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Summary: It is well known that hardware impairments (HWIs) can worthy reduce the wireless system performance at high carrier frequencies by showing random effects. Most current researches for 5 GB systems assume that transmitters and receivers (transceivers) are perfectly equipped. But wireless transceivers (TxRx) are affected by HWIs in practice. Considering the previous studies in the literature, it is reported that HWIs have devastating effects on the performance of OFDM and OFDM‐index modulation (IM) systems with fading channels. In this paper, in‐phase and quadrature phase imbalance (IQI), which is the one of most HWIs between transmitter and receiver in wireless communication systems, is examined on OFDM‐IM system over Rayleigh and Nakagami‐ m fading channels. Two well‐known detectors, the maximum likelihood (ML) detector and the log‐likelihood ratio (LLR) detector are used under the effect of the IQI at TxRx. Error performance analyzes over fading channels of the IQI effect on OFDM‐IM system are realized first theoretically and then by computer simulations. Results obtained for the presence of IQI at TxRx show that a performance evaluation based only on the presence of IQI in the receiver would be optimistic and misleading in terms of the performance of real‐life OFDM‐IM systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new data-aided (DA) joint angle and delay (JADE) maximum likelihood (ML) estimator. The latter consists of a substantially modified and, hence, significantly improved gray wolf optimization (GWO) technique by fully integrating and embedding within it the powerful importance sampling (IS) concept. This new approach, referred to hereafter as GWOEIS (for "GWO embedding IS"), guarantees global optimality, and offers higher resolution capabilities over orthogonal frequency division multiplex (OFDM) (i.e., multi-carrier and multi-path) single-input multiple-output (SIMO) channels. The traditional GWO randomly initializes the wolfs' positions (angles and delays) and, hence, requires larger packs and longer hunting (iterations) to catch the prey, i.e., find the correct angles of arrival (AoAs) and time delays (TDs), thereby affecting its search efficiency, whereas GWOEIS ensures faster convergence by providing reliable initial estimates based on a simplified importance function. More importantly, and beyond simple initialization of GWO with IS (coined as IS-GWO hereafter), we modify and dynamically update the conventional simple expression for the convergence factor of the GWO algorithm that entirely drives its hunting and tracking mechanisms by accounting for new cumulative distribution functions (CDFs) derived from the IS technique. Simulations unequivocally confirm these significant benefits in terms of increased accuracy and speed Moreover, GWOEIS reaches the Cramér–Rao lower bound (CRLB), even at low SNR levels. [ABSTRACT FROM AUTHOR]

Baccaurea is a group of fruit-producing plants found in wild forests. Many of these plant species have not yet explored their potential. The high rate of deforestation in West Sumatra poses a threat of extinction to the genetic resources of the genus Baccaurea before being explored and identified. The research aims to analyze the sequence characters and phylogenetic of Baccaurea found in West Sumatra using the MatK molecular marker. Phylogenetic analysis using the Maximum Likelihood (ML) method in MEGA X application. The results of the analysis of the six species of Baccaurea found that the sequence length ranged from 854-1019bp, the percentage of G+C base composition is 33.4%, the percentage of A+T base composition is 66.6%, the genetic distance range is 0-4% with a conservative character of 484bp and informative characters of 4bp. While the phylogenetic analysis using the ML method grouping the six species of Baccaurea to form a monophyletic clade with a bootstrap value of 100%, all species collected were in the same clade. These results reveal the first time that the MatK sequences from six species Baccaurea native to West Sumatra will be included in NCBI for use by other studies in conducting broader phylogenetic research. [ABSTRACT FROM AUTHOR]

In this article, the estimation of random channel gain is studied for a single-input single-output (SISO) visible light communication (VLC) system. Five different estimators, namely maximum likelihood (ML), least square (LS), maximum posteriori probability (MAP), linear minimum mean square error (LMMSE), and minimum mean square error (MMSE), are proposed. The performances of these estimators are compared with the derived Bayesian Cramér–Rao lower bound (BCRLB), which can be used as a benchmark to evaluate the efficiency of the unbiased estimators. The presented analytical results, corroborated with Monte Carlo simulations, indicate that the MMSE estimator provides the best results. Additionally, the increasing number of pilot symbols as well as the ascending transmitted power improve the system performance. On the other hand, the noise variance has a negative effect on the channel estimation in terms of mean square error (MSE), and thus, it can dramatically reduce the performance of the estimators. [ABSTRACT FROM AUTHOR]

This paper analyzes the bit error rate (BER) of multicarrier index keying—orthogonal frequency division multiplexing (MCIK-OFDM) with selection combining (SC) diversity reception. Particularly, we propose a generalized framework to derive the BER for both the low-complexity greedy detector (GD) and maximum likelihood (ML) detector. Based on this, closed-form expressions for the BERs of MCIK-OFDM with the SC using either the ML or the GD are derived in presence of the channel state information (CSI) imperfection. The asymptotic analysis is presented to gain helpful insights into effects of different CSI conditions on the BERs of these two detectors. More importantly, we theoretically provide opportunities for using the GD instead of the ML under each specific CSI uncertainty, which depend on the number of receiver antennas and the M-ary modulation size. Finally, extensive simulation results are provided in order to validate our theoretical expressions and analysis. [ABSTRACT FROM AUTHOR]

The aim of this study is to extract impervious surfaces and show their spatial distribution, using different machine learning algorithms. For this purpose, geoprocessing and remote sensing techniques were used and three classification methods for digital images were compared, namely Support Vector Machines (SVM), Maximum Likelihood (ML) and Random Trees (RT) classifiers. The study area is one of the most prestigious and the largest housing estates in Warsaw (Poland), the Fort Bema housing complex, which is also an exemplary model for hydrological solutions. The study was prepared on the Geographic Information System platform (GIS) using aerial optical images, orthorectified and thus provided with a suitable coordinate system. The use of these data is therefore supported by the accuracy of the resulting infrared channel product with a pixel size of 0.25 m, making the results much more accurate compared to satellite imagery. The results of the SVM, ML and RT classifiers were compared using the confusion matrix, accuracy (Root Mean Square Error /RMSE/) and kappa index. This showed that the three algorithms were able to successfully discriminate between targets. Overall, the three classifiers had errors, but specifically for impervious surfaces, the highest accuracy was achieved with the SVM classifier (the highest percentage of overall accuracy), followed by ML and RT with 91.51%, 91.35% and 84.52% of the results, respectively. A comparison of the visual results and the confusion matrix shows that although visually the RT method appears to be the most detailed classification into pervious and impervious surfaces, the results were not always correct, e.g., water/shadow was detected as an impervious surface. The NDVI index was also mapped for the same spatial study area and its application in the evaluation of pervious surfaces was explained. The results obtained with the GIS platform, presented in this paper, provide a better understanding of how these advanced classifiers work, which in turn can provide insightful guidance for their selection and combination in real-world applications. The paper also provides an overview of the main works/studies dealing with impervious surface mapping, with different methods for their assessment (including the use of conventional remote sensing, NDVI, multisensory and cross-source data, 'social sensing' and classification methods such as SVM, ML and RT), as well as an overview of the research results. [ABSTRACT FROM AUTHOR]

Target localization is widely applied in wireless sensor networks (WSNs). In this article, we tackle the problem of position estimation for multiple stationary targets using Doppler frequency shifts and angles by moving sensor arrays. The computational load for the exhaustive maximum likelihood (ML) direct position determination (DPD) search is insufferable. Based on Pincus’ theorem and the importance sampling (IS) concept, we propose a novel noniterative ML DPD method, and the circular mean is used for superior position estimation performance; meanwhile, a concrete criterion is also proposed for the choice of the importance function. The computational complexity of the proposed method is modest, and the off-grid problem that most existing DPD techniques face is significantly alleviated. Moreover, it can be implemented in parallel separately. In addition, we present the closed-form Cramér–Rao lower bound (CRLB) for the DPD with moving sensor arrays and stationary targets. Simulation results demonstrate that the proposed ML DPD estimator can achieve better estimation accuracy than state-of-the-art DPD techniques. With a reasonable parameter choice, the estimation performance of the proposed technique is very close to the CRLB, even in the adverse conditions of low signal-to-noise ratio (SNR) levels. [ABSTRACT FROM AUTHOR]

Urban land-cover change is increasing dramatically in most emerging countries. In Iraq and in the capital city (Baghdad). Active socioeconomic progress and political stability have pushed the urban border into the countryside at the cost of natural ecosystems at ever-growing rates. Widely used classifier of Maximum Likelihood was used for classification of 2003 and 2021 Landsat images. This classifier achieved 83.20% and 99.58% overall accuracies for 2003 and 2021 scenes, respectively. This study found that the urban area decreases by 16.4% and the agriculture area decrease by 5.4% over the period. On the other hand, barren land has been expanded up to more than 7% as well as increasing in water land that should probably due to flooding (almost 15% more than 2003). To reduce the undesirable effects of land-cover changes over urban ecosystems in Baghdad and in the municipality in specific, it is suggested that Baghdad develops an urban development policy. The emphasis of policy must be the maintenance an acceptable balance among urban infrastructure development, ecological sustainability and agricultural production. [ABSTRACT FROM AUTHOR]

When industrial relics, such as obsolete buildings, sites, and infrastructures, enter into a process of adaptive reuse, they become transformation engines capable of shaping the urban fabric. They provide tangible and intangible links to our past and have the potential to play a significant role in today's cities' futures. One unresolved issue is the quantification of the externalities of these transformation processes. If undertaken correctly, adaptive reuse can contribute to the development of social and cultural capital, environmental sustainability, urban regeneration, and, most importantly, economic benefits to the surrounding community. In this sense, understanding the value of heritage is particularly important in light of the new European urban environmental policy movement based on the circular economy, which aims to change the way Member States consume and produce materials and energy. After a review of the externalities generated by the adaptive reuse of disused industrial heritage, the paper will concentrate on the estimation of economic benefits given by a transformation process that affected Turin's Aurora district (Northern Italy) during the last years. The hedonic pricing method (HPM) was used to investigate the effects of the construction of new headquarters and the redevelopment of an old power plant converted into a museum and conference center. This study used econometric models to identify a significant increase in market prices within 800 m of the site and calculated a EUR 16,650,445 capitalized benefit from the transformation on the surrounding residential building stock. The study thus contributed to the awareness that reused heritage not only improves the lives of residents, but it also has a positive impact on the real estate market, in terms of transactions, as well as market values. [ABSTRACT FROM AUTHOR]

This communication presents an efficient iterative approach for locating the near-field (NF) coherent sources. In each iteration, the covariance matrices only containing single source information are constructed by using alternating oblique projection. Then based on the principle of vector dot products, a new iterative direction-of-arrival (DOA) estimator is proposed. After the DOA of each separated signal is estimated, the paired ranges are obtained from the 1-D maximum likelihood (ML) estimator. The proposed algorithm avoids high-dimensional spectral searches, subspace extraction, and any preprocessing such as spatial smoothing, leading to low computational complexities and high estimation accuracy. Comparative simulations show the efficiency and merits of the proposed method. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation based on Maximum Likelihood is a common method in array signal processing, with many practical applications, but the huge amount of calculation limits the practical application. To deal with such an Maximum Likelihood (ML) DOA estimation problem, firstly, the DOA estimation model with ML for acoustic vector sensor array is developed, where the optimization standard in various cases can be unified by converting the maximum of objective function to the minimum. Secondly, based on the Invasive Weed Optimization (IWO) method which is a novel biological evolutionary algorithm, a new Improved IWO (IIWO) algorithm for DOA estimation of the acoustic vector sensor array is proposed by using ML estimation. This algorithm simulates weed invasion process for DOA estimation by adjusting the non-linear harmonic exponent of IWO algorithm adaptively. The DOA estimation accuracy has been improved, and the computation of multidimensional nonlinear optimization for the ML method has been greatly reduced in the IIWO algorithm. Finally, compared with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE) method and Tuna Swarm Optimization(TSO) algorithm, numerical simulations show that the proposed algorithm has faster convergence rate, improved accuracy in terms of Root Mean Square Error (RMSE), lower computational complexity and more robust estimation performance for ML DOA estimation. The experiment with tracking the orientation of the motorboat by Microelectronic mechanical systems (MEMS) vector hydrophone array shows the superior performance of proposed IIWO algorithm in engineering application. Therefore, the proposed ML-DOA estimation with IIWO algorithm can take into account both resolution and computation. which can meet the requirements of real-time calculation and estimation accuracy in the actual environment. [ABSTRACT FROM AUTHOR]

Generalized spatial modulation (GSM) technology is an extension of spatial modulation (SM) technology, and one of its main advantages is to further improve band efficiency. However, the multiple active antennas for transmission also brings the demodulation difficulties at the receiver. To solve the problem of high computational complexity of the optimal maximum likelihood (ML) detection, two sub-optimal detection algorithms are proposed through reducing the number of transmit antenna combinations (TACs) detected at the receiver. One is the maximum ratio combining detection algorithm based on repetitive sorting strategy, termed as (MRC-RS), which uses MRC repetitive sorting strategy to select the most likely TACs in detection. The other is the maximum ratio combining detection algorithm, which is based on the iterative idea of the orthogonal matching pursuit, termed the MRC-MP algorithm. The MRC-MP algorithm reduces the number of TACs through finite iterations to reduce the computational complexity. For M-QAM constellation, a hard-limited maximum likelihood (HLML) detection algorithm is introduced to calculate the modulation symbol. For the M-PSK constellation, a low-complexity maximum likelihood (LCML) algorithm is introduced to calculate the modulation symbol. The computational complexity of these two algorithms for calculating the modulation symbol are independent of modulation order. The simulation results show that for GSM systems with a large number of TACs, the proposed two algorithms not only achieve almost the same bit error rate (BER) performance as the ML algorithm, but also can greatly reduce the computational complexity. [ABSTRACT FROM AUTHOR]

In this article, the signal detection problem in indoor visible light communication (VLC) system aided by generalized space shift keying (GSSK) is modeled as a sparse signal reconstruction problem, which has lower computational complexity by exploiting the sparse reconstruction algorithms in compressed sensing (CS). In order to satisfy the measurement matrix property to perform sparse signal reconstruction, a preprocessing approach of measurement matrix is proposed based on singular value decomposition (SVD), which theoretically guarantees the feasibility of utilizing CS based sparse signal detection method in indoor GSSK-VLC system. Then, by adopting classical orthogonal matching pursuit (OMP) algorithm and compressed sampling matching pursuit (CoSaMP) algorithm, the GSSK signals are efficiently detected in the considered indoor GSSK-VLC system. Furthermore, a more efficient detection algorithm combined with OMP and maximum likelihood (ML) is also presented especially for SSK scenario. Finally, the effectiveness of the proposed sparsity aided detection algorithms in indoor GSSK-VLC system are verified by computer simulations. The results show that the proposed algorithms can achieve better bit error rate (BER) and lower computation complexity than ML based detection method. Specifically, a signal-to-noise ratio (SNR) gain as high as 12 dB is observed in the SSK scenario and about 5 dB in case of a GSSK scenario upon employing our proposed detection methods. [ABSTRACT FROM AUTHOR]

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This article addresses the 3-D reconstruction of urban areas using a minimal number of Synthetic Aperture Radar (SAR) acquisitions, that is, a set of three images, characterized by intermediate spatial resolution features. In such extreme conditions, conventional tomographic techniques reveal unadapted to refined 3-D imaging purposes, either due to the resulting intrinsic coarse vertical resolution, or to the low dimensionality of the data set, that prevents any separation of complex mixed scattering patterns. A new high-resolution (HR) tomographic estimator, based on a polarimetric signal subspace fitting criterion, is proposed to overcome these limitations, as this method adapts to the statistical behavior of the backscattered signals using robust metrics. The optimization of the corresponding focusing criterion is led through a new polarimetric alternating projection algorithm, characterized by a low computational cost, which may also be used to optimize the polarimetric the deterministic maximum likelihood criterion. The proposed polarimetric signal subspace fitting technique is shown to outperform the other studied HR techniques over both simulated signals and data acquired by the DLR’s ESAR sensor at L-band over Dresden city, Germany. Finally full-rank polarimetric tomographic estimators are proposed that generalize nonparametric polarimetric estimators, and permit to estimate second-order polarimetric representations in 3-D, instead of unitary rank target vector with their conventional versions. This approach makes it possible to characterize polarimetric scattering mechanisms in 3-D. [ABSTRACT FROM AUTHOR]

Due to the severe impact of dynamic plasma sheath on electromagnetic (EM) waves, the communication quality of hypersonic vehicles deteriorates, even resulting in communication blackouts during the reentry process. In this article, the hypersonic vehicle downlink integrated channels that cascade the plasma sheath channel and Rice fading channel, i.e., the downlink telemetry channels, are first established, and then the demodulation method and performance of typical telemetry modulations including the M-ary phase shift keying (MPSK), M-ary amplitude shift keying (MASK), and M-ary frequency shift keying (MFSK) are studied. Considering the high dynamics of the plasma sheath, the pilot signals are used to detect the signal correctly for MPSK, and the non-coherent demodulation is adopted for MASK and MFSK. Especially, an adaptive maximum likelihood (ML) receiver for ASK is proposed based on a reduced reversible jump Markov chain Monte Carlo (RRJ-MCMC) algorithm to estimate the probability density function (pdf) of the received signal. The simulation results show that the communication performance of PSK and ASK is improved with the modulation order $M$ decreasing; the performance of non-coherent FSK is improved with the modulation order $M$ increasing. Meanwhile, the performance follows the order of NC-MFSK (M ≥ 8) > BPSK > NC-4FSK > NC-2FSK > 2ASK. For NC-8FSK, when the electron density peak value ${Ne}_{\mathrm {peak}}$ = {2, 4, 6, 8, 10} $\times 10^{18}\,\,\text{m}^{-3}$ , the signal to noise ratio (SNR) required to reduce the bit error rate (BER) to 10−6 are 17, 18, 19, 21, and 34 dB, respectively. [ABSTRACT FROM AUTHOR]

A multiple-input multiple-output (MIMO) radarwith widely separated antennas on moving platforms suffers from the effects of platform deviations on the target parameter estimation since the trajectories of the moving platforms are sensitive to environmental factors, such as strong wind. This article addresses the joint estimation of multiple target positions and velocities as well as radar system deviations to minimize the impact of platform deviations. The proposed algorithm can also be regarded as a self-calibration technique. First, the grid search dimensions for parameter estimation are reduced via a generalized maximum likelihood (GML) algorithm. Second, the adaptive gradient (AdaGrad) method is used to implement the GML estimation for multitarget echo delays and Doppler shifts. Finally, to address the nonlinear estimation problem of interest, the iterative least squares method is used to estimate the multiple target positions and velocities as well as radar system deviations based on the estimated delays and Doppler shifts. Prior information, such as target positions or the probability distribution of the echo coefficient, is not needed in the proposed method. The parameter identifiability is also derived in this article. Numerical simulations show that compared to a method without the estimation of system deviations, the proposed method is more efficient with respect to the derived Cramér–Rao bound. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient channel estimation (CE) to determine the frequency response of overall subcarriers for universal filtered multicarrier systems, which promises excellent performance without a significant increase in computational complexity. Specifically, based on the even-subcarrier received signal, we design a pilot-assisted scheme combined with a partial inverse fast Fourier transform operation to obtain an estimate of the channel impulse response. Then, to alleviate the power efficiency loss caused by discarding the odd subcarriers, a performance-enhanced CE using the Neumann series expansion technique is proposed. This provides a performance comparable to that of the maximum likelihood-based approach involving a prohibitively burdensome computation. A closed-form mean square error expression and computational complexity analysis are derived to quantify the achievable advantages. Simulation study confirms the effectiveness of the proposed CE. [ABSTRACT FROM AUTHOR]

In two-way time-of-arrival (TOA) systems, a user device (UD) obtains its position and timing information by round-trip communications to a number of anchor nodes (ANs) at known locations. Compared with the one-way TOA technique, the two-way TOA scheme is easy to implement and has higher localization and synchronization accuracy. Existing two-way TOA methods assume a stationary UD. This will cause uncompensated position and timing errors. In this article, we propose an optimal maximum likelihood (ML) based two-way TOA localization and synchronization method, namely TWLAS. Different from the existing methods, it takes the UD mobility into account to compensate the error caused by the UD motion. We analyze its estimation error and derive the Cramér-Rao lower bound (CRLB). We show that the conventional two-way TOA method is a special case of the TWLAS when the UD is stationary, and the TWLAS has high estimation accuracy than the conventional one-way TOA method. We also derive the estimation error in the case of deviated UD velocity information. Numerical result demonstrates that the estimation accuracy of the new TWLAS for a moving UD reaches CRLB, better than that of the conventional one-way TOA method, and the estimation error caused by the deviated UD velocity information is consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

For 2-D causal systems, the variables depend both on time, and on spatial coordinates. This article develops two identification algorithms for two-dimensional causal systems. First, a maximum likelihood estimation algorithm is developed for two-dimensional causal systems when there is no missing data. Second, an expectation–maximization based auxiliary model algorithm, and an expectation–maximization based modified Kalman filtering and smoothing algorithm are derived for 2-D causal systems with missing outputs. It is demonstrated that the modified Kalman filtering, and smoothing algorithm is more effective for systems with missing outputs. The effectiveness of these two algorithms is verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this study, we assess the potential of X-band Interferometric Synthetic Aperture Radar imagery for automated classification of sea ice over the Baltic Sea. A bistatic SAR scene acquired by the TanDEM-X mission over the Bothnian Bay in March of 2012 was used in the analysis. Backscatter intensity, interferometric coherence magnitude, and interferometric phase have been used as informative features in several classification experiments. Various combinations of classification features were evaluated using Maximum likelihood (ML), Random Forests (RF) and Support Vector Machine (SVM) classifiers to achieve the best possible discrimination between open water and several sea ice types (undeformed ice, ridged ice, moderately deformed ice, brash ice, thick level ice, and new ice). Adding interferometric phase and coherence-magnitude to backscatter-intensity resulted in improved overall classification performance compared to using only backscatter-intensity. The RF algorithm appeared to be slightly superior to SVM and ML due to higher overall accuracies, however, at the expense of somewhat longer processing time. The best overall accuracy (OA) for three methodologies were achieved using combination of all tested features were 71.56, 72.93, and 72.91% for ML, RF and SVM classifiers, respectively. Compared to OAs of 62.28, 66.51, and 63.05% using only backscatter intensity, this indicates strong benefit of SAR interferometry in discriminating different types of sea ice. In contrast to several earlier studies, we were particularly able to successfully discriminate open water and new ice classes. [ABSTRACT FROM AUTHOR]

This article deals with the problem of adaptive target detection in the presence of homogeneous Gaussian interference with frequency diverse array multiple-input multiple-output radar. Adaptive detectors are devised according to the generalized likelihood ratio test criterion, where the position of the target within each range cell is assumed unknown. To obtain the maximum likelihood estimate of the target incremental range under the $H_1$ hypothesis, three different optimization strategies are pursued. They are, respectively, based on semidefinite programming, discrete grid search, and Newton method. At the analysis stage, a detection performance comparison is carried on among the new proposed adaptive detectors, benchmark, and mismatched receivers. Numerical results corroborate the effectiveness of the developed receivers. [ABSTRACT FROM AUTHOR]

Image segmentation lies at the heart of multiple image processing chains, and achieving accurate segmentation is of utmost importance as it affects later processing. Image segmentation has recently gained interest in the field of remote sensing, mostly due to the widespread availability of remote sensing data. This increased availability poses the problem of transmitting and storing large volumes of data. Compression is a common strategy to alleviate this problem. However, lossy or near-lossless compression prevents a perfect reconstruction of the recovered data. This letter investigates the image segmentation performance in data reconstructed after a near-lossless or a lossy compression. Two image segmentation algorithms and two compression standards are evaluated on data from several instruments. Experimental results reveal that segmentation performance over previously near-lossless and lossy compressed images is not markedly reduced at low and moderate compression ratios (CRs). In some scenarios, accurate segmentation performance can be achieved even for high CRs. [ABSTRACT FROM AUTHOR]

This paper proposes a new method to get explicit expressions of some quantities associated with performance analysis of the maximum likelihood DOA algorithm in the presence of an additive Gaussian noise on the antenna elements. The motivation of the paper is to make a quantitative analysis of the ML DOA algorithm in the case of multiple incident signals. We present a simple method to derive a closed-form expression of the MSE of the DOA estimate based on the Taylor series expansion. Based on the Taylor series expansion and approximation, we get explicit expressions of the MSEs of estimates of azimuth angles of all incident signals. The validity of the derived expressions is shown by comparing the analytic results with the simulation results. [ABSTRACT FROM AUTHOR]

As bias estimation methods are developed, it becomes necessary to obtain the bound on bias estimation for more complex bias and sensor models. Three-dimensional (3-D) sensors, such as radars commonly used in applications, contain both scale and additive biases in sine space which result in a nonlinear estimation problem that may have poor observability and accuracy depending on the geometry of the sensors. By converting the sine space and range measurements to Cartesian using an unbiased conversion, it is possible, via creation of pseudomeasurements, to eliminate the need to estimate the target's state thereby reducing the sensor bias estimator complexity. The present paper evaluates the Cramér–Rao lower bound (CRLB) for estimating scale and additive biases in sine space for 3-D sensors and compares it with a maximum likelihood formulation implemented via iterated least squares, which is thereby shown to be statistically efficient. Additionally, the importance of measurement diversity is investigated with respect to the CRLB. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel scheme termed layered orthogonal frequency division multiplexing with index modulation (L-OFDM-IM) to increase the spectral efficiency (SE) of OFDM-IM systems. In L-OFDM-IM, all subcarriers are first divided into multiple layers, each determining the active subcarriers and their modulated symbols. The index modulation (IM) bits are carried on the indices of the active subcarriers of all layers, which are overlapped and distinguishable with different signal constellations so that the number of the IM bits is larger than that in traditional OFDM-IM. A low-complexity detection is proposed to alleviate the high burden of the optimal maximum-likelihood detection at the receiver side. A closed-form upper bound on the bit error rate, the achievable rate, and diversity order are derived to characterize the performance of L-OFDM-IM. To enhance the diversity performance of L-OFDM-IM, we further propose coordinate interleaving L-OFDM-IM (CI-L-OFDM-IM), which interleaves the real and imaginary parts of the modulated symbols over two different subchannels. Computer simulations verify the theoretical analysis, and results show that L-OFDM-IM outperforms the conventional OFDM-IM scheme. Moreover, it is also confirmed that CI-L-OFDM-IM obtains an additional diversity order in comparison with L-OFDM-IM. [ABSTRACT FROM AUTHOR]

This paper addresses the performance characterization of a direction of arrival (DoA) estimator in the low signal-to-noise-ratio (SNR) region. The case of a sensor array simultaneously collecting signals emitted at multiple carrier frequencies by a single source is considered. A maximum likelihood (ML) approach is used as a reference method for DoA estimation and its accuracy is characterized in terms of mean square error (MSE). It is well known that for SNR values included in the so-called threshold region, the DoA estimation accuracy decreases rapidly, due to the presence of outliers. This effect can be possibly mitigated when multiple frequency channels are jointly exploited. However, the capability to predict this performance degradation is fundamental either for assessing the robustness of an existing sensor or for supporting its design. Therefore, the scope of this paper is to introduce appropriate approximations to the MSE of a multifrequency ML DoA estimator in order to provide a reliable characterization of its performance in the threshold region. Two models for the source signals are considered and separately discussed, namely the deterministic (or conditional) and stochastic (or unconditional). An extensive simulated analysis is reported to prove the tightness of the approximations and to characterize the benefits steming from the exploitation of signals emitted at multiple carriers. [ABSTRACT FROM AUTHOR]

We consider range estimation and range-Doppler imaging using signed measurements of a radar system. Known time-varying thresholds are investigated for taking the signed measurements through one-bit sampling, and are compared with unknown dithering with known probability density function. The maximum likelihood (ML) approach is considered for signal parameter estimation. Since the ML algorithm is computationally prohibitive, a relaxation-based approach, referred to as the One-Bit RELAX algorithm, is used for signal parameter estimation. The conventional RELAX algorithm proposed for high-resolution sampling is also considered for comparison purposes. Moreover, a model-order selection tool, namely the Bayesian information criterion, is used to determine the number of scatterers within the scene of interest. Both numerical and experimental examples are provided to demonstrate the performance of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper introduces sparse low-power sensor networks using passive electric potential sensors for crowd-aware smart buildings. The proposed networks can detect human presence, track their positions, and estimate room occupancy by measuring the electric field disturbances caused by human movement. In addition, the proposed passive sensing system can remotely monitor human physiological signals of nearby stationary occupants (standoff ~1.5 m) when the ambient 60-Hz fields are filtered out. Based on an experimentally calibrated source range model, we further propose an improved multiple-occupant near-field indoor localization method using a maximum likelihood algorithm combined with dividing rectangular search. The tradeoff between search efficiency and localization accuracy is also discussed. Experimental results in two different rooms for 1 week duration show the effectiveness of our proposed sensing system: human identification with an accuracy of 98.3% on six participants, occupant localization methods with room occupancy estimation accuracy of 89.03%, and average localization error less than 0.3 m. These results open up new possibilities in security, indoor navigation or positioning systems, human–machine interfaces, and tele-health applications. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method to assess the social activity maintained by psychiatric patients using information and communication technologies. In particular, we model the daily usage patterns of phone calls and social and communication apps using point processes. We propose a novel nonhomogeneous Poisson process model with periodic (circadian) intensity function using a truncated Fourier series expansion, which is inferred using a trust-region algorithm. We also extend the model using a mixture of periodic intensity functions to cope with the different daily patterns of a person. The analysis of the usage of phone calls and social and communication apps of a cohort of 259 patients reveals common patterns shared among patients with relatively high homogeneity and differences among patient pathologies. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the Probability Mass Function (PMF) of a discrete random vector (RV) from partial observations, namely when some elements in each observed realization may be missing. Since the PMF takes the form of a multi-way tensor, under certain model assumptions the problem becomes closely associated with tensor factorization. Indeed, in recent studies it was shown that a low-rank PMF tensor can be fully recovered (under some mild conditions) by applying a low-rank (approximate) joint factorization to all estimated joint PMFs of subsets of fixed cardinality larger than two (e.g., triplets). The joint factorization is based on a Least Squares (LS) fit to the estimated lower-order sub-tensors. In this letter we take a different estimation approach by fitting the partial factorization directly to the observed partial data in the sense of Kullback-Leibler divergence (KLD). Consequently, we avoid the need for particular selection and direct estimation of sub-tensors of a particular order, as we inherently apply proper weighting to all the available partial data. We show that our approach essentially attains the Maximum Likelihood estimate of the full PMF tensor (under the low-rank model) and therefore enjoys its well-known properties of consistency and asymptotic efficiency. In addition, based on the Bayesian model interpretation of the low-rank model, we propose an Estimation-Maximization (EM) based approach, which is computationally cheap per iteration. Simulation results demonstrate the advantages of our proposed KLD-based hybrid approach (combining alternating-directions minimization with EM) over LS fitting of sub-tensors. [ABSTRACT FROM AUTHOR]

Channel estimation is of great challenge for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. The underlying reason can be attributed to two facts. One is the huge dimension of MIMO channel matrix, since mmWave systems typically employ large antenna arrays at both the transmitter and receiver to realize sufficient link margin. The other fact is the limited number of radio-frequency chains available for transmitter/receiver array, due to the power and cost limitations. This paper proposes a two-stage accurate channel estimation scheme for mmWave MIMO. Initially, we utilize sparse Bayesian learning to obtain a coarse channel estimate. Then we refine the channel estimate by iteratively maximizing the likelihood function of channel parameters. It is shown through simulations that the proposed scheme significantly outperforms the counterparts, and can achieve accurate channel estimation performance. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of censoring outliers in a class of complex multivariate elliptically contoured distributed radar data, which is a vital issue in radar signal processing applications, such as adaptive radar detection and space-time adaptive processing. The maximum likelihood (ML) estimate of the outlier subset is derived resorting to the generalized likelihood function (GLF) criterion. Since the ML estimate involves the solution of a combinatorial problem, a reduced complexity but approximate ML (AML) procedure is also considered. At the analysis stage, the performance of the AML method is evaluated in the presence of both simulated and real radar data, also in comparison with the conventional generalized inner product (GIP) and the reiterative censored GIP (RCGIP) algorithms. The results highlight that the AML technique achieves a satisfactory performance level and can outperform both GIP and RCGIP in some situations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate maximum likelihood (ML) time delay (TD) and carrier frequency offset (CFO) synchronization in multi-node decode-and-forward cooperative relaying systems operating over time-varying channels. This new synchronization scheme is embedded into a distributed multiple input multiple output (MIMO)-relay beamforming transceiver structure to avoid the drawbacks of multidimensional ML estimation at the destination and to minimize the overhead cost. By accounting for a perfect Doppler spread value, the new synchronization solution delivers accurate TD and CFO estimates. For real-world operation, however, this new technique can be jointly implemented with any Doppler spread estimator in a new iterative scheme using a time-constant channel (TCC)-based synchronization method at the initialization step. The resulting TD and CFO estimates along with the channel estimates are then fed into a distributed MIMO-relay beamforming transceiver of $K$ single-antenna nodes, for pre-compensation at each node of the transmitted signals, to ensure constructive maximum ratio combining (MRC) at the destination. Simulation results show significant synchronization accuracy improvement over previous distributed multi-node synchronization techniques assuming TCCs. The latter translates into noticeable gains in terms of useful link-level throughput, more so at higher Doppler or with more relaying nodes. [ABSTRACT FROM AUTHOR]

The product model is assumed to be an appropriate statistical model for multilook polarimetric synthetic radar data (PolSAR). According to this model, the observed signal is considered as the product of independent random variates of a complex Gaussian speckle and a non-Gaussian texture. With different texture distributions, the product model leads to different expressions for the compound distribution considered as an infinite mixture model. In this paper, the maximum-likeli-hood (ML) estimator is derived to jointly estimate the speckle and texture parameters in the compound distribution model using the multilook polarimetric radar data. In particular, we estimate: 1) the equivalent number of looks; 2) the covariance matrix of the speckle component; and 3) the texture distribution parameters. The expectation–maximization algorithm is developed to compute the ML estimates of the unknown parameters. The hybrid Cramer–Rao bounds (HCRBs) are also derived for these parameters. First, a general HCRB expression is derived under an arbitrary texture distribution. Then, this expression is simplified for a specific texture distribution. The performance of the ML is compared with the performance of other known estimators using the simulated and real multilook PolSAR data. For real data, a goodness of fit of multilook PolSAR data histograms is used to assess the fitting accuracy of the compound distributions using different estimators. [ABSTRACT FROM AUTHOR]

Symbol timing offset (STO) estimation constitutes an important part in orthogonal frequency-division multiplexing (OFDM) signal synchronization, and many blind methods based on the maximum likelihood (ML) principle have been proposed. A theoretical analysis of the estimation performance, however, is very difficult, due in part to the discrete nature of the STO. As a result, most studies on OFDM STO estimation have relied only on computer simulation for performance evaluation. This paper presents a theoretical performance analysis for ML-based blind OFDM STO estimation. We start with a review of the formulation of ML blind STO estimation problem and its solution. We then conduct the said performance analysis. The analysis turns out to involve a study of the eigenvalues of some matrix functions of the autocorrelation of the received signal. As the general case leads to highly complicated mathematics, we treat the case of full-band OFDM in additive white Gaussian noise in more detail. In this case, we are able to obtain mathematically tractable bounds and approximation to the estimation error probability and the corresponding mean-square error. In high signal-to-noise ratio (SNR), these bounds and approximation show inverse power-law dependence on the SNR. We also compare the bounds with simulation results and with an existing approximation in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes a novel carrier frequency offset (CFO) estimator for the coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems using the matched-filter (MF) concept. We consider an OFDM symbol with $N$ subcarriers so that the receiver takes $N$ time samples of the received noisy CO-OFDM signal. Our idea is to first append these $N$ received samples with $(L-1)N$ zeros at the end to get a sequence of $LN$ time samples. By taking the discrete Fourier transform of these $LN$ samples, we compute the spectrum of the CO-OFDM symbol at $LN$ discrete frequency points. We think of this spectrum as being made up of $L$ sets of $N$ points each, each set consisting of the frequency points $\lbrace \frac{2\pi }{LN}l, \frac{2\pi }{LN}l+\frac{2\pi }{N}, \ldots, \frac{2\pi }{LN}l+\frac{2\pi (N-1)}{N}\rbrace$ , for each value of $l$ , where $l=0,1,\ldots,L-1$. Each set of $N$ points for one value of $l$ can be considered as the spectrum of the CO-OFDM symbol corresponding to one hypothesized value $\frac{2\pi }{LN}l$ of the CFO. The receiver can now obtain the maximum likelihood (ML) CFO estimate by determining the hypothesized value that best matches the spectrum of the CO-OFDM symbol received from the channel. In the case of data-aided (DA) ML estimation, we treat the OFDM symbol as a pilot symbol in which we know the data in all the subcarriers, and this pilot symbol is used as the reference signal for the MF. In the case of blind (BL) ML estimation, the data in all the subcarriers are unknown, and the receiver uses an OFDM symbol with no data modulation in all the subcarriers as the reference signal. After making the ML decision of the hypothesized value of the CFO, a fine search will be carried out to determine the actual value more accurately. It turns out only one step is necessary to locate the actual value of the CFO. The DA MF ML algorithm can achieve full-range (integral and fractional part) CFO estimation with high accuracy, while the BL MF ML algorithm has low computational complexity but focuses on the fractional CFO estimation only. We discuss the complexity and performance of this MF ML algorithm, and present simulation results to demonstrate the estimation error variance for 16-PSK/QAM modulations. The simulation results show that the estimation error variance of the DA MF ML algorithm can achieve the Cramér–Rao lower bound in the absence of the laser phase noise. [ABSTRACT FROM AUTHOR]

In this paper, an iterative maximum likelihood (ML) finite impulse response (FIR) filter is proposed for discrete-time state estimation in dynamic mechanical systems with better robustness than the Kalman filter (KF). The ML FIR filter and the error covariance matrix are derived in batch forms and further represented with fast iterative algorithms to have a clearer insight into the ML FIR filter performance. Provided that all of the model parameters are known, the ML FIR filter has an intermediate accuracy between the robust unbiased FIR (UFIR) filter and the KF. Under the uncertainties in not exactly known noisy environments, the ML FIR filter performs much better than the KF. A fundamental feature of the ML FIR estimate is that it develops gradually from the UFIR estimate on small horizons to the KF estimate on large horizons. Properties of the ML FIR filter are learned in more detail based on the drifting stochastic resonator and rotary flexible joint. [ABSTRACT FROM AUTHOR]

Focusing on every individual electric vehicle (EV) while optimally charging a significant number of EV units at the workplace is normally computationally burdensome. Such charging optimization requires not only a long runtime but also a large CPU memory due to numerous decision variables involved. This paper develops a new combined state of charge (SOC) based methodology to calculate day-ahead combined probabilistic charging loads for a large number of EV units. Here, several models are proposed to estimate different combined statistical parameters based on historical data. The proposed methodology determines the transition of the combined SOC distribution of EV units from one timeslot to the next using these estimated parameters. Various strategies of SOC-based charging (e.g., unfair and fair modes) are investigated to control EV loads. Numerical results show that the proposed SOC-based charging can reduce the number of decision variables significantly, and require less computational time and memory accordingly. [ABSTRACT FROM PUBLISHER]

This paper addresses the self-interference (SI) cancellation for full-duplex operation in the presence of imperfect radio-frequency (RF) components. In particular, we develop a new scheme to jointly estimate and cancel the in-phase/quadrature mixer imbalance, power amplifier nonlinearities, up-/down-conversion phase noise, and the SI channel. First, we develop a detailed baseband model that captures the most significant transceiver RF imperfections, for both separate- and common-oscillator structures used in the up- and down-conversions. Then, a basis expansion model is derived to approximate the time-varying phase noise and to transform the problem of estimating the time-varying phase noise into the estimation of a set of time-invariant coefficients. Subsequently, the likelihood function is derived in the presence of the unknown intended signal to formulate the joint estimation of the intended channel, SI channel, nonlinear impairments, and phase noise, under the maximum likelihood (ML) criterion. An iterative procedure is developed to find the ML estimate of the different parameters based on the known transmitted data, the known pilot symbols, and the statistics of the unknown intended signal received from the intended transmitter. The full use of the received signal significantly reduces the required number of pilot symbols as compared to training-based techniques. We consider the two pilot-insertion structures used in LTE for the frequency-multiplexed pilots and the time-multiplexed pilots. Simulation results indicate that the proposed ML algorithms can offer a superior SI-cancellation performance with the resulting intended-signal-to-SI-and-noise ratio very close to the intended-signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

For InSAR topographic mapping, multi-baseline InSAR height estimation is known to be an effective way to facilitate phase unwrapping by significantly increasing the ambiguity intervals and maintaining good height measurement sensitivity, especially in mountainous areas. In this paper, an efficient multi-baseline SAR interferometry approach based on maximum likelihood estimation is developed for refined topographic mapping in mountainous areas. In the algorithm, maximum likelihood (ML) height estimation is used to measure the topographic details and avoid the complicated phase unwrapping process. In order to be well-adapted to the mountainous terrain conditions, the prior height probability is re-defined to take the local terrain conditions and neighboring height constraint into consideration in the algorithm. In addition, three strategies are used to optimize the maximum likelihood height estimation process to obtain higher computational efficiency, so that this method is more suitable for spaceborne InSAR data. The strategies include substituting a rational function model into the complicated conversion process from candidate height to interferometric phase, discretizing the continuous height likelihood probability, and searching for the maximum likelihood height with a flexible step length. The experiment with simulated data is designed to verify the improvement of the ML height estimation accuracy with the re-defined prior height distribution. Then the optimized processing procedure is tested with the multi-baseline L-band ALOS/PALSAR data covering the Mount Tai area in China. The height accuracy of the generated multi-baseline InSAR DEM can meet both standards of American DTED-2 and Chinese national 1:50,000 DEM (mountain) Level 2. [ABSTRACT FROM AUTHOR]

In this letter, we propose a reduced-complexity optimal modified sphere decoding (MSD) detection scheme for sparse code multiple access (SCMA). As SCMA systems are characterized by a number of resource elements that are less than the number of the supported users, the channel matrix is rank-deficient, and SD cannot be directly applied. Inspired by the Tikhonov regularization, we formulate a new full-rank detection problem that it is equivalent to the original rank-deficient detection problem for constellation points with constant modulus and an important subset of non-constant modulus constellations. By exploiting the SCMA structure, the computational complexity of MSD is reduced compared with the conventional SD. We also employ list MSD to facilitate channel coding. Simulation results demonstrate that in uncoded SCMA systems, the proposed MSD achieves the performance of the optimal maximum likelihood detection. Additionally, the proposed MSD benefits from a lower average complexity compared with message passing algorithm. [ABSTRACT FROM PUBLISHER]

Some practical systems such as blast furnaces and turbofan engines have degradation processes with memory effects. The term of memory effects implies that the future states of the degradation processes depend on both the current state and the past states because of the interaction with environments. However, most works generally used a memoryless Markovian process to model the degradation processes. To characterize the memory effects in practical systems, we develop a new type of degradation model, in which the diffusion is represented as a fractional Brownian motion (FBM). FBM is actually a special non-Markovian process with long-term dependencies. Based on the monitored data, a Monte Carlo method is used to predict the remaining useful life (RUL). The unknown parameters in the proposed model can be estimated by the maximum likelihood algorithm, and then the distribution of the RUL is predicted. The effectiveness of the proposed model is fully verified by a numerical example and a practical case study. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of time delay estimation (TDE) from single-carrier (SC) or multi-carrier (MC) direct-sequence spread spectrum (DSSS) multipath transmissions in the presence of multiple transmit and/or receive antennas that will characterize future 5G radio interface technologies (RITs), such as coded-domain nonorthogonal multiple access. We derive for the first time a closed-form expression for the Cramer-Rao lower bound (CRLB) and develop two maximum likelihood (ML) multipath TDEs for SC DSSS single-input multiple-output (SIMO) in the non-data-aided (NDA) case. The first TDE, based on iterative expectation maximization (EM), provides accurate estimates whenever a good initial guess of the parameters is available at the receiver. The second TDE implements the ML criterion in a non-iterative way and finds the global maximum of the compressed likelihood function using the importance sampling (IS) technique without requiring any initialization. We also extend both the SC DSSS SIMO CRLB and the two new SC DSSS SIMO ML NDA TDEs to MC DSSS RITs and to multiple-input multiple-output structures with any diversity versus multiplexing pre-coding type before generalizing them all to the data-aided (DA) case. Simulations suggest that the EM TDE is suitable for large observation in space, time, and/or frequency, whereas the IS TDE is preferred in the opposite case of very short data records. Moreover, we show in the NDA case, both analytically and by simulations, that spatial (transmit and receive), temporal, and frequency samples interchangeably have the same impact on estimation accuracy and performance bound regardless of the channel correlation type and amount present in each dimension. Furthermore, we are able to properly cope with such channel correlations that do indeed arise in practice and, hence, become very challenging both in estimation and CRLB derivation in the DA case, but that have been so far overlooked in previous works. [ABSTRACT FROM PUBLISHER]

Passive source localization via a maximum likelihood (ML) estimator can achieve a high accuracy but involves high calculation burdens, especially when based on time-of-arrival and frequency-of-arrival measurements for its internal nonlinearity and nonconvex nature. In this paper, we use the Pincus theorem and Monte Carlo importance sampling (MCIS) to achieve an approximate global solution to the ML problem in a computationally efficient manner. The main contribution is that we construct a probability density function (PDF) of Gaussian distribution, which is called an important function for efficient sampling, to approximate the ML estimation related to complicated distributions. The improved performance of the proposed method is attributed to the optimal selection of the important function and also the guaranteed convergence to a global maximum. This process greatly reduces the amount of calculation, but an initial solution estimation is required resulting from Taylor series expansion. However, the MCIS method is robust to this prior knowledge for point sampling and correction of importance weights. Simulation results show that the proposed method can achieve the Cramér-Rao lower bound at a moderate Gaussian noise level and outperforms the existing methods. [ABSTRACT FROM AUTHOR]

This contribution analyses the performance of efficient multiple-input-multiple-output (MIMO) detectors under correlated channels and imperfect coefficients channel estimation. A number of signal detection principles and techniques, including the minimum mean squared error detector with and without ordered successive interference cancellation; the sphere decoding MIMO detection, as well as promising near-orthogonal transformation techniques combined with these detectors, namely the lattice reduction and the QR decomposition are analysed under the perspective of complexity-performance tradeoff. While in most of available works perfect channel state information and uncorrelated channels have been considered, herein the complexity-performance tradeoff has been analysed and compared with the maximum likelihood (ML) limit under specific but practical scenarios of interest, namely: high spectral efficiency scenario; channel error estimates; channel/antenna correlation; combined channel errors and correlated channels. Under performance-complexity perspective, the optimum ML-MIMO detector is deployed as reference aiming to evaluate the efficiency and performance degradation of those sub-optimal MIMO detectors operating under hostile channel conditions. [ABSTRACT FROM AUTHOR]

Multichannel synthetic aperture radar (SAR) is a significant breakthrough to the inherent limitation between high-resolution and wide-swath (HRWS) compared with conventional SAR. Moving target indication (MTI) is an important application of spaceborne HRWS SAR systems. In contrast to previous studies of SARMTI, the HRWS SAR mainly faces the problem of under-sampled data of each channel, causing single-channel imaging and processing to be infeasible. In this study, the estimation of velocity is equivalent to the estimation of the cone angle according to their relationship. The maximum likelihood (ML) based algorithm is proposed to estimate the radial velocity in the existence of Doppler ambiguities. After that, the signal reconstruction and compensation for the phase offset caused by radial velocity are processed for a moving target. Finally, the traditional imaging algorithm is applied to obtain a focused moving target image. Experiments are conducted to evaluate the accuracy and effectiveness of the estimator under different signal-to-noise ratios (SNR). Furthermore, the performance is analyzed with respect to the motion ship that experiences interference due to different distributions of sea clutter. The results verify that the proposed algorithm is accurate and efficient with low computational complexity. This paper aims at providing a solution to the velocity estimation problem in the future HRWS SAR systems with multiple receive channels. [ABSTRACT FROM AUTHOR]

One application for time-difference-of-arrival (TDOA) estimation is in emitter localization. A signal from an emitter reaching a group of sensors, each in a separate location, will have different arrival times. Finding the TDOAs between the output of pairs of sensors will provide the necessary measurements for the hyperbolic localization of the emitter. When the sensors acquire the signal by compressed sensing (CS), their outputs are reduced dimension linear transformation of the time samples of the signal. This shuffling of the time samples breaks up their time relation. Thus, a cross correlation of the CS output of two sensors cannot determine the TDOA. To apply cross correlation, it is necessary to reconstruct the time samples. This letter proposes an alternative that uses only the coefficients of the discrete Fourier transform (DFT) of the CS samples. It begins with the derivation of the maximum likelihood (ML) equation and the ML estimator. This estimator requires known values of signal and noise powers. Substituting these values by their estimates lead to the approximate ML estimator. The phase of the product of two DFT coefficients from each sensor is proportional to the unknown TDOA. Hence, these coefficients can provide an estimation of the TDOA. Simulation results show that although ML is the best, as expected, all these estimators have very close performance. [ABSTRACT FROM PUBLISHER]