In this paper, the focus is on the gain and phase calibration of sparse sensor arrays to localize more sources than the number of physical sensors. The proposed technique is a blind calibration method as it does not require any calibrator sources. Joint estimation of the gain errors, phase errors, and source directions is a complicated non-convex optimization problem, which is transformed into a convex optimization problem by exploiting the underlying algebraic structure. It is shown that the developed solver is suitable for analog as well as one-bit measurements. Numerical experiments based on sparse rulers are provided to illustrate the developed theory.

Orthogonal signal-division multiplexing (OSDM) is a promising modulation scheme that provides a generalized framework to unify orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-domain equalization. By partitioning each data block into vectors, it allows for a flexible configuration to trade off resource management flexibility with peak-to-average power ratio. In this paper, an OSDM system is proposed for underwater acoustic communications. The channel Doppler effect after front-end resampling is modeled as a common time-varying phase on all propagation paths. It leads to a special signal distortion structure in the OSDM system, namely, intervector interference, which is analogous to the intercarrier interference in the conventional OFDM system. To counteract the related performance degradation, the OSDM receiver performs iterative detection, integrating joint channel impulse response and phase estimation, equalization, and decoding in a loop. Meanwhile, to avoid inversion of large matrices in channel equalization, frequency-domain per-vector equalization is designed, which can significantly reduce the computational complexity. Furthermore, the performance of the proposed OSDM system is evaluated through both numerical simulations and a field experiment, and its reliability over underwater acoustic channels is confirmed.

Multiple-input multiple-output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. Although higher angular resolution, improved parameter identifiability, and better target detection are achieved, the hardware costs (due to multiple transmitters and multiple receivers) and high-energy consumption (multiple pulses) limit the usage of MIMO radars in large scale networks. On one hand, higher angle and velocity estimation accuracy is required, but on the other hand, a lower number of antennas/pulses is desirable. To achieve such a compromise, in this paper, the Cramér-Rao lower bound (CRLB) for the angle and velocity estimator is employed as a performance metric to design the antenna and the pulse placement. It is shown that the CRLB derived for two targets is a more appropriate criterion in comparison with the single-target CRLB since the two-target CRLB takes into account both the mainlobe width and the sidelobe level of the ambiguity function. In this paper, several algorithms for antenna and pulse selection based on convex and submodular optimization are proposed. Numerical experiments are provided to illustrate the developed theory.

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multiantenna communications to graph signal processing, to validate the developed theory.

In large-scale wireless acoustic sensor networks (WASNs), many of the sensors will only have a marginal contribution to a certain estimation task. Involving all sensors increases the energy budget unnecessarily and decreases the lifetime of the WASN. Using microphone subset selection, also termed as sensor selection, the most informative sensors can be chosen from a set of candidate sensors to achieve a prescribed inference performance. In this paper, we consider microphone subset selection for minimum variance distortionless response (MVDR) beamformer based noise reduction. The best subset of sensors is determined by minimizing the transmission cost while constraining the output noise power (or signal-to-noise ratio). Assuming the statistical information on correlation matrices of the sensor measurements is available, the sensor selection problem for this model-driven scheme is first solved by utilizing convex optimization techniques. In addition, to avoid estimating the statistics related to all the candidate sensors beforehand, we also propose a data-driven approach to select the best subset using a greedy strategy. The performance of the greedy algorithm converges to that of the model-driven method, while it displays advantages in dynamic scenarios as well as on computational complexity. Compared to a sparse MVDR or radius-based beamformer, experiments show that the proposed methods can guarantee the desired performance with significantly less transmission costs.

An analytical algebraic approach for distributed network identification is presented in this paper. The information propagation in the network is modeled using a state-space representation. Using the observations recorded at a single node and a known excitation signal, we present algorithms to compute the eigenfrequencies and eigenmodes of the graph in a distributed manner. The eigenfrequencies of the graph may be computed using a generalized eigenvalue algorithm, while the eigenmodes can be computed using an eigenvalue decomposition. The developed theory is demonstrated using numerical experiments.

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available sensors, referred to as sparse sensing, that meets both the budget and performance requirements is highly desirable. Unfortunately, the subset selection problem for detection under dependent observations is combinatorial in nature and suboptimal subset selection algorithms must be employed. In this work, different from the widely used convex relaxation of the problem, we leverage submodularity, the diminishing returns property, to provide practical near-optimal algorithms suitable for large-scale subset selection. This is achieved by means of low-complexity greedy algorithms, which incur a reduced computational complexity compared to their convex counterparts.

In this work, we address the problem of identifying the underlying network structure of data. Different from other approaches, which are mainly based on convex relaxations of an integer problem, here we take a distinct route relying on algebraic properties of a matrix representation of the network. By describing what we call possible ambiguities on the network topology, we proceed to employ sub-modular analysis techniques for retrieving the network support, i.e., network edges. To achieve this we only make use of the network modes derived from the data. Numerical examples showcase the effectiveness of the proposed algorithm in recovering the support of sparse networks.

Factor analysis decomposition, i.e., decomposition of a covariance matrix as a sum of a low-rank positive semidefinite matrix and a diagonal matrix is an important problem in a variety of areas, such as signal processing, machine learning, system identification, and statistical inference. In this letter, the focus is on computing the factor analysis decomposition from a set of quadratic (or symmetric rank-one) measurements of a covariance matrix. Commonly used minimum trace factor analysis heuristic can be adapted to solve this problem when all the measurements are available. However, the resulting convex program is not suitable for processing large-scale or streaming data. Therefore, this letter presents a low-complexity iterative algorithm, which recovers the unknowns through a series of rank-one updates. The iterative algorithm performs better than the convex program when only a finite number of data snapshots are available.

In this paper, we propose sensor selection strategies, based on convex and greedy approaches, for designing sparse samplers for composite detection. Particularly, we focus our attention on sparse samplers for matched subspace detectors. Differently from previous works, that mostly rely on random matrices to perform compression of the sub-spaces, we show how deterministic samplers can be designed under a Neyman-Pearson-like setting when the generalized likelihood ratio test is used. For a less stringent case than the worst case design, we introduce a submodular cost that obtains comparable results with its convex counterpart, while having a linear time heuristic for its near optimal maximization.

In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The proposed scheme is particularly useful for processing signals on large-scale product graphs. The sampling sets are designed using a low-complexity greedy algorithm and can be proven to be near-optimal. To illustrate the developed theory, numerical experiments based on real datasets are provided for sampling 3D dynamic point clouds and for active learning in recommender systems.

In this paper the focus is on sampling and reconstruction of signals supported on nodes of arbitrary graphs or arbitrary signals that may be represented using graphs, where we extend concepts from generalized sampling theory to the graph setting. To recover such signals from a given set of samples, we develop algorithms that incorporate prior knowledge on the original signal when available such as smoothness or subspace priors related to the underlying graph. For reconstructing arbitrary signals, we constrain the reconstruction to the graph, and provide a consistent reconstruction method, in which both the reconstructed signal and the input yield exactly the same measurements. Given a set of graph frequency domain samples, the sampling and interpolation operations may be efficiently implemented using linear shift-invariant graph filters.

Distributed multiple-input multiple-output (MIMO) radars can use multiple transmitters and receivers simultaneously to detect targets.In order to maximize the probability of target detection,it is necessary to allocate the available transmit power resources suitably. The optimal allocation requires calculating the probability of detection, which is a computationally complex task, so using the exact distribution is very difficult in a dynamic scenario.In order to alleviate this problem,we propose an approximate distribution that is computationally simpler. This approximation is compared with the exact distribution as well as other cost functions that depend on the distribution of the test statistic, including the Kullback-Leibler divergence. It is demonstrated that the approximate distribution works well in the power allocation problem for MIMO radar target detection.

In this work, we introduce subset selection strategies for signal reconstruction based on kernel methods, particularly for the case of kernel-ridge regression. Typically, these methods are employed for exploiting known prior information about the structure of the signal of interest. We use the mean squared error and a scalar function of the covariance matrix of the kernel regressors to establish metrics for the subset selection problem. Despite the NP-hard nature of the problem, we introduce efficient algorithms for finding approximate solutions for the proposed metrics. Finally, numerical experiments demonstrate the applicability of the proposed strategies.

In this paper, we present a calibration algorithm for acoustic vector sensors arranged in a uniform linear array configuration. To do so, we do not use a calibrator source, instead we leverage the Toeplitz blocks present in the data covariance matrix. We develop linear estimators for estimating sensor gains and phases. Further, we discuss the differences of the presented blind calibration approach for acoustic vector sensor arrays in comparison with the approach for acoustic pressure sensor arrays. In order to validate the proposed blind calibration algorithm, simulation results for direction-of-arrival (DOA) estimation with an uncalibrated and calibrated uniform linear array based on minimum variance distortion less response and multiple signal classification algorithms are presented. The calibration performance is analyzed using the Cramér-Rao lower bound of the DOA estimates.