way interference channel. In this scheme, a new frame structure is designed to exploit the dependency of the channels between consecutive fading blocks. Then, the IA problem is reformulated as a minor subspace tracking problem, and the low computational complexity fast data projection method algorithm is integrated with the BAMST-IA scheme to update the IA solutions. Moreover, the update uses only observed data without any channel state information, thus requires lower signalling overhead. Simulation results are presented to show that the proposed BAMST-IA scheme is fit for slowly fading channels.

It has long been recognized that atomic emission of radiation is not an immutable property of an atom, but is instead dependent on the electromagnetic environment 1 and, in the case of ensembles, also on the collective interactions between the atoms 2 – 6 . In an open radiative environment, the hallmark of collective interactions is enhanced spontaneous emission—super-radiance 2 —with non-dissipative dynamics largely obscured by rapid atomic decay 7 . Here we observe the dynamical exchange of excitations between a single artificial atom and an entangled collective state of an atomic array 9 through the precise positioning of artificial atoms realized as superconducting qubits 8 along a one-dimensional waveguide. This collective state is dark, trapping radiation and creating a cavity-like system with artificial atoms acting as resonant mirrors in the otherwise open waveguide. The emergent atom–cavity system is shown to have a large interaction-to-dissipation ratio (cooperativity exceeding 100), reaching the regime of strong coupling, in which coherent interactions dominate dissipative and decoherence effects. Achieving strong coupling with interacting qubits in an open waveguide provides a means of synthesizing multi-photon dark states with high efficiency and paves the way for exploiting correlated dissipation and decoherence-free subspaces of quantum emitter arrays at the many-body level 10 – 13 . An array of superconducting qubits in an open one-dimensional waveguide is precisely controlled to create an artificial quantum cavity–atom system that reaches the strong-coupling regime without substantial decoherence.

A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal distortion. However, most current methods for estimating the dimension threshold rely on experience, such as observing the signal waveforms and spectrum, which may render the results too subjective and lacking in quantitative accuracy. Therefore, this study proposes a method to automatically estimate a suitable threshold. Time–frequency transformations are performed on the evoked state data to obtain the neural signal of interest and the noise signal in a specific time–frequency band, which are then used to construct the objective function describing the degree of noise suppression and signal distortion. The optimal value of the threshold in the selected range is obtained using the weighted-sum method. Our method was tested on two classical subspace projection algorithms using simulation and two sensory stimulation experiments. The thresholds estimated by the proposed method enabled the algorithms to achieve the best waveform recovery and source location error. Therefore, the threshold selected in this method enables subspace projection algorithms to achieve the best balance between noise removal and neural signal preservation in subsequent MEG analyses.