Kumar Vijay Mishra

Ahmet M. Elbir, Wei Shi, Kumar Vijay Mishra et al.

This paper addresses two major challenges in terahertz (THz) channel estimation: the beam-split phenomenon, i.e., beam misalignment because of frequency-independent analog beamformers, and computational complexity because of the usage of ultra-massive number of antennas to compensate propagation losses. Data-driven techniques are known to mitigate the complexity of this problem but usually require the transmission of the datasets from the users to a central server entailing huge communication overhead. In this work, we introduce a federated multi-task learning (FMTL), wherein the users transmit only the model parameters instead of the whole dataset, for THz channel and user direction-of-arrival (DoA) estimation to improve the communications-efficiency. We first propose a novel beamspace support alignment technique for channel estimation with beam-split correction. Then, the channel and DoA information are used as labels to train an FMTL model. By exploiting the sparsity of the THz channel, the proposed approach is implemented with fewer pilot signals than the traditional techniques. Compared to the previous works, our FMTL approach provides higher channel estimation accuracy as well as approximately 25 (32) times lower model (channel) training overhead, respectively.

Samuel Pinilla, Kumar Vijay Mishra, Igor Shevkunov et al.

Phase retrieval in optical imaging refers to the recovery of a complex signal from phaseless data acquired in the form of its diffraction patterns. These patterns are acquired through a system with a coherent light source that employs a diffractive optical element (DOE) to modulate the scene resulting in coded diffraction patterns at the sensor. Recently, the hybrid approach of model-driven network or deep unfolding has emerged as an effective alternative to conventional model-based and learning-based phase retrieval techniques because it allows for bounding the complexity of algorithms while also retaining their efficacy. Additionally, such hybrid approaches have shown promise in improving the design of DOEs that follow theoretical uniqueness conditions. There are opportunities to exploit novel experimental setups and resolve even more complex DOE phase retrieval applications. This paper presents an overview of algorithms and applications of deep unfolding for bootstrapped - regardless of near, middle, and far zones - phase retrieval.

Ahmet M. Elbir, Wei Shi, Kumar Vijay Mishra et al.

With the deployment of the fifth generation (5G) wireless systems gathering momentum across the world, possible technologies for 6G are under active research discussions. In particular, the role of machine learning (ML) in 6G is expected to enhance and aid emerging applications such as virtual and augmented reality, vehicular autonomy, and computer vision. This will result in large segments of wireless data traffic comprising image, video and speech. The ML algorithms process these for classification/recognition/estimation through the learning models located on cloud servers. This requires wireless transmission of data from edge devices to the cloud server. Channel estimation, handled separately from recognition step, is critical for accurate learning performance. Toward combining the learning for both channel and the ML data, we introduce implicit channel learning to perform the ML tasks without estimating the wireless channel. Here, the ML models are trained with channel-corrupted datasets in place of nominal data. Without channel estimation, the proposed approach exhibits approximately 60% improvement in image and speech classification tasks for diverse scenarios such as millimeter wave and IEEE 802.11p vehicular channels.

Conrad D. Hougen, Lance M. Kaplan, Magdalena Ivanovska et al.

In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagation to the setting of second-order Bayesian networks, giving rise to Second-Order Loopy Belief Propagation (SOLBP). For second-order Bayesian networks, SOLBP generates inferences consistent with those generated by sum-product networks, while being more computationally efficient and scalable.

Ahmet M. Elbir, Sinem Coleri, Kumar Vijay Mishra

Channel estimation is a critical task in intelligent reflecting surface (IRS)-assisted wireless systems due to the uncertainties imposed by environment dynamics and rapid changes in the IRS configuration. To deal with these uncertainties, deep learning (DL) approaches have been proposed. Previous works consider centralized learning (CL) approach for model training, which entails the collection of the whole training dataset from the users at the base station (BS), hence introducing huge transmission overhead for data collection. To address this challenge, this paper proposes a federated learning (FL) framework to jointly estimate both direct and cascaded channels in IRS-assisted wireless systems. We design a single convolutional neural network trained on the local datasets of the users without sending them to the BS. We show that the proposed FL-based channel estimation approach requires approximately 60% fewer pilot signals and it exhibits 12 times lower transmission overhead than CL, while maintaining satisfactory performance close to CL. In addition, it provides lower estimation error than the state-of-the-art DL-based schemes.

Kumar Vijay Mishra, Ahmet M. Elbir, Koichi Ichige

In the past few years, deep learning (DL) techniques have been introduced for designing sparse arrays. These methods offer the advantages of feature engineering and low prediction-stage complexity, which is helpful in tackling the combinatorial search inherent to finding a sparse array. In this chapter, we provide a synopsis of several direction finding applications of DL-based sparse arrays. We begin by examining supervised and transfer learning techniques that have applications in selecting sparse arrays for a cognitive radar application. Here, we also discuss the use of meta-heuristic learning algorithms such as simulated annealing for the case of designing two-dimensional sparse arrays. Next, we consider DL-based antenna selection for wireless communications, wherein sparse array problem may also be combined with channel estimation, beamforming, or localization. Finally, we provide an example of deep sparse array technique for integrated sensing and communications (ISAC) application, wherein a trade-off of radar and communications performance makes ISAC sparse array problem very challenging. For each setting, we illustrate the performance of model-based optimization and DL techniques through several numerical experiments. We discuss additional considerations required to ensure robustness of DL-based algorithms against various imperfections in array data.

Sunder Ram Krishnan, Junaid Farooq, Kumar Vijay Mishra et al.

While stochastic geometry provides a powerful framework for the analysis of cellular networks, standard Monte Carlo simulations often suffer from slow convergence due to the stochasticity of the infinite far-field. This work introduces the \textit{Rao-Blackwellized Hybrid Estimator} (RBHE), which enhances simulation efficiency by analytically marginalizing the residual far-field interference via the conditional Laplace functional. By partitioning the interference field into $K$ dominant interferers and an infinite tail, we derive an estimator that combines exact spatial sampling with a rigorous analytical representation. We prove that the RBHE is an unbiased estimator for any finite truncation, while its systematic bias relative to the infinite-plane benchmark decays at a rate of $\mathcal{O}(K^{1-η/2})$. Numerical results demonstrate significant sample parsimony; in the high-reliability regime ($T = -10$ dB) with $K=2$, the RBHE yields a variance reduction gain of $90.75\times$, enabling a $98.90\%$ reduction in the spatial realizations required to reach a target precision. This framework effectively bridges the gap between tractable analytical models and high-fidelity simulations.

Kumar Vijay Mishra, M. Ashok Kumar, Ting-Kam Leonard Wong

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information, sufficient statistics, and efficient estimators. Today, information geometry has emerged as an interdisciplinary field that finds applications in diverse areas such as radar sensing, array signal processing, quantum physics, deep learning, and optimal transport. This article presents an overview of essential information geometry to initiate an information theorist, who may be unfamiliar with this exciting area of research. We explain the concepts of divergences on statistical manifolds, generalized notions of distances, orthogonality, and geodesics, thereby paving the way for concrete applications and novel theoretical investigations. We also highlight some recent information-geometric developments, which are of interest to the broader information theory community.

Samuel Pinilla, Kumar Vijay Mishra, Brian M. Sadler et al.

The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its Doppler-shifted and delayed replicas. We consider the inverse problem of designing a radar transmit waveform that satisfies the specified AF magnitude. This process may be viewed as a signal reconstruction with some variation of phase retrieval methods. We provide a trust-region algorithm that minimizes a smoothed non-convex least-squares objective function to iteratively recover the underlying signal-of-interest for either time- or band-limited support. The method first approximates the signal using an iterative spectral algorithm and then refines the attained initialization based on a sequence of gradient iterations. Our theoretical analysis shows that unique signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies or time samples. Numerical experiments demonstrate that our method recovers both time- and band-limited signals from sparsely and randomly sampled, noisy, and noiseless AFs.

Himali Singh, Arpan Chattopadhyay, Kumar Vijay Mishra

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the purpose of predicting the adversary's future steps has led to recent formulations of inverse Kalman filter (I-KF). In this context of inverse filtering, we address the key challenges of non-linear process dynamics and unknown input to the forward filter by proposing an inverse extended Kalman filter (I-EKF). The purpose of this paper and the companion paper (Part II) is to develop the theory of I-EKF in detail. In this paper, we assume perfect system model information and derive I-EKF with and without an unknown input when both forward and inverse state-space models are non-linear. In the process, I-KF-with-unknown-input is also obtained. We then provide theoretical stability guarantees using both bounded non-linearity and unknown matrix approaches and prove the I-EKF's consistency. Numerical experiments validate our methods for various proposed inverse filters using the recursive Cramér-Rao lower bound as a benchmark. In the companion paper (Part II), we further generalize these formulations to highly non-linear models and propose reproducing kernel Hilbert space-based EKF to handle incomplete system model information.

Samuel Pinilla, Kumar Vijay Mishra, Brian M. Sadler

Retrieving a signal from its triple correlation spectrum, also called bispectrum, arises in a wide range of signal processing problems. Conventional methods do not provide an accurate inversion of bispectrum to the underlying signal. In this paper, we present an approach that uniquely recovers signals with finite spectral support (band-limited signals) from at least $3B$ measurements of its bispectrum function (BF), where $B$ is the signal's bandwidth. Our approach also extends to time-limited signals. We propose a two-step trust region algorithm that minimizes a non-convex objective function. First, we approximate the signal by a spectral algorithm and then refine the attained initialization based on a sequence of gradient iterations. Numerical experiments suggest that our proposed algorithm is able to estimate band-/time-limited signals from its BF for both complete and undersampled observations.

Kumar Vijay Mishra, M. Ashok Kumar

We examine the role of information geometry in the context of classical Cramér-Rao (CR) type inequalities. In particular, we focus on Eguchi's theory of obtaining dualistic geometric structures from a divergence function and then applying Amari-Nagoaka's theory to obtain a CR type inequality. The classical deterministic CR inequality is derived from Kullback-Leibler (KL)-divergence. We show that this framework could be generalized to other CR type inequalities through four examples: $α$-version of CR inequality, generalized CR inequality, Bayesian CR inequality, and Bayesian $α$-CR inequality. These are obtained from, respectively, $I_α$-divergence (or relative $α$-entropy), generalized Csiszár divergence, Bayesian KL divergence, and Bayesian $I_α$-divergence.

Ahmet M. Elbir, Kumar Vijay Mishra, Symeon Chatzinotas

Wireless communications and sensing at terahertz (THz) band are increasingly investigated as promising short-range technologies because of the availability of high operational bandwidth at THz. In order to address the extremely high attenuation at THz, ultra-massive multiple-input multiple-output (MIMO) antenna systems have been proposed for THz communications to compensate propagation losses. However, the cost and power associated with fully digital beamformers of these huge antenna arrays are prohibitive. In this paper, we develop wideband hybrid beamformers based on both model-based and model-free techniques for a new group-of-subarrays (GoSA) ultra-massive MIMO structure in low-THz band. Further, driven by the recent developments to save the spectrum, we propose beamformers for a joint ultra-massive MIMO radar-communications system, wherein the base station serves multi-antenna user equipment (RX), and tracks radar targets by generating multiple beams toward both RX and the targets. We formulate the GoSA beamformer design as an optimization problem to provide a trade-off between the unconstrained communications beamformers and the desired radar beamformers. To mitigate the beam split effect at THz band arising from frequency-independent analog beamformers, we propose a phase correction technique to align the beams of multiple subcarriers toward a single physical direction. To further decrease the ultra-massive MIMO computational complexity and enhance robustness, we also implement deep learning solutions to the proposed model-based hybrid beamformers. Numerical experiments demonstrate that both techniques outperform the conventional approaches in terms of spectral efficiency and radar beampatterns, as well as exhibiting less hardware cost and computation time.

Ahmet M. Elbir, Sinem Coleri, Kumar Vijay Mishra

Millimeter wave multiple-input multiple-output (mmWave-MIMO) systems with small number of radio-frequency (RF) chains have limited multiplexing gain. Spatial path index modulation (SPIM) is helpful in improving this gain by utilizing additional signal bits modulated by the indices of spatial paths. In this paper, we introduce model-based and model-free frameworks for beamformer design in multi-user SPIM-MIMO systems. We first design the beamformers via model-based manifold optimization algorithm. Then, we leverage federated learning (FL) with dropout learning (DL) to train a learning model on the local dataset of users, who estimate the beamformers by feeding the model with their channel data. The DL randomly selects different set of model parameters during training, thereby further reducing the transmission overhead compared to conventional FL. Numerical experiments show that the proposed framework exhibits higher spectral efficiency than the state-of-the-art SPIM-MIMO methods and mmWave-MIMO, which relies on the strongest propagation path. Furthermore, the proposed FL approach provides at least 10 times lower transmission overhead than the centralized learning techniques.

Ahmet M. Elbir, Sinem Coleri, Kumar Vijay Mishra

Many of the machine learning (ML) tasks are focused on centralized learning (CL), which requires the transmission of local datasets from the clients to a parameter server (PS) leading to a huge communication overhead. Federated learning (FL) overcomes this issue by allowing the clients to send only the model updates to the PS instead of the whole dataset. In this way, FL brings the learning to edge level, wherein powerful computational resources are required on the client side. This requirement may not always be satisfied because of diverse computational capabilities of edge devices. We address this through a novel hybrid federated and centralized learning (HFCL) framework to effectively train a learning model by exploiting the computational capability of the clients. In HFCL, only the clients who have sufficient resources employ FL; the remaining clients resort to CL by transmitting their local dataset to PS. This allows all the clients to collaborate on the learning process regardless of their computational resources. We also propose a sequential data transmission approach with HFCL (HFCL-SDT) to reduce the training duration. The proposed HFCL frameworks outperform previously proposed non-hybrid FL (CL) based schemes in terms of learning accuracy (communication overhead) since all the clients collaborate on the learning process with their datasets regardless of their computational resources.

Ahmet M. Elbir, Kumar Vijay Mishra

Cognitive communications have emerged as a promising solution to enhance, adapt, and invent new tools and capabilities that transcend conventional wireless networks. Deep learning (DL) is critical in enabling essential features of cognitive systems because of its fast prediction performance, adaptive behavior, and model-free structure. These features are especially significant for multi-antenna wireless communications systems, which generate and handle massive data. Multiple antennas may provide multiplexing, diversity, or antenna gains that, respectively, improve the capacity, bit error rate, or the signal-to-interference-plus-noise ratio. In practice, multi-antenna cognitive communications encounter challenges in terms of data complexity and diversity, hardware complexity, and wireless channel dynamics. DL solutions such as federated learning, transfer learning and online learning, tackle these problems at various stages of communications processing, including multi-channel estimation, hybrid beamforming, user localization, and sparse array design. This article provides a synopsis of various DL-based methods to impart cognitive behavior to multi-antenna wireless communications for improved robustness and adaptation to the environmental changes while providing satisfactory spectral efficiency and computation times. We discuss DL design challenges from the perspective of data, learning, and transceiver architectures. In particular, we suggest quantized learning models, data/model parallelization, and distributed learning methods to address the aforementioned challenges.

Ahmet M. Elbir, Kumar Vijay Mishra

Intelligent reflecting surfaces (IRSs) have recently received significant attention for 6G wireless communications as they enable the control of the wireless propagation environment. The use of IRS also provides reducing the hardware complexity, physical size, weight as well as cost of conventional large antenna arrays. However, deployment of the IRS entails dealing with multiple channel links between the base station (BS) and the users. Further, the BS and IRS beamformers require a joint design, wherein the IRS elements must be rapidly reconfigured. Data-driven techniques, such as deep learning (DL), are critical in addressing these challenges. The lower computation time and model-free nature of DL make it robust against data imperfections and environmental changes. At the physical layer, DL has been shown to be effective for IRS signal detection, channel estimation, and active/passive beamforming using architectures such as supervised, unsupervised, and reinforcement learning. This article provides a synopsis of these techniques for designing DL-based IRS-assisted wireless systems.

Saeid Sedighi, Kumar Vijay Mishra, M. R. Bhavani Shankar et al.

Several Internet-of-Things (IoT) applications provide location-based services, wherein it is critical to obtain accurate position estimates by aggregating information from individual sensors. In the recently proposed narrowband IoT (NB-IoT) standard, which trades off bandwidth to gain wide coverage, the location estimation is compounded by the low sampling rate receivers and limited-capacity links. We address both of these NB-IoT drawbacks in the framework of passive sensing devices that receive signals from the target-of-interest. We consider the limiting case where each node receiver employs one-bit analog-to-digital-converters and propose a novel low-complexity nodal delay estimation method using constrained-weighted least squares minimization. To support the low-capacity links to the fusion center (FC), the range estimates obtained at individual sensors are then converted to one-bit data. At the FC, we propose target localization with the aggregated one-bit range vector using both optimal and sub-optimal techniques. The computationally expensive former approach is based on Lasserre's method for multivariate polynomial optimization while the latter employs our less complex iterative joint r\textit{an}ge-\textit{tar}get location \textit{es}timation (ANTARES) algorithm. Our overall one-bit framework not only complements the low NB-IoT bandwidth but also supports the design goal of inexpensive NB-IoT location sensing. Numerical experiments demonstrate feasibility of the proposed one-bit approach with a $0.6$\% increase in the normalized localization error for the small set of $20$-$60$ nodes over the full-precision case. When the number of nodes is sufficiently large ($>80$), the one-bit methods yield the same performance as the full precision.

Jiawei Liu, Kumar Vijay Mishra, Mohammad Saquib

We consider a spectral sharing problem in which a statistical (or widely distributed) multiple-input multiple-output (MIMO) radar and an in-band full-duplex (IBFD) multi-user MIMO (MU-MIMO) communications system concurrently operate within the same frequency band. Prior works on joint MIMO-radar-MIMO-communications (MRMC) systems largely focus on either colocated MIMO radars, half-duplex MIMO communications, single-user scenarios, omit practical constraints (clutter, uplink [UL]/downlink [DL] transmit powers, UL/DL quality-of-service, and peak-to-average-power ratio), or MRMC co-existence that employs separate transmit/receive units. The purpose of this and companion papers (Part II and III) is to co-design an MRMC framework that addresses all of these issues. In this paper, we propose signal processing for a distributed IBFD MRMC, where radar receiver is designed to additionally exploit the downlink communications signals reflected from a radar target. Extensive numerical experiments show that our methods improve radar target detection over conventional codes and yield a higher achievable data rate than standard precoders. The following companion paper (Part II) describes the theory and procedure of our algorithm to solve the non-convex design problem. The final companion paper (Part II) considers the case of multiple targets and examines the tracking performance of our MRMC system.

Ahmet M. Elbir, Kumar Vijay Mishra

Sparse sensor array selection arises in many engineering applications, where it is imperative to obtain maximum spatial resolution from a limited number of array elements. Recent research shows that computational complexity of array selection is reduced by replacing the conventional optimization and greedy search methods with a deep learning network. However, in practice, sufficient and well-calibrated labeled training data are unavailable and, more so, for arbitrary array configurations. To address this, we adopt a deep transfer learning (TL) approach, wherein we train a deep convolutional neural network (CNN) with data of a source sensor array for which calibrated data are readily available and reuse this pre-trained CNN for a different, data-insufficient target array geometry to perform sparse array selection. Numerical experiments with uniform rectangular and circular arrays demonstrate enhanced performance of TL-CNN on the target model than the CNN trained with insufficient data from the same model. In particular, our TL framework provides approximately 20% higher sensor selection accuracy and 10% improvement in the direction-of-arrival estimation error.

Kumar Vijay Mishra, M. Ashok Kumar

The relative $α$-entropy is the Rényi analog of relative entropy and arises prominently in information-theoretic problems. Recent information geometric investigations on this quantity have enabled the generalization of the Cramér-Rao inequality, which provides a lower bound for the variance of an estimator of an escort of the underlying parametric probability distribution. However, this framework remains unexamined in the Bayesian framework. In this paper, we propose a general Riemannian metric based on relative $α$-entropy to obtain a generalized Bayesian Cramér-Rao inequality. This establishes a lower bound for the variance of an unbiased estimator for the $α$-escort distribution starting from an unbiased estimator for the underlying distribution. We show that in the limiting case when the entropy order approaches unity, this framework reduces to the conventional Bayesian Cramér-Rao inequality. Further, in the absence of priors, the same framework yields the deterministic Cramér-Rao inequality.

M. Ashok Kumar, Kumar Vijay Mishra

We study the geometry of probability distributions with respect to a generalized family of Csiszár $f$-divergences. A member of this family is the relative $α$-entropy which is also a Rényi analog of relative entropy in information theory and known as logarithmic or projective power divergence in statistics. We apply Eguchi's theory to derive the Fisher information metric and the dual affine connections arising from these generalized divergence functions. This enables us to arrive at a more widely applicable version of the Cramér-Rao inequality, which provides a lower bound for the variance of an estimator for an escort of the underlying parametric probability distribution. We then extend the Amari-Nagaoka's dually flat structure of the exponential and mixer models to other distributions with respect to the aforementioned generalized metric. We show that these formulations lead us to find unbiased and efficient estimators for the escort model. Finally, we compare our work with prior results on generalized Cramér-Rao inequalities that were derived from non-information-geometric frameworks.

Ahmet M. Elbir, Kumar Vijay Mishra, M. R. Bhavani Shankar et al.

Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. However, lack of fully digital beamforming in hybrid architectures and short coherence times at mm-Wave impose additional constraints on the channel estimation. Prior works on addressing these challenges have focused largely on narrowband channels wherein optimization-based or greedy algorithms were employed to derive hybrid beamformers. In this paper, we introduce a deep learning (DL) approach for channel estimation and hybrid beamforming for frequency-selective, wideband mm-Wave systems. In particular, we consider a massive MIMO Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system and propose three different DL frameworks comprising convolutional neural networks (CNNs), which accept the raw data of received signal as input and yield channel estimates and the hybrid beamformers at the output. We also introduce both offline and online prediction schemes. Numerical experiments demonstrate that, compared to the current state-of-the-art optimization and DL methods, our approach provides higher spectral efficiency, lesser computational cost and fewer number of pilot signals, and higher tolerance against the deviations in the received pilot data, corrupted channel matrix, and propagation environment.

Fabio Giovanneschi, Kumar Vijay Mishra, Maria Antonia Gonzalez-Huici et al.

Ground penetrating radar (GPR) target detection and classification is a challenging task. Here, we consider online dictionary learning (DL) methods to obtain sparse representations (SR) of the GPR data to enhance feature extraction for target classification via support vector machines. Online methods are preferred because traditional batch DL like K-SVD is not scalable to high-dimensional training sets and infeasible for real-time operation. We also develop Drop-Off MINi-batch Online Dictionary Learning (DOMINODL) which exploits the fact that a lot of the training data may be correlated. The DOMINODL algorithm iteratively considers elements of the training set in small batches and drops off samples which become less relevant. For the case of abandoned anti-personnel landmines classification, we compare the performance of K-SVD with three online algorithms: classical Online Dictionary Learning, its correlation-based variant, and DOMINODL. Our experiments with real data from L-band GPR show that online DL methods reduce learning time by 36-93% and increase mine detection by 4-28% over K-SVD. Our DOMINODL is the fastest and retains similar classification performance as the other two online DL approaches. We use a Kolmogorov-Smirnoff test distance and the Dvoretzky-Kiefer-Wolfowitz inequality for the selection of DL input parameters leading to enhanced classification results. To further compare with state-of-the-art classification approaches, we evaluate a convolutional neural network (CNN) classifier which performs worse than the proposed approach. Moreover, when the acquired samples are randomly reduced by 25%, 50% and 75%, sparse decomposition based classification with DL remains robust while the CNN accuracy is drastically compromised.

Ahmet M. Elbir, Kumar Vijay Mishra, Yonina C. Eldar

Direction of arrival (DoA) estimation of targets improves with the number of elements employed by a phased array radar antenna. Since larger arrays have high associated cost, area and computational load, there is recent interest in thinning the antenna arrays without loss of far-field DoA accuracy. In this context, a cognitive radar may deploy a full array and then select an optimal subarray to transmit and receive the signals in response to changes in the target environment. Prior works have used optimization and greedy search methods to pick the best subarrays cognitively. In this paper, we leverage deep learning to address the antenna selection problem. Specifically, we construct a convolutional neural network (CNN) as a multi-class classification framework where each class designates a different subarray. The proposed network determines a new array every time data is received by the radar, thereby making antenna selection a cognitive operation. Our numerical experiments show that {the proposed CNN structure provides 22% better classification performance than a Support Vector Machine and the resulting subarrays yield 72% more accurate DoA estimates than random array selections.

Weiyu Xu, Jian-Feng Cai, Kumar Vijay Mishra et al.

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recover $1$-dimensional spectrally sparse signal. However, in spite of existing research efforts \cite{chi2013compressive}, it was still an open problem how to formulate an equivalent positive semidefinite program for atomic norm minimization in recovering signals with $d$-dimensional ($d\geq 2$) off-the-grid frequencies. In this paper, we settle this problem by proposing equivalent semidefinite programming formulations of atomic norm minimization to recover signals with $d$-dimensional ($d\geq 2$) off-the-grid frequencies.