Integrated sensing and communications (ISAC), which are recognized as a key enabler for sixth generation (6G), have brought new opportunities for intelligent, sustainable, and connected wireless networks. Multiple-input–multiple-output (MIMO) transceiver technology lies at the core of this paradigm, providing the degrees of freedom required for simultaneous data transmission and accurate radar sensing. The tight integration of sensing and communication (S&C) introduces unique security vulnerabilities that extend beyond conventional physical-layer security (PLS). In particular, high-power transmissions directed at sensing targets may empower adversarial eavesdroppers, whereas passive interception of ISAC echoes can reveal sensitive information such as target locations and mobility patterns. This article presents an overview of recent advances in MIMO ISAC transceiver design, considering transmitter perspectives, receiver architectures, and full-duplex implementations. We examine MIMO transceiver designs under unique security threats specific to ISAC and highlight emerging countermeasures, including secure signaling design, interference exploitation, and transceiver optimization under adversarial conditions. Finally, we discuss challenges and research opportunities for developing secure ISAC systems in next-generation wireless networks.

Joint sensing and communication (JSAC) has emerged as a promising technology in autonomous driving, as it allows simultaneous road sensing and two-way communication using a single shared platform. Meanwhile, intelligent reflective surface (IRS) enables sensing enhancement and communication with targets in a blind zone. In this paper, we propose an IRS-assisted JSAC design to address two issues of the limited sensing range of automotive radar and the likely occlusion among road targets. We co-design the IRS’ reflection coefficient vector to steer the beam towards the directions of radar targets as well as embed the communication symbols into the reflected signals. Considering the phase-only property of the passive IRS, we establish a constant modulus co-design problem. We seek to optimize the covariance matrix first and then obtain the optimal reflection coefficient vector via matrix decomposition. Subsequently we transform the constant modulus constraint into a rank-1 semidefinite programing (SDP) problem and solve it iteratively. Simulation results demonstrate the effectiveness of the proposed IRS-assisted JSAC design.

Sparse arrays have been recently applied to spectral sensing of wideband spectrum where the array is configured to estimate the directions of co-frequency emitters and also reconfigured, through antenna switching, for beamforming. The latter archives source signal isolation necessary for emitter identifications and signal modulation classifications and identifications. This paper examines the roles of the sparse array configuration and the sparse array weights in delivering the optimum and semi-optimum performance when adopting the criterion of maximum signal-to-interference and noise ratio (MaxSINR). Towards this end, we compare the source isolation performance based on the optimum sparse array configuration and array weights applied individually, jointly, or in sequence. The individually optimized sparse array configuration emerges when the array strives to orthogonalize the desired source steering vector and the interference subspace. Such sparse array can be followed by applying conventional beamformer weights or weights stemming from high interference to noise ratio assumption. HER curves are used in the comparison to delineate the offering of each array design approach.

The instantaneous velocity of any moving object can be decomposed into two orthogonal components with reference to the observing radar, namely, radial velocity along the radar line of sight (LoS) and transversal velocity perpendicular to the LoS. It has been shown that the measurement of transversal velocity can significantly improve the performance of both radar target tracking and classification. Furthermore, the precision of transversal velocity estimation is proportional to the baseline length using static interferometry. However, the large baseline is impractical in applications, such as automotive radar with restrictions on the packaging size. This letter proposes synthetic interferometry exploiting radar motions. A large virtual baseline can be synthesized by moving the side-looking radar and synchronizing the received signals at two locations, thus improving the accuracy of transversal velocity measurement. We derive the conditions of time synchronization for successful interferometry in terms of the maximum moving distance and the maximum observation time. Both simulations and experiments have been conducted to validate the feasibility and effectiveness of the proposed synthetic interferometry.

Deep learning has been shown to be a powerful tool in array processing. Sparse array reconfigurability can be an integral part of cognitive sensing in dynamic radio frequency (RF) environments. In this respect, fast-switching that avoids hardware complexity, insertion loss, and crosstalk distortion is paramount to a realizable perception-action cycle. In this paper, we design sparse arrays using binary switching per RF chain for optimum beamforming that maximizes signal-to-interference-and-noise ratio (SINR). We apply two binary switching strategies and examine their achievable sparse array classification rates and SINR using convolutional neural networks as well as the less complex structure of multilayer perceptron.

Radio frequency signal modulation classifications find broad applications in cognitive sensing and RF spectrum coexistence. Recently, deep neural networks have been shown to be a powerful tool for automatic modulation classification (AMC). Accounting for different signal variations is paramount towards reliable classifications. In this paper, we examine the performance of AMC under varying sampling rates and signal-to-noise ratio (SNR). We consider a dynamic environment where the signal modulation and channel conditions can be assumed constant over a number of consecutive observations. We also show that a single ResNet can be used for both modulation classification and estimating SNR which allows network training and testing at the same noise levels. It is shown that significant signal modulation classification accuracy improvement can be achieved using multiple observations and known SNR.

Post-quantum cryptography (PQC) has recently drawn substantial attention from various communities owing to the proven vulnerability of existing public-key cryptosystems against the attacks launched from well-established quantum computers. The Ring-Binary-Learning-with-Errors (RBLWE), a variant of Ring-LWE, has been proposed to build PQC for lightweight applications. As more Field-Programmable Gate Array (FPGA) devices are being deployed in lightweight applications like Internet-of-Things (IoT) devices, it would be interesting if the RBLWE-based PQC can be implemented on the FPGA with ultra-low complexity and flexible processing. However, thus far, limited information is available for such implementations. In this article, we propose novel RBLWE-based PQC accelerators on the FPGA with ultra-low implementation complexity and flexible timing. We first present the process of deriving the key operation of the RBLWE-based scheme into the proposed algorithmic operation. The corresponding hardware accelerator is then efficiently mapped from the proposed algorithm with the help of algorithm-to-architecture implementation techniques and extended to obtain higher-throughput designs. The final complexity analysis and implementation results (on a variety of FPGAs) show that the proposed accelerators have significantly smaller area-time complexities than the state-of-the-art designs. Overall, the proposed accelerators feature low implementation complexity and flexible processing, making them desirable for emerging FPGA-based lightweight applications.

The paper considers phase-only reconfigurable sparse arrays (RSAs) for receive beamforming to maximize signal-to-interference plus noise ratio (MaxSINR). We develop a design approach based on supervised deep neural network (DNN) to learn and mimic a phase-only sparse MaxSINR beamformer. The proposed approach strives to match the SINR performance of data driven sparse Capon beamformer. The problem is posed as a multi-label classification problem, where the received antenna correlations is the input to the fully connected neural network (FCNN) which outputs the optimum sensor locations for effective interference mitigation. We evaluate the performance of DNN based optimization of RSAs in terms of the ability of the classified sparse array to mitigate interference and maximize signal power using phase-only beamforming. The phase-only DNN-based sparse sensor placement reduces hardware requirements, shifts optimization algorithm complexity to satisfying training data sufficiency, and is amenable to real-time implementation.

Human activity classification based on micro-Doppler (m-D) signatures finds applications in surveillance, search and rescue operations, and healthcare. In this article, we propose a new approach for human activity classification. This approach deals with the situations of reduced limb movements that could be due to the presence of injury or an individual carrying objects. It applies a preprocessing step to separate human m-D signals of the limbs from the Doppler signal corresponding to the torso. The separated m-D signal is input to a two-layer convolutional principal component analysis network (CPCAN) for feature extraction and motion classification. The CPCAN comprises a simple network architecture for efficient training and implementation, and it automatically learns the highly discriminative features. Experiments involving multiple human subjects performing different activities show a high classification accuracy associated with small arm motions.

We consider a multiple-input multiple-output (MIMO) dual function radar communication (DFRC) system employing frequency hopping (FH) radar waveforms. The DFRC system embeds communication symbols using code-shift keying (CSK) strategy. Each symbol is represented by a phase modulated pulse code sequence which multiplies the radar hops in fast-time before transmitted from the MIMO radar platform. This strategy allows for reduced clutter modulation caused by changed radar waveforms within coherent processing interval (CPI). We analyze the effect of this communication symbol embedding scheme on range sildelobe levels (RSLs) and derive the DFRC probability of target detection. We show that the DFRC waveforms enhances target visibility leading to improved target detection compared with the FH radar without signal embedding.

Sparse array design aided by emerging fast sensor switching technologies can lower the overall system overhead by reducing the number of expensive transceiver chains. In this paper, we examine the active sparse array design enabling the maximum signal to interference plus noise ratio (MaxSINR) beamforming at the MIMO radar receiver. The proposed approach entails an entwined design, i.e., jointly selecting the optimum transmit and receive sensor locations for accomplishing MaxSINR receive beamforming. Specifically, we consider a colocated multiple-input multiple-output (MIMO) radar platform with orthogonal transmitted waveforms, and examine antenna selections at the transmit and receive arrays. The optimum active sparse array transceiver design problem is formulated as successive convex approximation (SCA) alongside the two-dimensional group sparsity promoting regularization. Several examples are provided to demonstrate the effectiveness of the proposed approach in utilizing the given transmit/receive array aperture and degrees of freedom for achieving MaxSINR beamforming.

Recent performance analysis of dual-function radar communications (DFRC) systems, which embed information using phase shift keying (PSK) into multiple-input multiple-output (MIMO) frequency hopping (FH) radar pulses, shows promising results for addressing spectrum sharing issues between radar and communications. However, the problem of decoding information at the communication receiver remains challenging, since the DFRC transmitter is typically assumed to transmit only information embedded radar waveforms and not the training sequence. We propose a novel method for decoding information at the communication receiver without using training data, which is implemented using a software-defined radio (SDR). The performance of the SDR implementation is examined in terms of bit error rate (BER) as a function of signal-to-noise ratio (SNR) for differential binary and quadrature phase shift keying modulation schemes and compared with the BER versus SNR obtained with numerical simulations.

Recent progress in compressive sensing underscores the importance of exploiting intrinsic structures in sparse signal reconstruction. In this letter, we propose a Markov random field (MRF) prior in conjunction with fast iterative shrinkage-thresholding algorithm (FISTA) for image reconstruction. The MRF prior is used to represent the support of sparse signals with clustered nonzero coefficients. The proposed approach is applied to the inverse synthetic aperture radar (ISAR) imaging problem. Simulations and experimental results are provided to demonstrate the performance advantages of this approach in comparison with the standard FISTA and existing MRF-based methods.

Sparse arrays are typically configured considering either the environmental dependent or independent design objectives. In this paper, we investigate hybrid sparse array design satisfying dual design objectives. We consider enhancing the source identifiability and maximizing the Signal-to-Interference-plus-noise-ratio (SINR) as our design criteria. We pose the problem as designing fully augmentable sparse arrays for receive beamforming achieving maximum SINR (MaxSINR) for desired point sources operating in an interference active environment. The problem is formulated as a re-weighted l1-norm squared quadratically constraint quadratic program (QCQP). Simulation results are presented to show the effectiveness of the proposed algorithm for designing fully augmentable arrays in case of under-determined scenarios.

Moving platforms enable sparse arrays to assume higher degrees of freedom and lead to increased number of lags. In essence, array motion can fill the holes in the spatial auto-correlation lags associated with a fixed platform and, therefore, increase the number of sources detectable by the same physical array. In this paper, we consider coprime arrays, and assume quasi-stationarity of the environment, where the source locations and waveforms are assumed invariant over array motion of half wavelength. Expressions of the synthetic array comprising the original coprime array and its shifted version are derived. Analysis of the difference co-array corresponding to the combined array positions before and after motion is provided. It is shown that majority, if not all, of the holes in the original array position can be filled by just a small translation shift along the coprime array axis.

A novel dilated nested array is presented to obtain an enhanced fully filled difference coarray exploiting array motions. The proposed sparse array is suitable for the cases when the sensing environment can be assumed stationary over an array motion of half wavelength or shorter. Closed-form expressions of the number of degrees of freedom in the difference coarray of the combined array before and after the translation motion are presented for direction-of-arrival (DOA) estimation. It is shown that the maximum number of consecutive lags for this case is three times that of the corresponding conventional two-level nested array. Numerical results of DOA estimation using the proposed array are provided for performance comparison and to validate array analyses.

Conventional compressive sensing (CS) aims at sparse signal recovery from the measurements with continuous values. Quantized CS (QCS) methods arise in digital implementations where quantization of the receiver data is performed prior to signal processing. The extreme case of QCS is the so-called 1-bit CS where each real-valued measurement maintains only the sign information with one bit. The 1-bit CS alleviates the burden of storage and transmission of large data volumes and reduces the cost of the analog-to-digital converter. Recently, the 1-bit CS has been successfully applied to inverse scattering and radar imaging. In high-resolution radar imaging scenarios, targets assume spatial extent and occupy clustering pixels. The real and imaginary components of a complex sparse signal are the projections of the same complex value onto two orthogonal axes and, therefore, share a joint sparsity pattern. In this paper, a new 1-bit CS algorithm, referred to as enhanced-binary iterative hard thresholding (E-BIHT), is proposed to improve quality of 1-bit radar imaging by exploiting the two-level block sparsity exhibited in the two properties of clustering and the joint sparsity pattern of the real and imaginary parts of the target image. Simulations and experimental results demonstrate that compared to commonly used 1-bit CS algorithms, the proposed E-BIHT provides more informative imaging resulting in higher target-to-clutter ratio.

The problem of optimum distribution of the available spatial degrees of freedom among two sparse antenna subarray beamfomers in shared aperture receiver is investigated. The two subarrays, forming a full array, co-exist on the same platform and could perform separate RF sensing and communications tasks. The sparsity and cardinality of the subarray configurations are joint optimization variables which considerably affect the output signal-to-interference plus noise ratios (SINR) of the two beamformer outputs. A minimum output SINR figure value is imposed to guarantee minimum performance. We solve this problem by utilizing Taylor series approximation to reformulate the initial non-convex problem to a convex one. Simulation results validate the effectiveness of the proposed method.

In recent years, radar has been employed as a fall detector, due to its superior sensing capabilities and penetration through walls. In this paper, we introduce a multi-linear subspace fall detection scheme that exploits the three radar signal variables: slow-time, fast-time, and Doppler frequency. The proposed approach attempts to find the optimum orthonormal subspaces that minimize the reconstruction error for different modes of the radar data cube. Experimental results based on real radar data obtained from multiple subjects and aspect angles demonstrate that the proposed multi-dimensional principal component analysis (MPCA) yields the highest overall classification accuracy among other methods including physically interpretable pre-defined features and spectrogram-based standard PCA.

Optimum sparse array design for maximum output signal-to-noise ratio (MaxSNR) and signal-to-interference ratio (MaxSINR) have been shown to yield significant performance improvement compared to random or environmental-independent structured arrays, with the same number of antennas. We examine the MaxSNR problem in presence of local scatterings which may follow specific deterministic or statistical scattering models. It is shown that if the scatterers assume a Gaussian distribution centered around the source angular position, the optimum array configuration for maximizing the SNR is the commonly used uniform linear array (ULA). If the scatterers circulate the source, the optimum design yields sparse array topologies with superior performance over ULAs. Simulation results are presented to show the effectiveness of array configurability in the case of both Gaussian and circularly spread sources.

The problem of optimum sparse array beamformer design to maximize output signal-to-interference-plus-noise ratio (SINR) in the case of multiple narrowband sources was recently investigated. This was based on seeking both optimum sensor placement as well as optimum a single beamformer for all sources in the array field of view. In this paper, we consider multiple beamformers with a common sparse array. That is, we deal with a more prevalent case in radar and communications where each source is assigned its own beam. This could be the case for both switched and simultaneous or staring beams. The paper considers optimum sparse array design for both narrowband and wideband sources. Analysis and simulation examples demonstrate that the optimum sparse array configuration depends on both the arrival angle and the frequency of the incoming signal and it plays a vital role in determining the performance of multiple beamformer receivers.

We present an image-domain adaptive likelihood ratio tests (LRT) detector for low-signature target detection in forward-looking ground-penetrating radar. We exploit multiview tomographic images of the scene under investigation to iteratively adapt the statistics of the targets and clutter arising from the interface roughness. Using numerical electromagnetic data, it is shown that the proposed adaptive LRT detector provides significantly lower false-alarm rates compared with its nonadaptive counterpart while providing comparable detection performance.

In this paper, we propose a two-level block matching pursuit (TLBMP) algorithm based on a probabilistic graph model for polarimetric through-wall radar imaging (TWRI). In typical L-band to X-band TWRI, indoor targets assume a spatial extent and occupy clustered pixels. When polarimetric sensing is used to obtain independent observations, radar images of clustered targets can be enhanced within the joint sparsity framework. Toward this objective, TLBMP is devised to exploit both the clustered property and the joint sparsity pattern of multiple polarimetric through-wall radar images. Simulations and experimental results based on polarimetric through-wall radar data demonstrate that compared to commonly used algorithms for solving the same underlying problem, TLBMP provides more informative imaging with higher target-to-clutter ratio.

Radar for indoor monitoring has recently attracted much attention that is driven by its safety, privacy-preserving, and non-wearable sensing mode. Micro-Doppler signatures offered by radars operating in the K-band can disclose intricate details and characteristics of human gait. This paper reveals key Doppler features associated with human legs in gait motions which have been overlooked or ignored by existing work in this area, including biomechanics simulators and electromagnetic modeling. These features are used to detect gait abnormalities and distinguish gait from other translational motions which exhibit similar signatures in the time-frequency domain, such as assistive walking devices.

In this paper, we consider optimum array configurations for multiple satellite signals in interference-free environment. The two measures of maximum output signal-to-noise ratio (SNR) and equal gains towards all sources incident on the array are considered for the array design. As it is computationally exhaustive to enumerate all configurations and implement eigenvalue decomposition to compare respective maximum eigenvalues, we resort to the relaxation of maximizing the lower bound of the output SNR. Subsequently, an iterative linear fractional programming method is proposed to maximize the spectral norm of the source covariance matrix. Simulation examples confirm that the array configuration plays a vital role in determining the array processing performance in interference-free scenarios. The selected optimum subarrays achieve maximum performance preservations with a dramatically reduced cost.

In this paper, we consider robust direction-of-arrival (DOA) estimation for an array that contains mis-calibrated sensors with unknown gain and phase uncertainties. We develop two robust DOA estimation algorithms based on the maximum correntropy criterion (MCC). In the first algorithm, adaptively optimized weighting factors are obtained and applied to each sensor to effectively mitigate the effect of calibration error and array manifold distortions, and the results are fed into sparse reconstruction methods for DOA estimation. In the second algorithm, we further estimate the gain and phase errors of the mis-calibrated sensors so that the entire array is fully calibrated for improved DOA estimation. The effectiveness of the proposed techniques is verified using simulation results.

A single-snapshot fast computational Fourier-based direction-of-arrival (DOA) estimation method is introduced. This method applies the fast Fourier transform (FFT) to sensor data and performs effective cancellation of spectral leakage caused by sidelobe interactions, leading to unbiased DOA estimates of multiple sources. Successful elimination of spectral leakage is achieved by a sequential removal of strong sinc functions in the spatial frequency domain through an iterative interpolation process. The simulation results demonstrate superior performance of the proposed method over beamforming and other iterative FFT-based DOA estimation techniques as well as the high-resolution Root-MUSIC algorithm.

Human motion recognition plays a key role in various fields including health monitoring. Radar is a type of sensor that has shown remarkable success in the classification of human motions. Different data representation domains have been used for the analysis of radar returns. Each domain provides one aspect of the observed motion not readily discernible in other domains. In this letter, we propose an approach to quantify the domain suitability in representing a human motion. In order to evaluate the proposed approach, we consider the time-frequency domain and the range map. Additionally, based on the demonstrated domain effectiveness, we propose a classification scheme that seeks to incorporate each domain consistent with its offerings. Experimental results show the importance of investigating domain offerings prior to the classification process.

Although radar and communication systems so far have been considered separately, recent advances in passive radar systems have motivated us to propose a unified system, capable of fulfilling the requirements of both radar and communications. In this paper, we provide performance tradeoff analysis for a system consisting of a transmitter, a passive radar receiver, and a communication receiver (CR). The total power is allocated for transmitting the radar waveforms and information signals in such a way that the probability of detection (PD) is maximized, while satisfying the information rate requirement of the CR. An exact closed-form expression for the probability of false alarm (PFA) is derived, whereas PD is approximated by assuming that the signal-to-noise ratio corresponding to the reference channel is often much larger than that corresponding to the surveillance channel. The performance tradeoff between the radar and communication subsystems is then characterized by the boundaries of the PFA-rate and PD-rate regions.

Group-sparsity-based method is applied to the 2qth-order difference coarray for underdetermined wideband direction of arrival (DOA) estimation. For complexity reduction, a focused compressive-sensing-based approach is proposed, without sacrificing its performance. Different from the conventional focusing approach, in the proposed one, focusing is applied to the virtual arrays and no preliminary DOA estimation is required. Simulation results are provided to demonstrate the effectiveness of the proposed methods.

Forward-looking ground-penetrating radar (FL-GPR) permits standoff sensing of shallow in-road threats. A major challenge facing this radar technology is the high rate of false alarms stemming from the vulnerability of the target responses to interference scattering arising from interface roughness and subsurface clutter. In this paper, we present a multiview approach for target detection in FL-GPR. Various images corresponding to the different views are generated using a tomographic algorithm, which considers the near-field nature of the sensing problem. Furthermore, for reducing clutter and maintaining high cross-range resolution over the imaged area, each image is computed in a segmentwise fashion using coherent integration over a suitable set of measurements from multiple platform positions. We employ two fusion approaches based on likelihood ratio tests detector to combine the multiview images for enhanced target detection. The superior performance of the multiview approach over single-view imaging is demonstrated using electromagnetic modeling data.

Increased demand on spectrum sensing over a broad frequency band requires a high sampling rate and thus leads to a prohibitive volume of data samples. In some applications, e.g., spectrum estimation, only the second-order statistics are required. In this case, we may use a reduced data sampling rate by exploiting a low-dimensional representation of the original high-dimensional signals. In particular, the covariance matrix can be reconstructed from compressed data by utilizing its specific structure, e.g., the Toeplitz property. In this paper, we propose a general coprime sampling concept that implements effective compression of Toeplitz covariance matrices. Given a fixed number of data samples, we examine different schemes on covariance matrix acquisition, based on segmented data sequences. The effectiveness of the proposed technique is verified using simulation results.

In this paper, we address the suppression of frequency modulated jammers in a multi-sensor Global Navigation Satellite System (GNSS) receiver. In particular, we consider the case of sparsely sampled signals and compressed observations. In this case, applying conventional time-frequency (TF) analysis for jammer characterization produces noise-like artifacts which, if not properly considered, would obscure the jammer TF representation and lead to considerable errors in jammer signal estimation and excision. In the proposed approach, a multi-sensor data-dependent TF kernel is applied for effective mitigation of artifacts due to missing samples. Sparse reconstruction methods are then applied to obtain nonparametric instantaneous frequency estimation. We apply the continuous-structure aware Bayesian compressive sensing method to exploit the contiguous nature of the jammer TF signature, leading to enhanced localization and suppression.

Radar imaging is typically based on linear models of the electromagnetic scattering phenomenon. These models are robust and computationally efficient, but do not account for mutual interactions among targets in the scene and between the targets and the surrounding environment. As a result, the radar images are characterized by spurious targets, i.e., multipath ghosts, which appear at positions where no physical targets exist. In this letter, we compare two key approaches for clutter suppression. The first approach applies multiplicative fusion of the images corresponding to subapertures of the deployed array, whereas the second approach is based on coherence factor filtering, which enhances the image quality by suppressing low-coherence features. We assess the performance of these two methods in terms of imaging and detection capabilities. Numerical results based on synthetic data are reported to support the comparative analysis.

In passive bistatic radars, weak target echoes may often be masked by direct path interference, multipath components, and strong target echoes, making weak target detection a challenging problem. The conventional 1-D adaptive cancelation algorithms, such as the normalized least mean square (NLMS), cannot effectively suppress strong target echoes when their Doppler frequencies spread. In addition, the continuous distribution of the NLMS weight vector does not match the sparse characteristics of strong multipath components and target echoes, thus resulting in degraded cancelation performance. Motivated by this fact, a novel 2-D sparse-weight NLMS filtering scheme is proposed by extending the NLMS to a 2-D structure, in which the weight vector is sparsely distributed and adaptively adjusted based on the sparse strong multipath components and target echoes.

Distributed radar networks for through-the-wall radar imaging (TWRI) have the advantage of flexibility, high accuracy, and fault tolerance. We propose a modified distributed orthogonal matching pursuit (MDOMP) algorithm with an efficient communication scheme for the sparse scene reconstruction in TWRI applications. The communication costs, computational complexity, and reconstruction performance are analyzed for the proposed algorithm and compared with existing distributed sparse reconstruction methods. Simulated and experimental data are used to demonstrate that the MDOMP provides desirable performance at moderate communication and computation costs.

This special issue addresses various jammers and their effect on different processing stages and overall Global Navigation Satellite System (GNSS) receiver performance, and presents countermeasures and solutions to combat interference.

This paper establishes the role of sparse arrays and sparse sampling in antijam global navigation satellite systems (GNSS). We show that both jammer direction of arrival estimation methods and mitigation techniques benefit from the design flexibility of sparse arrays and their extended virtual apertures or coarrays. Taking advantage of information redundancy, significant reduction in hardware and computational cost materializes when selecting a subset of array antennas without sacrificing jammer nulling or localization capabilities. In addition to the spatial array sparsity, antijam can utilize sparsity of jammers in the spatio-temporal frequency domains. By virtue of their finite number, jammers in the field of view are sparse in the azimuth and elevation directions. For the class of frequency modulated jammers, sparsity is also exhibited in the joint time-frequency signal representation. These spatial and signal characteristics have called for the development of sparsity-aware antijam techniques for the accurate estimation of jammer space-time-frequency signature, enabling its effective sensing and excision. Both theory and simulation examples demonstrate the utility of coarrays, sparse reconstructions, and antenna selection techniques for antijam GNSS.

Conventional space-time adaptive processing suffers from the requirement of a large number of secondary samples. In this paper, a novel method is proposed to accurately estimate the clutter covariance matrix based on a small number of secondary samples, by exploiting the common clutter support across nearby range cells in the angle-Doppler domain. By taking advantage of the intrinsic sparsity of the clutter in the angle-Doppler domain, the recently developed sparse Bayesian learning technique is employed for high-resolution clutter profile estimation. The proposed method does not require the independent and identically distributed secondary sample assumption, and the required number of secondary data samples can be significantly reduced. In addition, we propose a sparse reconstruction-based approach to acquire the 2-D motion parameters of moving targets, by exploiting their group sparsity in the velocity domain in the multistatic passive radar systems. Simulation results verify the effectiveness of the proposed algorithm.

Hermite functions are an effective tool for improving the resolution of the single-window spectrogram. In this paper, we analyze the Hermite functions in the ambiguity domain and show that the higher order terms can introduce undesirable cross-terms in the multiwindow spectrogram. The optimal number of Hermite functions depends on the location and spread of signal auto-terms in the ambiguity domain. We apply and compare several sparsity measures, namely ℓ1norm, the Gini index and the time-frequency concentration measure, for determining the optimal number of Hermite functions, leading to the most desirable time-frequency representation. Among the employed measures, the Gini index provides the sparsest solution. This solution corresponds to a well-concentrated and cross-term reduced time-frequency signature.

In this paper, we consider multipath exploitation and sparse reconstruction in a network of distributed multistatic radar units for stationary target localization behind walls. Multipath exploitation leverages prior information of the indoor scattering environment to eliminate ghosts targets. However, uncertainties in interior wall positions severely impair the effectiveness of multipath exploitation. We develop a multipath signal model for the distributed radar network configuration, which parameterizes the wall locations, and perform joint optimization for simultaneously recovering the target and wall positions. Supporting simulation results are provided, which validate the effectiveness of the proposed method.

For spatially distributed targets encountered in radar and sonar applications, direct application of subspace-based methods usually do not lead to an accurate estimation of the direction and angular extent of the signal arrivals. If the spatial distribution of the targets can be parameterized with a known model a priori, the direction-of-arrival (DOA) estimation problems can be simplified as parameter estimation problems. However, these methods do not apply when the targets are not parameterizable. Motivated by this fact, we propose an effective approach for the DOA estimation of nonparametric spatially extended targets. In the proposed approach, the spatially extended targets are modeled as a continuous sparse structure, which are effectively estimated using the Bayesian compressive sensing techniques based on a paired spike-and-slab prior accounting for the angular target spread. In particular, the problem is examined under a collocated multiple-input multiple-output (MIMO) radar platform. Signal transmission at multiple coprime transmit frequencies are also considered to achieve increased degrees-of-freedom. The group sparsity of the targets across different frequencies is exploited to achieve improved DOA estimation performance.

In this paper, we consider antenna selection and array reconfiguration in the presence of multiple interferences based on the spatial correlation coefficient (SCC) which characterizes the spatial separation between the desired signal and interference subspace. Minimizing the SCC increases the separation between these two subspaces and leads to enhanced beamforming performance. We formulate this problem as a difference of two concave functions, which we solve through the convex-concave procedure (CCP). We derive the lower bound of the SCC as a function of the number of selected antennas which permits us to determine the required number for achieving the desired performance. We suggest two algorithms for implementing the antenna selection and present simulation results to validate the effectiveness of the proposed strategy.

In this paper, we utilize Bayesian Compressive Sensing (BCS) for direction-of-arrival (DOA) estimation based on the coarray. This enables estimation of more sources than the number of physical antennas. We adopt the covariance vectorization technique to construct the received signal vectors of coarrays for both fully and partially augmentable arrays. We then apply the single measurement vector BCS (SMV-BCS) for DOA estimation. Supporting simulation results for both sparse linear arrays and circular arrays demonstrate the effectiveness of the proposed approach in terms of high resolution and estimation accuracy compared to the MUSIC and sparse signal reconstruction based methods.

In this paper, we propose a novel structured compressive sensing algorithm based on non-parametric Bayesian framework for the reconstruction of sparse entries with a continuous structure. A paired spike-and-slab prior is first employed to impose signal sparsity. A logistic Gaussian kernel model, which involves the logistic model and location-dependent Gaussian kernel, is then proposed to encourage the underlying structure of a sparse signal. A closed-form and analytical posterior inference is carried out in a Gibbs sampling scheme. Simulation results demonstrate that the proposed algorithm outperforms existing state-of-the-art sparse Bayesian learning algorithms.

The large diffusion of wireless infrastructures in public and private areas is currently stimulating research on surveillance radar systems capable of exploiting network transmissions as potential sources of opportunity. Since these sources are generally narrowband, we propose in this letter a single-frequency approach for imaging targets by using passive arrays deployed around the scattering scene. Single-frequency data allow casting the imaging as an inverse source problem, which avoids the need to retrieve information about the sources prior to imaging. The drawbacks of the highly coarse resolution and blinding effects due to the sources are overcome by employing a multiarray image fusion strategy in conjunction with a change detection scheme for imaging moving targets. The proposed approach is tested via numerical experiments based on full-wave synthetic data corresponding to an indoor scenario.

Time-frequency (TF) representations are a powerful tool for analyzing Doppler and micro-Doppler signals. These signals are frequently encountered in various radar applications. Data interpolators play a unique role in TF signal representations under missing samples. When applied in the instantaneous autocorrelation domain over the time variable, the low-pass filter characteristic underlying linear interpolators lends itself to cross-terms reduction in the ambiguity domain. This is in contrast to interpolation performed over the lag variable or a direct interpolation of the raw data. We demonstrate the interpolator performance in both the time domain and the time-lag domain and compare it with sparse signal reconstruction, which exploits the local sparsity property assumed by most Doppler radar signals.

In this letter, direction-of-arrival (DOA) estimation of a mixture of coherent and uncorrelated targets is performed using sparse reconstruction and active nonuniform arrays. The data measurements from multiple transmit and receive elements can be considered as observations from the sum coarray corresponding to the physical transmit/receive arrays. The vectorized covariance matrix of the sum coarray observations emulates the received data at a virtual array whose elements are given by the difference coarray of the sum coarray (DCSC). Sparse reconstruction is used to fully exploit the significantly enhanced degrees-of-freedom offered by the DCSC for DOA estimation. Simulated data from multiple-input multiple-output minimum redundancy arrays and transmit/receive co-prime arrays are used for performance evaluation of the proposed sparsity-based active sensing approach.

Antenna array configurations play an important role in direction of arrival (DOA) estimation. In this letter, performance enhancement of DOA estimation is achieved by reconfiguring the multi-antenna receiver through an antenna selection strategy. We derive the Cramer-Rao Bound (CRB) in terms of the selected antennas and associated subarray for both peak sidelobe level (PSL) constrained isotropic and directional arrays in single source cases. Since directional arrays are angle dependent, a Dinklebach type algorithm and convex relaxation are introduced to maintain the optimum selection by adaptively reconfiguring the directional subarrays using semi-definite programming. Simulation results validate the effectiveness of the proposed antenna selection strategy.

Space-time adaptive processing (STAP) is an effective strategy for clutter suppression in airborne radar systems. Limited training data, high computational load and the heterogeneity of training data constitute the main challenges in STAP. In this letter, we propose a new detection strategy based on selecting an optimum subset of antenna-pulse pairs associated with maximum separation between the target and the clutter trajectory. The proposed strategy reduces redundancy while addressing the above three interlinked challenges for detecting slow-moving targets especially in heterogeneous cases. An iterative Min-Max algorithm is proposed to solve the antenna-pulse selection problem, which is NP-hard combinatorial optimization. Extensive simulation results confirm the effectiveness of the proposed strategy.

In this letter, we propose a multi-task compressive sensing algorithm for the reconstruction of clustered sparse entries based on hierarchical Bayesian framework. By extending a paired spike-and-slab prior to a general multi-task model, the proposed algorithm has the capability of modeling both inter-task and intra-task dependencies of the observation data. The latter is achieved by imposing a clustered prior on non-zero entries and finds applications in radar where targets exhibit spatial extent. Simulation results verify that the proposed algorithm outperforms state-of-the-art group sparse Bayesian learning algorithms.

A class of low-complexity compressive sensing-based direction-of-arrival (DOA) estimation methods for wideband co-prime arrays is proposed. It is based on a recently proposed narrowband estimation method, where a virtual array model is generated by directly vectorizing the covariance matrix and then using a sparse signal recovery method to obtain the estimation result. As there are a large number of redundant entries in both the auto-correlation and cross-correlation matrices of the two sub-arrays, they can be combined together to form a model with a significantly reduced dimension, thereby leading to a solution with much lower computational complexity without sacrificing performance. A further reduction in complexity is achieved by removing noise power estimation from the formulation. Then, the two proposed low-complexity methods are extended to the wideband realm utilizing a group sparsity based signal reconstruction method. A particular advantage of group sparsity is that it allows a much larger unit inter-element spacing than the standard co-prime array and therefore leads to further improved performance.

Detection and localization of stationary targets behind walls is primarily challenged by the presence of the overwhelming electromagnetic signature of the front wall in the radar returns. In this paper, we use the discrete prolate spheroidal sequences to represent spatially extended stationary targets, including exterior walls. This permits the formation of a linear block sparse model relating the range profile and observation vectors. Effective wall clutter suppression can then be performed prior to sparse signal image reconstruction. We consider stepped-frequency radar with two cases of frequency measurement distributions over antenna positions. In the first case, the same subset of frequencies is used for each antenna in physical or synthetic aperture arrays, whereas the other case allows different sets of few frequency observations to be available at different antennas. Using experimental data, we demonstrate that the proposed scheme enables sparsity-based image reconstruction techniques to effectively detect and localize behind-the-wall stationary targets from reduced measurements.

Tracking moving targets hidden behind visually opaque structures as building walls is a crucial issue in many surveillance, rescue, and security applications. The electromagnetic waves at the low microwave frequency range penetrate into common building materials and thereby enable the radar to expose behind the wall scene. However, due to complexity of the scattering scenario, the radar signal undergoes multipath propagation phenomena. These typically manifest themselves as environmental clutter which may impair detection and tracking of true targets. In this paper, a signal processing strategy is proposed to track multiple extended targets in a scene by means of a wide-band monostatic through-wall radar. The system collects data sets at regular time steps which are first processed by a microwave tomographic technique. Then, a detection/tracking stage is implemented in order to track the position and dynamics of targets in real time. An extended target-tracking approach is applied to properly exploit at the tracking stage the information related to extended nature of targets. The effectiveness of the proposed signal processing chain is assessed by numerical tests based on full-wave data pertaining to an indoor scenario.

One of the main challenges in through-the-wall radar imaging (TWRI) is the strong exterior wall returns, which tend to obscure indoor stationary targets, rendering target detection and classification difficult, if not impossible. In this paper, an effective wall clutter mitigation approach is proposed for TWRI that does not require knowledge of the background scene nor does it rely on accurate modeling and estimation of wall parameters. The proposed approach is based on the relative strength of the exterior wall returns compared to behind-wall targets. It applies singular value decomposition to the data matrix constructed from the space-frequency measurements to identify the wall subspace. Orthogonal subspace projection is performed to remove the wall electromagnetic signature from the radar signals. Furthermore, this paper provides an analysis of the wall and target subspace characteristics, demonstrating that both wall and target subspaces can be multidimensional. While the wall subspace depends on the wall type and building material, the target subspace depends on the location of the target, the number of targets in the scene, and the size of the target. Experimental results using simulated and real data demonstrate the effectiveness of the subspace projection method in mitigating wall clutter while preserving the target image. It is shown that the performance of the proposed approach, in terms of the improvement factor of the target-to-clutter ratio, is better than existing approaches and is comparable to that of background subtraction, which requires knowledge of a reference background scene.

A new approach for sparse nonstationary signal reconstruction based on multiple windows is introduced. Signals which are localizable in the time-frequency (TF) domain give rise to sparsity in the same domain. When combined, sparse reconstructions, applied to randomly sampled data and corresponding to different selected windows, provide enhanced TF signature estimation. Among possible orthogonal windows, we consider those which characterize the eigen-decomposition of reduced-interference quadratic time-frequency distribution kernels. The highly overlapping TF support of the windows' full-data spectrograms inspires the use of the multiple measurement vectors, in lieu of individual windowed signal recovery. It is shown that the proposed approach outperforms other reconstruction methods when only a single window is applied and is superior to reduced interference time-frequency distributions of random observations.

Through-the-wall radar imaging aims at determining the locations and velocities of obscured targets. The slow velocities of indoor targets are in particular difficult to detect and estimate. It is shown by theoretical considerations and simulation that indirect propagation paths contain significant information on the target movements, which can be utilized for improved sensing. We propose a compressive sensing based method that exploits a multipath model to improve the velocity resolution of the reconstruction. Simulation results demonstrate the effectiveness of the proposed approach.

The problem of estimating motion parameters of multiple closely located ground moving targets in a multistatic passive radar system is considered, with a focus on weak signal conditions. The proposed method provides a means of combining signal energy from all available, spatially separated, illuminators of opportunity to achieve multistatic diversity and overall signal enhancement. The proposed technique is based on sparse signal recovery and exploits a two-step process that sequentially estimates the acceleration and velocity vectors in order to reduce the dimensionality of parameter search space.

An effective complex multitask Bayesian compressive sensing (CMT-BCS) algorithm is proposed to recover sparse or group sparse complex signals. The existing multitask Bayesian compressive sensing (MT-CS) algorithm is powerful in recovering multiple real-valued sparse solutions. However, a large class of sensing problems deal with complex values. A simple approach, which decomposes a complex value into independent real and imaginary components, does not take into account the group sparsity of these two components and thus yields poor recovery performance. In this paper, we first introduce the CMT-BCS algorithm that jointly treats the real and imaginary components, and then derive a fast and accurate algorithm for the estimation of the prior parameters by solving a surrogate convex function. The proposed CMT-BCS algorithm achieves effective complex sparse signal recovery and outperforms MT-CS and complex group Lasso.

In this paper, we propose effective coprime array configurations in which the minimum interelement spacing is much larger than the typical half-wavelength requirement. Such configurations are important in many applications where the half-wavelength requirement cannot be met due to the physical sensors size or to avoid spatial oversampling in wideband operations. The application of such coprime arrays in direction-of-arrival estimations is examined using different algorithms.

We address the problem of detecting building dominant scatterers using a reduced number of measurements with applications to through-the-wall radar (TWR) and urban sensing. We consider oblique illumination, which specially enhances the radar returns from the corners formed by the orthogonal intersection of two walls. This letter uses a novel type of image descriptor, named correlogram, which encodes information about spatial correlation of complex amplitudes of each TWR image pixel. The proposed technique compares the known correlogram of the scattering response of an isolated canonical corner reflector with the correlogram of the received radar signal. The feature-based nature of the proposed detector enables corner separation from other indoor scatterers, such as humans.

Multipath propagation can create ghost targets that severely affect the reconstruction quality of through-the-wall radar images. We propose a compressive sensing (CS) based reconstruction method, which inverts a specular multipath model through exploitation of the structured sparsity in the scene. This allows suppression of the ghost targets and increased signal-to-clutter ratio at the target locations, leading to `clean' images of stationary scenes. Simulation results demonstrate the effectiveness of the proposed approach.

In this paper, we propose co-prime arrays for effective direction-of-arrival (DOA) estimation. To fully utilize the virtual aperture achieved in the difference co-array constructed from a co-prime array structure, sparsity-based spatial spectrum estimation technique is exploited. Compared to existing techniques, the proposed technique achieves better utilization of the co-array aperture and thus results in increased degrees-of-freedom as well as improved DOA estimation performance.

Over-the-horizon radar (OTHR) systems provide wide-area surveillance capabilities to detect and track targets far beyond the range of conventional line-of-sight radars. Because of the narrowband waveforms, OTHR systems do not achieve reliable altitude estimation. In this paper, we develop a new technique to track the instantaneous altitude of maneuvering targets by exploiting the estimated multi-component Doppler signatures. The main contribution of this paper is to apply effective non-stationary signal analysis for estimating the time-varying Doppler signature of each individual multipath, which is then applied to an extended Kalman filter to reliably track the instantaneous target altitude.

A two-stage fuzzy image fusion approach, which combines multiple radar images of the same scene, is proposed to produce a more informative image. In this approach, two different image fusion methods are first applied. Then, a fuzzy logic fusion method is applied to the outputs of the first fusion stage. The performance of the proposed approach is evaluated on through-the-wall radar images obtained using different polarizations. Experimental results show that the proposed approach enhances image quality by producing outputs with high target intensity values and low clutter.

The L-estimate transforms and time-frequency representations are presented within the framework of compressive sensing. The goal is to recover signal or local auto-correlation function samples corrupted by impulse noise. The signal is assumed to be sparse in a transform domain or in a joint-variable representation. Unlike the standard L-statistics approach, which suffers from degraded spectral characteristics due to the omission of samples, the compressive sensing in combination with the L-estimate permits signal reconstruction that closely approximates the noise free signal representation.

We consider sparsity-driven change detection (CD) for human motion indication in through-the-wall radar imaging and urban sensing applications. Stationary targets and clutter are removed via CD, which converts a populated scene into a sparse scene of a few human targets moving inside enclosed structures and behind walls. We establish appropriate CD models for various possible human motions, ranging from translational motions to sudden short movements of the limbs, head, and/or torso. These models permit scene reconstruction within the compressive sensing framework. Results based on laboratory experiments show that a sizable reduction in the data volume is achieved using the proposed approach without a degradation in system performance.

Compressive sensing (CS) for urban operations and through-the-wall radar imaging has been shown to be successful in fast data acquisition and moving target localizations. The research in this area thus far has assumed effective removal of wall electromagnetic backscatterings prior to CS application. Wall clutter mitigation can be achieved using full data volume which is, however, in contradiction with the underlying premise of CS. In this paper, we enable joint wall clutter mitigation and CS application using a reduced set of spatial-frequency observations in stepped frequency radar platforms. Specifically, we demonstrate that wall mitigation techniques, such as spatial filtering and subspace projection, can proceed using fewer measurements. We consider both cases of having the same reduced set of frequencies at each of the available antenna locations and also when different frequency measurements are employed at different antenna locations. The latter casts a more challenging problem, as it is not amenable to wall removal using direct implementation of filtering or projection techniques. In this case, we apply CS at each antenna individually to recover the corresponding range profile and estimate the scene response at all frequencies. In applying CS, we use prior knowledge of the wall standoff distance to speed up the convergence of the orthogonal matching pursuit for sparse data reconstruction. Real data are used for validation of the proposed approach.

This paper addresses the problem of combining multiple radar images of the same scene to produce a more informative composite image. The proposed approach for probabilistic fuzzy logic-based image fusion automatically forms fuzzy membership functions using the Gaussian-Rayleigh mixture distribution. It fuses the input pixel values directly without requiring fuzzification and defuzzification, thereby removing the subjective nature of the existing fuzzy logic methods. In this paper, the proposed approach is applied to through-the-wall radar imaging in urban sensing and evaluated on real multi-view and polarimetric data. Experimental results show that the proposed approach yields improved image contrast and enhances target detection.

Although partial relay selection (PRS) for amplify-and-forward relay systems requires only the knowledge of source-relay (S-R) channels, in general, it incurs a significant performance loss. In cooperative systems with all single-antenna nodes, irrespective of the number of relays, the diversity order of PRS is limited to only one. This paper proposes a novel relay selection method for improving the performance of PRS scheme. In particular, as in the conventional PRS scheme, the relay that gives the best first-hop signal-to-noise ratio (SNR) is selected. However, this selection is made from only a subset of relays, for which the corresponding S-R and relay-destination (R-D) links are not in outage. An R-D link is considered to be in outage if its SNR is below the predefined threshold value of the end-to-end SNR plus some adjustable margin. The additional overhead required for implementing the proposed scheme is comparable to that of the conventional PRS method. For conciseness and better exposition of the proposed method, we limit our theoretical analysis to a system with two to three relays. The exact expressions of the end-to-end outage probability are derived and it is shown that full diversity order is achieved. Simulation results verify theoretical analysis and show that the proposed method significantly outperforms the conventional PRS method. Moreover, the results demonstrate that, for properly selected margin, the performance of the proposed method is very close or comparable to the method with full channel state information.

This paper investigates performance limits of a two-hop multi-antenna amplify-and-forward (AF) relay system in the presence of a multi-antenna energy harvesting receiver. The source and relay nodes of the two-hop AF system employ orthogonal space-time block codes for data transmission. We derive joint optimal source and relay precoders to achieve different tradeoffs between the energy transfer capability and the information rate, which are characterized by the boundary of the so-called rate-energy (R-E) region. Numerical results demonstrate the effect of different parameters on the boundary of the R-E region.

Multipath signals arise in many active sensing modalities, such as radar and sonar. Moving targets cause Doppler effects that could vary for different paths. Target Doppler information corresponding to direct and non-direct paths is important for moving target localizations and classifications, particularly when narrowband signals are involved. This information, however, becomes difficult to reveal when dealing with nonlinear time-varying multi-component Doppler signals. In this paper, we introduce a new time-frequency analysis technique based on the local phase information to accurately extract complex Doppler signature of each signal arrival. This is achieved through short-time polynomial phase modeling of data segments. The global behavior is obtained by fusion of the phases across neighboring segments using the data phase continuity property. The offering of the proposed technique is demonstrated using synthetic data in an over-the-horizon radar platform.

In this paper, we propose a Gausssian-Rayleigh mixture modeling approach to segment indoor radar images in urban sensing applications. The performance of the proposed method is evaluated on real 2D polarimetric data. Experimental results show that the proposed method enhances image quality by distinguishing between target and clutter regions. The proposed method is also compared to an existing Neyman-Pearson (NP) target detector that has been recently devised for through-the-wall radar imaging. Performance evaluation of both methods shows that the proposed method outperforms the NP detector in enhancing the input images.

In this paper, we consider ultrasound imaging of flaws in a metallic alloy where the presence of strong bottom surface reflection and other interference signals constitutes a challenging problem. A subspace-based approach is developed for removing, or significantly reducing, bottom surface reflections to enhance ultrasound imaging. In constructing the surface reflection, or clutter, subspace, we account for rough surface scatterings which, due to various possible propagation time delays between the transmitter and receiver, expand the subspace dimension beyond that corresponding to ideal propagation. We also estimate and compensate, using signal correlation methods, for changes in the same time delays due to imperfect sensor displacements on the top surface of the alloy. Experimental results show that substantial clutter suppression can be achieved with negligible effects to the flaw signals.

The source and relay precoders are jointly optimized for an amplify-and-forward multiple-input multiple-output relay system. Both the source and relay nodes employ orthogonal space-time block codes (OSTBC), and have imperfect channel state information of the source-relay and relay-destination channels, respectively. Using the worst-case robust design approach, we show that the problem of maximizing the minimum signal-to-noise ratio at the destination can be exactly reformulated as a convex optimization problem. Further, we provide an approximate semi-analytical approach which significantly reduces the computational cost of solving the convex problem. Numerical results show that this approximation is accurate and the proposed design outperforms OSTBC with eigen beamforming, OSTBC with equal power allocation, and currently available worst-case robust beamforming design without OSTBC.

Anti-jamming techniques are critical to maintain the integrity and functionality of GPS systems in various applications. One of the major problems with existing array-based anti-jamming GPS receivers is the errors introduced in the carrier phase, affecting the GPS solution. In this letter, we propose a novel anti-jamming GPS receiver structure that preserves the GPS signal phase continuity. The effectiveness of the proposed technique is verified by simulation results.

We consider the problem of through-the-wall radar imaging (TWRI), in which polarimetric imaging is used for automatic target detection. Two generalized statistical detectors are proposed which perform joint detection and fusion of a set of multipolarization radar images. The first detector is an extension of a previously proposed iterative target detector for multiview TWRI. This extension allows the detector to automatically adapt to statistics that may vary, depending on target locations and electromagnetic-wave polarizations. The second detector is based on Bayes' test and is of interest when target pixel occupancies are known from, e.g., secondary data. Properties of the proposed detectors are delineated and demonstrated by real data measurements using wideband sum-and-delay beamforming, acquired in a semicontrolled lab environment. We examine the performance of the proposed detectors when imaging both metal objects and humans.

Space-time block code designs based on algebraic field extension for full rate, large diversity product, and nonvanishing minimum determinant of codewords have received great attention. There are many different types of codes available for two-transmitter antennas, such as cyclotomic space-time block codes, the golden space-time block code, and rotation-based space-time block codes. In this paper, a more general space-time block code design scheme, which is called quadratic space-time block coding, is proposed for the two-transmitter antennas using quadratic field extension. The optimal design of the quadratic space-time block codes in terms of a diversity product criterion is also presented. It is shown that the optimal quadratic space-time block codes designed in this paper do not belong to the existing space-time block code family such as the cyclotomic, golden, and rotation-based space-time block codes. The simulation results demonstrate that the average codeword error rate of the optimal quadratic space-time block code attains about 0.5 dB signal to noise ratio gain over those of the optimal cyclotomic and golden space-time block codes.

We consider the problem of detecting targets behind walls using radar imaging technology. An image-domain based detection technique is proposed that allows to adapt to specific targets of interest. By doing so, clutter as well as targets of no-interest are strongly reduced in the radar image. The proposed detector is automatic in the sense that no or only little prior knowledge on the image statistics is required. The detection procedure is detailed, including the choice of suitable optimality criteria. The evaluation of the proposed technique is performed using data collected from Through-the-Wall radar imaging experiments whereby we specifically consider on the detection of humans.

An approach to multiwindow time-frequency analysis that provides robust performance in noisy environment is proposed. The concept of robust estimates of instantaneous frequency is used to define the optimal weighting coefficients for the multiwindow spectrogram. The proposed form of multiwindow spectrogram provides improved instantaneous frequency estimation for nonstationary signals in the presence of additive Gaussian noise. The efficiency of the proposed approach is tested in the experiments.

We establish the multipath model which encompasses the target and its multipath “ghosts” in urban and through-the-wall synthetic aperture radar (SAR). The focused downrange and crossrange locations of multipath ghosts are derived and validated using numerical and experimental data. The multipath model permits an implementation of a multipath exploitation algorithm, which maps each target ghost to its corresponding true target location. In doing so, the proposed algorithm improves the radar system performance by aiding in ameliorating the false positives in the original SAR image as well as increasing the SNR at the target locations, culminating in enhanced behind the wall target detection and localization.

This paper addresses the problem of Through-the-Wall Radar Imaging (TWRI) using the Multiple-Measurement Vector (MMV) compressive sensing model. TWR image formation is reformulated as a compressed sensing (CS) problem, seeking a sparse representation in the spatial domain. In traditional CS-based through-the-wall radar imaging (TWRI) methods, the measurement matrix is vectorized so that a single measurement vector (SMV) model is applied to generate a sparse solution, which represents a scene comprising point-like targets. For multiple measurement TWRI problems, the SMV model may produce a sub-optimum sparse solution. On the other hand, the proposed MMV model for TWRI generates a more sparse scene by processing all the measurements simultaneously. To evaluate the effectiveness of the proposed method, it is applied to fuse multiple polarization data to form the radar image. Based on simulated data with different number of measurements and noise levels, the proposed MMV-based TWRI method produces better TWR images in terms of image quality and detection accuracy.

In this paper we consider the exploitation of spatial time-frequency distribution (STFD) in multiple-input multiple-output (MIMO) radar systems. STFD has been found useful in solving various array processing problems, such as direction finding and blind separation, where nonstationary signals are involved. Such treatment has been primarily limited to traditional array processing whereas its use in MIMO radar scenario has received less attention. The emphasis of this paper lies in the reexamination of the STFD framework in an MIMO radar platform for the processing of maneuvering targets with nonstationary signatures. Within this framework, we consider the use of joint transmit and receive apertures for the enhancement and improved estimation of time-frequency signature and the application of STFD in joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimations. As a result, it becomes clear that STFD is effective in MIMO radar processing when the targets are of signatures that are highly localized in the time-frequency domain.

We derive a multipath model for sensing through walls using radars. The model considers propagation through a front wall and specular reflections at interior walls in an enclosed room under surveillance. The model is derived such that additional eigenrays can be easily accommodated. A synthetic aperture radar (SAR) system is considered, and stationary or slowly moving targets are assumed. The focused downrange and crossrange locations of multipath ghosts are established and validated using numerical, as well as experimental data. The multipath model permits an implementation of a multipath exploitation algorithm, which associates, as well as maps, each target ghost back to its corresponding true target location. In doing so, the proposed algorithm improves the radar system performance by aiding in ameliorating the false positives in the original SAR image, as well as increasing the signal-to-clutter ratio at the target locations, culminating in enhanced behind the wall target detection and localization.

This paper deals with the problem of automatic target classification or Through-the-Wall radar imaging. The proposed scheme considers stationary objects in enclosed structures and works on the SAR image rather than the raw data. It comprises segmentation, feature extraction based on superquadrics, and classification. We present a recursive splitting tree to obtain optimum parameters for feature extraction. Support vector machines and nearest neighbor classifiers are then applied to successfully classify among different indoor targets. The classification methods are tested and evaluated using real data generated from synthetic aperture Through-the-Wall radar imaging experiments.

The problem of distributed detection and decision fusion in Through-the-Wall Radar Imaging (TWRI) is considered. We deal with the multi-viewing case in which images corresponding to different radar locations can be collected. We present a method to adapt conventional distributed detection schemes to the scenario when no a priori knowledge about image statistics from any view is available. Further, a new scheme for estimating quality information of local detectors in a distributed detection scenario is proposed. We apply bootstrap techniques to draw inference from the radar measurements of the behind the wall scene. Simulation results as well as experimental data are used to demonstrate the performance of the proposed approach.

There are increasing demands on Through-the-Wall Radar Imaging (TWRI) systems to deliver high resolution images in both range and cross range. This requires using wideband signals and large array apertures, respectively. Wideband signals are typically implemented by transmitting a series of the narrowband signals. As such, the TWRI system operation involves transmitting and receiving multiple step-frequencies at each antenna location in either a physical or a synthetic aperture radar. Compressive sensing (CS) is an effective approach for decreasing the number of samples and, subsequently, reducing the data acquisition and post-processing time. In this paper, we propose a TWRI scheme based on CS in which a sizable reduction in the number of samples along the frequency axis is achieved without significant degradation in the image. The proposed approach applies the well-known Fourier-like measurement matrix and generates radar images of almost the same desirable quality as the image employing all data samples.

This paper deals with waveform design for improved detection and classification of targets behind walls and enclosed structures. The target impulse response is incorporated in an optimum design of the transmitted waveform which aims at maximizing the signal-to-interference and noise ratio (SINR) at the receiver output. The interference represents signal-dependent clutter which, along with the wall, degrades the receiver performance compared to the free-space and zero-clutter case. Computer simulations show sensitivity of the optimum waveform to target orientation but depict an SINR enhancement over chirped waveform radar emissions at all aspect angles. Numerical electromagnetic modeling is used to provide the impulse response of typical indoor stationary targets, namely, tables, chairs, and humans.

This paper considers the maximization of the sum capacity of a multiuser cooperative wireless network through the joint optimization of power allocation among source nodes and distributed beamforming weights across the relay nodes. The distributed beamforming techniques offer the capability of enhancing the sum network capacity by achieving spatial multiplexing to support concurrent communications of multiple source-destination pairs. In this paper, we consider a two-hop cooperative wireless network consisting of single-antenna nodes in which multiple concurrent links are relayed by a number of cooperative nodes. When a large number of relay nodes are available, the channels of the different source-destination pairs can be orthogonalized, yielding enhanced sum network capacity. Such an advantage is particularly significant in high signal-to-noise ratio (SNR) regime, in which the capacity follows a logarithm law with the SNR, whereas exploiting spatial multiplexing of multiple links yields capacity increment linear to the number of users. However, the capacity performance is compromised when the input SNR is low and/or when the number of relay nodes is limited. Joint optimization of source power allocation and distributed relay beamforming is important when the input SNR and/or the number of relay nodes are moderate or wireless channels experience different channel variances. In these cases, the joint optimization of source power and distributed beamforming weights achieves significant capacity increment over both source selection and equal source power spatial multiplexing schemes.

We consider the problem of target detection in Through-the-wall Radar Imaging when no a priori knowledge about the image statistics is available. An iterative approach which adapts itself to the unknown image statistics and thus allows for automatic target detection is presented. Two variants, based on 2D median filtering and morphological operations, are described in details. The proposed detection schemes are tested using experimental data, considering the problem of 3D reconstruction of a scene hidden behind a concrete wall.

Carrier diverse radars employing two different frequencies, termed as dual-frequency radars, prove effective in determining the target range in urban sensing and through-the-wall applications. In this paper, we derive the maximum likelihood (ML) estimator for the dual frequency radar returns for a micro-Doppler motion profile, which is commonly exhibited by indoor moving targets. Unlike linear models, the respective ML estimator does not have a closed form. We solve the ML estimator for dual frequency radar operations, using iterative reweighted least squares (IRLS). The ML-IRLS algorithm is applied to experimental radar returns for estimating the motion parameters of indoor targets.

Accurate target localization is an important task in various commercial and military applications. One way to achieve this goal is to use the time-of-arrival (TOA) or time-delay-of-arrival (TDOA) information observed at multiple distributed sensors. On the other hand, there is a great need to use moving sensors to form a radar platform with synthetic apertures. In this paper, we consider the problem of target localization based on the range information estimated from two-way time-of-flight (TW-TOF) at multiple synthetic array locations, where the position of these synthetic array locations is subject to certain random errors. The nonconvex estimation problem is approximated by a convex optimization problem using the semidefinite relaxation (SDR) approach. Simulation results show that the proposed estimator provides mean square position error performance close to the Cramer-Rao lower bound.

The 15 papers in this special issue focus on remote sensing of building interior and can be categorized into: 1) system design and instrumentation; 2) advanced imaging techniques for elimination of glint from large flat wall structures; 3) radar polarimetry; 4) passive microwave radiometry; 5) advanced forward models based on high-frequency methods as well as full-wave solutions based on finite-difference time-domain technique for large-scale problems; and 6) detection and identification techniques of behind the wall stationary and moving concealed and unconcealed targets.

A detector of targets behind walls and in enclosed structures is presented. The detector is applied to through-the-wall radar images obtained by wideband delay and sum beamforming. We consider the detection problem using single- and multiple-view imaging. The statistics of noise, clutter, and target images are examined and formulated using sample scenes. The effects of wall parameter errors on the image statistics are shown. An iterative detection scheme, which adapts itself to the image statistics, is presented. The proposed detection schemes are evaluated using real data.

Radio-frequency imaging of targets behind walls is of value in several civilian and defense applications. Wall reflections are often stronger than target reflections, and they tend to persist over a long duration of time. Therefore, weak and close by targets behind walls become obscured and invisible in the image. In this paper, we apply spatial filters across the antenna array to remove, or at least significantly mitigate, the spatial zero-frequency and low-frequency components which correspond to wall reflections. Unmasking the behind-the-wall targets via the application of spatial filters recognizes the fact that the wall electromagnetic (EM) responses do not significantly differ when viewed by the different antennas along the axis of a real or synthesized array aperture which is parallel to the wall. The proposed approach is tested with experimental data using solid wall, multilayered wall, and cinder block wall. It is shown that the wall reflections can be effectively reduced by spatial preprocessing prior to beamforming, producing similar imaging results to those achieved when a background scene without the target is available.

We present a constant-false alarm rate detection scheme for use in Through-the-Wall Radar Imaging. We consider multiple-viewing scenarios with an arbitrary number of vantage points. Classical detection theory is used to fuse the obtained radar images to one reference image. By doing so, clutter and noise artifacts which are strongly represented in the individual images are reduced and targets of interest are more clearly visible.

An important task in urban sensing applications is to accurately localize moving and vibrating targets in the presence of significant background clutter. A dual-frequency CW radar, which estimates the range of a target based on the phase difference between two closely spaced frequencies, has been shown to be a cost-effective approach for range estimation of a moving target. Previous work has shown that the use of Fourier transform and time-frequency analysis techniques provides an estimate of Doppler signature and enhanced signal-to-noise ratio (SNR), thereby enabling the range estimation of moving targets and significantly improving the estimation accuracy. In this paper, we consider the combined use of these technologies with a synthetic aperture array for the localization of inanimate moving targets. The synthetic array aperture provides the capability of high-resolution spatial localization of inanimate moving targets, as well as determining the orientation of the rotation or vibration.

Multibeam antennas (MBAs) can be used in ad hoc networks to improve throughput performance as a result of increased spatial reuse and extended coverage. For random access scheduling (RAS) protocol, contention resolution is required to overcome the potential collisions. Multipath propagation increases the contention, particularly when an MBA is implemented using the multiple fixed-beam antenna (MFBA) technique. It is desirable to incorporate priority-based channel access scheduling (CAS) into RAS for contention resolution and service differentiation. In this paper, we introduce two priority-based CAS algorithms for contention resolution respectively in single-path and multipath propagation environments, and analyze the one-hop throughput performance of the CAS schemes in an analytical framework. The impact of both quasi-stationary multipath propagation and the CAS algorithms is rigourously examined.

Through-the-wall imaging and urban sensing is an emerging area of research and development. The incorporation of the effects of signal propagation through wall material in producing an indoor image is important for reliable through-the-wall mission operations. We have previously analyzed wall effects, such as refraction and change in propagation speed, and designed a wideband beamformer for 2D imaging using line arrays. In this letter, we extend the analysis to 3D imaging via delay-and-sum beamforming in the presence of a single uniform wall. The third dimension provides valuable information on target heights that can be used for enhancing target discrimination/identification. Supporting simulation results are provided.

A dual-frequency radar, which estimates the range of a target based on the phase difference between two closely spaced frequencies, has been shown to be a cost-effective approach to accomplish both range-to-motion estimation and tracking. This approach, however, suffers from two drawbacks: it cannot deal with multiple moving targets, and it has poor performance in noisy environments. In this letter, we propose the use of time-frequency signal representations to overcome these drawbacks. The phase, and subsequently the range information, is obtained based on the moving target instantaneous Doppler frequency law, which is provided through time-frequency signal representations. The case of multiple moving targets is handled by separating the different Doppler signatures prior to phase estimation.

In this paper, we efficiently solve the maximum likelihood (ML) time-delay estimation problem for GNSS signals in a multipath environment. Exploiting the GNSS signal model structure and the spreading code periodicity, we develop an efficient implementation of the Newton iterative likelihood maximization method by finding simple analytical expressions for the first and second derivatives of the likelihood function. The proposed fast iterative ML algorithm (FIMLA) for timedelay estimation, which uses the correlation function of the received signal with its local replica, is shown to be an attractive technique for mitigation of closely-spaced multipath arrivals. For the future modernized GPS and the European Galileo signals based on binary offset carrier (BOC) waveforms, the correlation function has multiple positive and negative peaks leading to potential tracking ambiguities. Instead of the standard crosscorrelation, we propose an implementation characterized by a different choice of the local replica so as to cancel the sub-carrier phase, thus eliminating ambiguities. The asymptotic performance of FIMLA is analyzed by deriving the corresponding Cramer-Rao bound (CRB). Representative simulation examples are included to illustrate the FIMLA is performance for delay estimations in the presence of multipath for both C/A code and BOC signals.

Recently, distributed space-time code designs with high cooperative diversity for wireless communication networks, such as ad hoc and sensor networks, have received much attention. Amplify forward and decoding forward are widely used protocols for the cooperative diversity in the wireless communication networks. In both protocols, the information received by relay terminals are "forwarded" to destination or next relay terminals. Since the signals transmitted by relay terminals and those transmitted from the source terminal are correlated, there is information redundancy. To improve the energy efficiency of cooperative networks, we propose an encoding protocol, which is referred to as a nested cooperative encoding protocol. In our proposed protocol, the received signal at each relay terminal is divided into several sub-signals with the nest lattice structure of source information. Each of the sub-signals contains only a partial information with a smaller size of constellation compared to the original information sent by the source terminal. Do a new encoding or modulation by using these sub-signals before transmitting at relay terminals. It is shown that the proposed new protocols can achieve both high cooperative diversity and high energy efficiency.

A wideband synthetic aperture radar system based on beamspace Capon beamforming is presented for urban sensing applications. Various effects of signal propagation through building materials are incorporated into the beamformer design. Proof of concept is provided using real data collected in a laboratory environment. Comparison between data-independent and scene-dependent beamformers is provided. The results show that the beamspace Capon beamformer outperforms the nonadaptive delay-and-sum beamformer.

This work deals with the estimation of near-field parameters using passive sensor arrays. A transformation of the array data is proposed which allows the extraction of near-field time-frequency signatures from data containing a mixture of far- and near-field sources. Spatial time-frequency distribution matrices are then used as a means for solving the near-field parameter estimation problem. The estimation accuracy of the proposed approach is compared to existing methods via simulation analysis. An experimental validation of theoretical ideas is also presented.

Signal multipath in GPS leads to undesirable tracking errors and inaccurate ranging information. The extent of the tracking error in compromising the receiver performance depends on the multipath amplitude, delay, and phase relative to the direct path. The coherent discriminator and the noncoherent early-minus-late power discriminator offer different tracking accuracy and sensitivity to multipath parameters. In this paper, we develop analytical expressions of the average performance of the two discriminators over the multipath phase distribution and other propagation channel variables.

In this paper, we introduce an optimal robust beamformer for detecting a desired signal in presence of noise, strong interferers of unknown directions-of-arrival (DOA), and multipath. The proposed approach achieves the highest possible signal-to-interference plus noise ratio (SINR) by optimally estimating the interference DOA, followed by a triply constrained robust Capon beamformer. More specifically, we maximize the SINR subject to nulling strong interferers and offer robustness against multipath and steering vector uncertainty. Unlike existing techniques, we examine explicitly the use of robust beamforming for multipath mitigation to enhance acquisition and tracking performance of GPS receivers.

In this paper, statistical bounds on dual-frequency range estimations are provided. Single frequency (Doppler) radars cannot be used in range estimation due to their range ambiguities. An additional frequency can be used to increase the maximum unambiguous range to accepted values for indoor range estimation of moving targets. The dual-frequency approach offers the benefit of reduced complexity, fast computation time, and real time target tracking. Indoor inanimate objects such as fans, vibrating machineries, and clock pendulums exhibit simple harmonic motions, whereas animate translation movements are typically linear. We provide Cramer-Rao bounds for the parameters defining both types of motions and show their dependency on the observation period and partial knowledge of motion and noise parameters.

The quality and reliability of through-the-wall radar imagery is governed, among other things, by the knowledge of the wall characteristics. Ambiguities in wall characteristics smear and blur the image, and also shift the imaged target positions. An autotechnique, b ased on higher order statistics, i s presented which corrects for errors under unknown walls. Simulation results show that the proposed technique provides high-quality focused images with target locations in close proximity to true target positions.

It is well known that a multiple-input-multiple-output (MIMO) system can provide spatial diversity gain as well as spatial multiplexing capability. The MIMO concent has been extended to cooperative wireless networks to form distributed MIMO systems using virtual antennas located at cooperating terminals. The primary interest of cooperative MIMO networks, however, has been focused on the cooperative diversity (C-DIV) approaches to achieve spatial diversity gain. Recent work proposed cooperative spatial multiplexing (C-SM) to simplify the transmit and receive processing requirement on the relay nodes while providing significant energy savings. So far C-SM has been only considered for single-hop relaying. In this paper, we propose the use of multi-hop relaying C-SM systems for transmit energy reduction and performance improvement.

An estimator for the phase parameters of mono- and multi-component FM signals, with both good numerical properties and statistical performance is proposed. The proposed approach is based on the Hough transform of the pseudo Wigner-Ville time-frequency distribution (PWVD). It is shown that the numerical properties of the estimator may be improved by varying the PWVD window length. The effect of the window time extent on the statistical performance of the estimator is delineated. Experimental data is used for validation of statistical properties

An interactive software written in Visual C# has been developed to provide real-time simulation capabilities for imaging behind the wall scenes. The software implements algorithms and techniques developed by the researchers at the Center for Advanced Communications in Villanova University, but is also amenable to house other imaging approaches. The software features a user friendly and flexible graphical interface that permits easy and interactive scene construction, from specification of the wall and array element locations to placement of objects at various locations behind the wall. All operations are performed using comprehensible dialog boxes and mouse drag-and-drop actions. For illustration, we present an example that demonstrates the usage of the real-time through-the-wall imaging radar simulator. The software serves as an educational tool for courses on radar imaging, introducing the students to the important emerging technology of through-the-wall imaging

In this paper, a novel multipath parameters estimation approach for GPS receivers using the maximum likelihood (ML) principle is proposed. Exploiting the replication property of the GPS C/A code within each symbol, we develop a coherent preprocessing approach based on a sample mean model. This model employs long integration time that improves the SNR and enhances receiver robustness against interference and weak signal effects. It also allows a simplified expression for the likelihood function which facilitates the use of computationally efficient iterative techniques for solving the complex ML optimization problem. In the proposed approach, the ML estimator is iteratively computed using the fast and low-complexity SAGE (Space-Alternating Generalized Expectation Maximization) algorithm. The proposed scheme is a candidate for indoor GPS navigation, as demonstrated by computer simulations.

We consider the problem of direction finding for nonstationary signals impinging on an array of sensors. Making use of a time-frequency representation of the data, we are able to exploit the non-stationary nature of the source signals. We employ a generalized Hough transform to estimate the time-frequency signature of each source. The proposed method also allows direction finding when there are more sources than the number of array sensors.

In this paper, we propose a known-host-state methodology for designing image watermarks that are particularly robust to compression. The proposed approach outperforms traditional spread spectrum watermarking across all JPEG quality factors. The fundamental approach uses 2D chirps as spreading functions, followed by a chirp transform, to recover the watermark. Because this method can spectrally shape the chirp to match image content and JPEG quantization, its performance is greatly enhanced. The energy localization of the chirp is exploited to embed low power watermark per image blocks while maintaining reliable detection performance.

This paper presents an approach for tracking nonstationary moving sources with both time-varying directions-of-arrival (DOA) and time-varying polarization signatures. The proposed approach is based on the spatial polarimetric time-frequency distributions (SPTFD). Unlike the conventional correlation matrix based approaches that sacrifice the source signal polarization properties and are not properly structured to utilize polarization diversity, the proposed approach uses the signal instantaneous polarization and instantaneous frequency information for improved target tracking and polarization estimation.

We propose an anti-jam GPS receiver which suppresses interference by projecting the received signal on the noise subspace obtained via subspace tracking. The resulting interference-free signal is then processed by a beamformer, whose weight vector is obtained by maximizing the signal-to-noise ratio at the beamformer output. It is shown that the proposed receiver can effectively eliminate interference and enhance the GPS signals at the receiver output.

This paper considers interference suppression and multipath mitigation in Global Navigation Satellite Systems (GNSSs). In particular, a self-coherence anti-jamming scheme is introduced which relies on the unique structure of the coarse/acquisition (C/A) code of the satellite signals. Because of the repetition of the C/A-code within each navigation symbol, the satellite signals exhibit strong self-coherence between chip-rate samples separated by integer multiples of the spreading gain. The proposed scheme utilizes this inherent self-coherence property to excise interferers that have different temporal structures from that of the satellite signals. Using a multiantenna navigation receiver, the proposed approach obtains the optimal set of beamforming coefficients by maximizing the cross correlation between the output signal and a reference signal, which is generated from the received data. It is demonstrated that the proposed scheme can provide high gains toward all satellites in the field of view, while suppressing strong interferers. By imposing constraints on the beamformer, the proposed method is also capable of mitigating multipath that enters the receiver from or near the horizon. No knowledge of either the transmitted navigation symbols or the satellite positions is required.

Bilinear synthesis of nonstationary signals impinging on a multi-antenna receiver has been recently introduced. The distinction in the spatial signatures of the sources provides a vehicle to reduce noise and source signal interactions in the time-frequency domain, and hence improves signal synthesis. In addition to the spatial domain information, we utilize polarization diversity for enhanced source time-frequency signal representations. It is shown that dual-polarization antennas call be used to mitigate cross-terms via combined spatial and polarization averaging. Significant reduction in cross-terms can be realized by providing large spatial diversity, large polarization diversity, or combined moderate values of the respective spatial and polarization correlations.

An enhanced technique for estimating the range and direction-of-arrival (DOA) of narrowband near-field sources is presented. This technique utilizes fourth-order cumulants of the received signal across an array of two orthogonally polarized sensors. It is shown that the incorporation of the source polarization in an ESPRIT-based angle and range estimation technique provides improved performance over the case where the polarization information is absent in the problem formulation.

This paper considers the problem of interference suppression in GPS coarse/acquisition (C/A) signals. Particularly, an anti-jam receiver is developed, utilizing the unique repetitive feature of the GPS C/A-signal. The proposed receiver does not require the knowledge of the transmitted GPS symbols or the satellite positions. It utilizes the repetition of the Gold code within each navigation symbol to simultaneously suppress the interference of all satellites.

Bilinear synthesis of nonstationary signals impinging on a multiantenna receiver has been recently introduced. The distinction in the spatial signatures of the sources provides a vehicle to reduce noise and source signal interactions in the time-frequency domain, and hence improves signal synthesis. In this letter, we utilize another form of diversity for enhanced source time-frequency signal representations. It is shown that cross-polarization antennas can be used to mitigate cross terms via simple polarization averaging.

We propose a blind separation technique for nonstationary sources that exploits both auto-terms and cross-terms of the time-frequency distributions. The technique is based on the simultaneous joint diagonalization and off-diagonalization of spatial time-frequency distributions. Computer simulations demonstrate the superiority of the approach in comparison with other time-frequency based methods.

A novel high-resolution time-frequency representation method is proposed for source detection and classification in over-the-horizon radar (OTHR) systems. A data-dependent kernel is applied in the ambiguity domain to capture the target signal components, which are then resolved using the root-MUSIC based coherent spectrum estimation. This method is particularly effective to analyze a multi-component signal with time-varying time-Doppler signatures. By using the different time-Doppler signatures embedded in the multipath signals, this proposed method can reveal important target maneuvering information, whereas other linear and bilinear time-frequency representation methods fail.

A coarray-based synthetic aperture beamformer using stepped-frequency signal synthesis and post-data acquisition processing is presented for wideband imaging of near-field scenes. The proposed beamformer formulation and implementation finds key applications in through-the-wall microwave imaging and landmine detection problems. While coarray techniques offer significant reduction in array elements for a given angular resolution, stepped-frequency realization of wideband systems simplifies implementation and offers flexibility in beamforming. Proof of concept is provided using real data collected in an anechoic chamber.

The problem of nonstationary signal detection using antenna arrays is considered. A method for detecting source signal auto-term regions in the time-frequency plane is presented, based on spatial time-frequency distribution (STFD) matrices. A general signal detection framework when using arbitrary time-frequency kernels is proposed and the trace of a whitened STFD matrix is used to form an appropriate test statistic. The expressions for the mean and variance of the statistic, necessary to evaluate the test, are provided. The detector performance using the Wigner-Ville distribution is investigated via simulated and theoretical results.

In over-the-horizon radar (OTHR) target detection, the signal-to-clutter ratio (SCR) is very low, typically from -50 dB to -60 dB. Furthermore, for maneuvering targets, such as aircraft and missiles, Doppler frequencies of their radar return signals may be time-varying. In this case, the Fourier transform based techniques and super resolution spectrum estimation techniques may not work well since they use sinusoidal signal models. We propose a signal subspace clutter rejection algorithm combined with an adaptive chirplet transform technique for maneuvering target detection with OTHR. Simulation results of adding simulated maneuvering targets into raw OTHR clutter data are presented to illustrate the effectiveness of the proposed algorithm. The simulation results show that moving targets with -53.5 dB SCR can be detected.

This paper considers applying the minimum mean square error (MMSE) criterion on the detection for space time coded multicarrier CDMA (STC-MC-CDMA) systems in frequency selective environments. In particular, we consider the Alamouti's space-time coding scheme that involves two transmit antennas. To acquire the channel information needed by the MMSE detector, a subspace-based blind channel identification algorithm, which utilizes only the second-order statistics of the received signal to perform the channel estimation, is employed. The performances of the MMSE detector are evaluated with computer simulations.

A dual-mode blind equalization technique for adaptive channel equalization of quadrature amplitude modulation signals is introduced. The equalizer uses the constant modulus algorithm (CMA) in the initial phase and then switches to a proposed constellation-matched error (CME) minimization algorithm at appropriate values of the mean-square error. The proposed CME cost function can be constructed using finite- or infinite-order polynomials with desirable properties over the constellation region. This dual-mode equalization technique is applied to a linear equalizer and is shown to provide superior performance or simplicity over the conventional CMA and some other dual-mode schemes.

An adaptive gradient technique is applied for the minimization of a hybrid cost function that consists of amplitude-dependent and constellation-dependent terms. A time-varying weighting coefficient is induced in the combined cost function to emphasize/de-emphasize the role of the two terms in determining the gradient during initializations, convergence, and steady state conditions. This coefficient is recursively updated and leads to improved global and local convergence properties. It is shown that the proposed technique is superior to the method in which the cost function involves fixed weighting.

The problem of selecting auto- and cross-terms of time-frequency distributions (TFDs) of nonstationary signals impinging on a multi-antenna receiver is considered. A detection approach is introduced which allows performance measurement and comparison of various schemes via receiver operating characteristics. Array averaging and array differencing techniques are both employed to form a basis for time-frequency (t-f) point selection. The proposed classification method is evaluated against the bootsrap-based method. It is shown that the former offers improved performance and simplified implementations.

We address the problem of characterizing the power attributed to local near-field scattering for the case of a linear equi-spaced array of sensors. The proposed method uses what we have termed the quadratic sensor angle distribution (SAD), previously called the spatial Wigner distribution. This distribution is a characterization of the power at every angle for each sensor in the array. In this distribution near-field sources have different angle for each sensor. The SAD is a joint-variable distribution and a dual in sensor number and angle to Cohen's class of time-frequency distributions. We use a known test source to illuminate the local scatterer distribution we wish to characterize and modify the received array snapshots to remove, via orthogonal projection, the direct propagation path from the test source so as to reveal the less powerful local scatter. An example is provided to demonstrate our technique.

In this paper, we propose a new nonstationary jammer suppression technique for DS/SS communications. This technique is based on combined operations of bilinear signal synthesis and projections. The time-frequency distributions (TFDs) is used to define the jammer time-frequency (t-f) signature. Multi-sensor array at the receiver allows both the spatial and temporal signatures of the signal arrivals to be utilized. To estimate the waveform of a jammer, a mask is constructed and applied such that the masked t-f region captures the jammer energy, but leaves out most of the DS/SS signals. The jammer signals are then synthesized from the masked TFDs that can be removed from the received signal by orthogonal projection.

We address the problem of blind source separation of non-stationary signals of which only instantaneous linear mixtures are observed. A blind source separation approach exploiting both auto-terms and cross-terms of the time-frequency (TF) distributions of the sources is considered. The approach is based on the simultaneous diagonalization and anti-diagonalization of spatial TF distribution matrices made up of, respectively, auto-terms and cross-terms. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach and compare its performances with existing TF-based methods.

Multiple source signals impinging on an antenna array can be separated by time-frequency synthesis techniques. Averaging of the time-frequency distributions of the data across the array permits the spatial signatures of sources to play a fundamental role in improving the synthesis performance. This improvement is achieved independent of the temporal characteristics of the source signals and without causing any smearing of the signal terms. Unlike the recently devised blind source separation methods using spatial time-frequency distributions, the proposed method does not require whitening or retrieval of the source directional matrix.

Blind source separation based on spatial time-frequency distributions (STFDs) has been previously introduced. This method provides improved performance over blind source separation methods based on second-order statistics, when dealing with nonstationary signals that are localizable in the time-frequency domain. In the STFD method, the covariance matrix is first used to whiten the signal vector, then the unitary matrix is estimated using high signal-to-noise ratio (SNR) time-frequency points. This paper modifies the STFD method by performing both whitening and estimation steps using STFD matrices. The eigenvectors of the signal subspace obtained from a properly selected STFD matrix are more robust to noise than those obtained from the covariance matrix and, therefore, are more appropriate to use, particularly for low SNR environments. Further, for small array apertures and high number of arrivals, the STFD whitening matrix can be used as means to reduce the number of signals considered by the blind source separation algorithm.

The previously developed concept of narrowband spatial time-frequency distributions (STFDs) is extended to the wideband case. A new STFD-based root-MUSIC estimator is proposed. This estimator exploits a short-window spatial pseudo Wigner-Ville distribution (SPWVD) to enable application of the subspace-based approach. To combine all relevant SPWVD points, the proposed technique employs an extended coherent signal-subspace (CSS) principle involving coherent averaging over a pre-selected set of time-frequency points rather than the conventional frequency-only averaging procedure.

The SNR analysis has been widely used to evaluate the performance of time-frequency (t-f) distributions. Often the SNR is defined at a specific t-f location or using the averaged variance over the entire t-f domain. In this paper, a new SNR measure is provided based on averaging along the signal t-f signature and its properties for linear FM signals are delineated. It is shown that the SNR increases for increased integration range, and is not highly sensitive to the FM sweeping rate.

This paper presents the performance analysis of the interference excision techniques in direct sequence spread spectrum (DSSS) communications using orthogonal subspace projections. It is shown that this technique is sensitive to the errors in the instantaneous frequency (IF) estimate of the interference over segments of the bit period. This paper discusses the effect of two different types of errors on the receiver SINR and compares the performance of the block-wise processing to the single block projection approach.

This letter introduces the spatial ambiguity functions (SAFs) and discusses their applications to direction finding and source separation problems. We emphasize two properties of SAFs that make them an attractive tool for array signal processing.

The recently developed concept of narrowband spatial time-frequency distributions (STFDs) is extended to the wide-band case. A new STFD-based wideband root-MUSIC estimator is proposed. This technique employs an extended coherent signal-subspace (CSS) principle involving coherent averaging over a pre-selected set of time-frequency points rather than the conventional frequency-only averaging procedure.

This paper presents a novel approach based on time-frequency distributions (TFDs) for separating signals received by a multiple antenna array. This approach provides a significant improvement in performance over the previously introduced spatial time-frequency distributions, specifically for signals with close time-frequency signatures. In this approach, spatial averaging of the time-frequency distributions of the sensor data is performed to eliminate the interactions of the sources signals in the time-frequency domain, and as such restore the realness property and the diagonal structure of the source TFDs, which are necessary for source separation. It is shown that the proposed approach yields improved performance over both cases of no spatial averaging and averaging using time-frequency smoothing kernels.

A new method is introduced for interference excision in spread-spectrum communications that is conducive to software-radio applications. Spare processing capacity in the receiver permits the use of time-frequency techniques to synthesize a nonstationary interference from the time-frequency domain using least squares methods. The synthesized signal is then subtracted from the incoming data in the time domain, leading to jammer removal and increased signal-to-interference-and-noise ratio at the input of the correlator. The paper focuses on jammers with constant modulus that are uniquely described by their instantaneous frequency characteristics. With this a priori knowledge, the jammer signal amplitude is restored by projecting each sample of the synthesized signal to a circle representing its constant modulus. With the phase matching provided by the least squares synthesis method and amplitude matching underlying the projection operation, a significant improvement in receiver performance/bit-error rates is achieved over the case where no projection is performed. Software-radio aspects including computational complexity and processing modes are also discussed.

A new method for the estimation of the signal subspace and noise subspace based on time-frequency signal representations is introduced. The proposed approach consists of the joint block-diagonalization (JBD) of a set of spatial time-frequency distribution matrices. Once the signal and noise subspaces are estimated, any subspace based approach, including the multiple signal classification (MUSIC) algorithm, can be applied for direction of arrival (DOA) estimation. Performance of the proposed time-frequency MUSIC (TF-MUSIC) for an impinging chirp signal using three different kernels is numerically evaluated.

A new method is introduced for interference excision in spread spectrum communications. Time-frequency synthesis techniques are used to synthesize the nonstationary jammer from the time-frequency domain using least-squares methods. The synthesized jammer is then subtracted from the incoming data in the time domain, leading to increased signal to interference ratio at the input of the correlator. The paper focuses on jammers with constant modulus where the jamming signal is a polynomial phase. With this a priori knowledge, the jammer signal amplitude is restored by projecting each sample of the synthesized signal to a circle representing its constant modulus. With the phase matching provided by the least-squares synthesis method and amplitude matching underlying the projection operation, the paper shows a significant improvement in receiver performance/bit error rates over the case where no projection is performed.

This paper addresses the problem of the blind source separation which consists of recovering a set of signals of which only instantaneous linear mixtures are observed. A blind source separation approach exploiting the difference in the time-frequency (t-f) signatures of the sources is considered. The approach is based on the diagonalization of a combined set of 'spatial time-frequency distributions'. Asymptotic performance analysis of the proposed method is performed. Numerical simulations are provided to demonstrate the effectiveness of our approach and to validate the theoretical expression of the asymptotic performance.

The zero-tracking time-frequency distribution (TFD) is introduced. The local autocorrelation function of the TFD, defined by an appropriate kernel, is used to form a polynomial whose roots correspond to the instantaneous frequencies of the multicomponent signal. Two techniques for zero-tracking based on the TFD are presented. The first technique requires updating all of the polynomial signal and extraneous zeros, and is based on the formula relating to the first order approximation, the changes in the polynomial roots and coefficients. The second technique employs the zero-finding Newton's method to only obtain the zero-trajectories of interest.

Direction of arrival (DOA) estimation techniques require knowledge of the sensor-to-sensor correlation of the noise, which constitutes a significant drawback. In the case of temporally correlated signals, it is possible to estimate the signal parameters without any assumptions made on the spatial covariance matrix of the noise. A new method for the estimation of the signal subspace and noise subspace is introduced. The proposed approach is based on a joint block-diagonalization (JBD) of a combined set of spatio-temporal correlation matrices. Once the signal and the noise subspaces are estimated, any subspace based approach can be applied for DOA estimation. A performance comparison of the proposed approach with an existing technique is provided.

The main purpose of this paper is to demonstrate that the adaptive weights obtained from different frequency channels can be used for high-resolution direction of arrival (DOA) estimation. It is shown that these weights have sufficient information which can be processed by eigenstructure methods to yield the signal and the noise subspaces. As such, with the availability of the adaptive weights in a multichannel nulling system, source localization using the data matrix or time-averaged estimation of the covariance matrix may, in most casts, prove unnecessary and can only add meager improvement over the proposed method. We present two approaches to extract the eigenstructures from the multichannel adaptive weights. Both approaches are based on coherent subspace averaging, namely the focusing techniques.

We introduce a new class of powers-of-two (PFT) kernels for fast real time implementations of time-frequency distributions. In this class, the local autocorrelation function is computed using a series of shifting and addition operations. PFT filter design techniques are not limited to the design of fixed kernels. They can also be used to design data-dependent kernels suitable for specific operating environments. In the time-frequency context, where the task is to identify the signal autoterms in the time-frequency domain, a discretized powers-of-two kernel shows little or no difference in performance from its infinite precision counterpart. A simple modification of the PFT design technique that significantly improves the approximation when small register lengths are used, is also introduced.

Time-frequency distribution kernels which satisfy the desirable time-frequency properties and simultaneously allow recursive implementations of the local autocorrelation and the ambiguity functions are computationally efficient and prove valuable for on-line processing. The authors introduce a class of recursive kernels which apply modified comb filters at different timelags. The generalized Hamming, Blackman, and half-sine kernels are members of this class. These kernels have well known low-pass filter characteristics, lead to computational invariance under the kernel extent, and compete in performance with existing nonrecursive t-f kernels.

We introduce a new class of powers-of-two (PFT) kernels for fast real-time implementations of time-frequency (t-f) distributions. In this class, the local autocorrelation function is computed using a series of shifting and addition operations. PFT filter design techniques can be applied to produce fixed kernels or to design data-dependent kernels suitable for specific operating environments. In the t-f context, where the task is to identify the signal autoterms in the t-f domain, a discretized PFT kernel shows little or no difference in performance from its infinite precision counterpart.

Point and derivative constraints are used to provide a wide class of kernels suitable for time-frequency representation of signals. The kernel design is viewed as a solution of linearly constrained minimization problem in which the desired t-f linear constraints constitute a constraint matrix and the time-frequency kernel is one dimensional. This formulation permits a closed form solution; similar to that encountered in beamforming, where the Quiescent pattern corresponds to the Born-Jordan kernel. The constraint matrix can be augmented by derivative constraints which extend the solution space to include kernels with various characteristics.>

Frequency tracking using traditional least-mean-square (LMS) adaptive algorithms and time-frequency distributions (TFD) are compared. Two problems arise when time-frequency distributions are used for frequency tracking: the presence of cross terms and sidelobes. Methods to adequately suppress the cross terms and sidelobes for frequency tracking purposes are discussed. The important parameters for both methods are presented, and the results demonstrate, in most cases, the superior performance of TFDs versus traditional LMS adaptive algorithms.>

The kernel associated with positive estimators including the periodograms is expressed as a linear combination of separable kernels, each defining a smoothed pseudo-Wigner distribution (SPWD). This is achieved by applying the singular value decomposition to the two-dimensional kernel matrix in time and lag variables. The SPWD corresponding to the maximum singular value is considered the rank one kernel estimator that is the closest to the full rank kernel periodogram. Error bounds are derived, and simulations are performed to demonstrate the effect of limiting the decomposition of the kernel matrix to dominant singular values.>

The least-squares estimation problem with non-minimum-norm constraints on the unknown model parameters is considered. Contrary to the quadratic-constraint least-squares solutions the approach presented does not necessarily satisfy the constraint, but rather relies on the nullity of the data matrix to maintain the unconstrained least-squares error value while trading off the minimum-norm solution by another with the shortest distance from the null space of the constraint. The singular value decomposition of the data matrix is used to obtain the necessary information about the minimum-norm solution as well as the basis of the null space. Closed-form expressions are derived for the case in which the constraint of interest is the smoothness of the model parameters. Examples of sinusoids in white noise are given for illustration.>

The problem of model parameter estimation subject to a simple class of nonlinear constraints in the time domain is addressed. The model parameters correspond to tap-delay filter weights and are used to approximate, within the constraints, a desired signal in the mean-square sense. The class of nonlinear constraints consists of convex quadratic functions with one-dimensional null space. This class, which includes the variance of the weight vector, allows the constrained optimization problem to be carried out by two successive unconstrained optimization algorithms implemented in multidimensional and unidimensional spaces. When the least-mean-squares (LMS) technique is used in both spaces, it is shown that the overall convergence time is not influenced by the constraint, i.e. it is primarily determined by the constraint-free LMS algorithm in the multidimensional space.>

It is shown that the use of exact values of the autocorrelation in place of their estimates at one or more lags may lead to two opposite effects on the variance of the corresponding nonparametric power spectrum estimator. The use of the exact values can increase the variance within some frequency bands while reducing it within other bands along the Nyquist interval. The location and the width of these different bands is primarily a function of the lag numbers at which the autocorrelation is known.>

The use of a multiple-pole filter in the time-average estimation of the autocorrelation allows the power spectrum estimates to be recursive in the order of multiplicity of the filter pole. The recursive generation of the estimates from various filter orders provides the flexibility to select the estimator of interest in terms of the variance and spectral and temporal resolution.>

The commenter points out that the recursive structure of the running Fourier transform has been investigated by a number of authors not quoted by Amin in his work (see ibid., vol.75, no.11, p.1537-1538, 1987). He also holds that the main idea behind the generalization presented in the third section stems from the properties of a yet more general class of features that can be computed using the same recursive structure. Additionally, he discusses Amin's treatment of the general form of a weighted running Fourier coefficient and points out drawbacks of expressing the weighting function as a sum of 2 M+1 geometric series and treating each term separately. The author replies to the various comments.>

The paper provides the conditions on the selection of the lap and the time windows in Wigner-Ville distribution when it is considered for time-varying power spectrum estimation. It is shown that the general class of non-stationary processes requires the inseparability of the two windows. The separation is adequate for a certain class of processes in which the autocorrelation is considered invariant along time intervals whose length is shorter for smaller lags. The paper presents a discussion which relates the time-averaging estimation of the autocorrelation function with the nature of its slow time-variation.

The Fourier transform of the autocorrelation estimates provided by applying a single-pole filter to the data-lagged product terms results in a recursive means of estimating the power spectrum. In this estimator, the number of computations required to update the spectrum estimate is independent of the number of lags employed to produce it.

In the recursive Fourier transform, the data window can be chosen such that the number of computations required to update the transform at each frequency upon reception of a new data sample is independent of the transform block length.

LMS adaptive filtering in the spectrum domain is addressed and applied to noise cancelling. The spectrum domain noise cancellor minimizes the noise power at each spectral bin of the primary input. It requires, however, the power spectra of the input data to be estimated prior to cancelling. The paper discusses the function of the proposed cancellor and describes its general structure.

In a general class of nonstationary processes, the autocorrelation may have different time variation rates at different lags. The estimation of each lag in a manner consistent with its nature of nonstationarity yields a reduction in the variance of the spectrum estimate at different frequencies.

This paper is concerned with Fourier-based non-parametric spectral estimation methods for time-varying environments. It presents a class of interactive spectrum estimators in which the number of computations required to update the estimate at each sample is independent of the number of the autocorrelation lags employed to produce the estimate. These estimators are termed lag invariant and form an important class due to their computational simplicity. (Memory requirements, however, do increase as greater autocorrelation lags are employed.) The estimators are based on the use of lagged-product windows specifically selected to form autocorrelation estimates which are then Fourier transformed to produce adaptive spectral estimators having the desired lag-invariant property. It is shown that the special requirements which lead to lag invariance are not always satisfied when the estimation process is based on the use of a data weighting window. In this paper, these requirements are formulated using a generalized lagged-product window approach and the conditions necessary to produce the lag invariance property are delineated.

The purpose of this paper is to discuss the use of linear phase adaptive filters in the tracking of time-varying sinusoids. Efficient algorithms for filters of this type have recently been proposed [1,2]. The filter of interest is an FIR operator consisting of 2M+1 coefficients. The center coefficient is constrained to be unity and the remaining coefficients have even symmetry about this point. Because of these constraints the filtering process may be viewed as one of symmetrically smoothing the input signal-hence the filter is termed the symmetric smoother. The filter coefficients are adapted so as to minimize a time weighted average of the square of the filter output. In this paper, two such algorithms considered: the exact least squares technique [2] and the LMS gradient algorithm [3]. Results illustrating the properties of the symmetric smoother in both a stationary and time-varying environment are presented. On the basis of these results, it is concluded that care must be exercised when interpreting the spectral estimates obtained from a linear phase filter.