Leveraging one-bit analog-to-digital converter (ADC) instead of high resolution ADC has been introduced as a promising solution for reducing the power consumption and hardware cost of massive millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. However, performance loss caused by discarding the amplitude information by one-bit quantizers is a significant impairment which calls for the development of more accurate channel estimators. To address this problem, a one-bit mmWave MIMO channel estimation method based on adaptive boosting (AdaBoost) which employs two-stage weak classifiers is developed. In the first stage of each weak classifier, an approximate Gaussian discriminant analysis (GDA) binary classifier is used. To capture the sparsity of mmWave channels in the angular domain, a hard thresholding operator is employed in the second stage of each weak classifier. Numerical simulations are included to demonstrate the efficiency and accuracy of the proposed channel estimator.

This paper addresses the problem of quickest change detection of an unknown mean-shift in multiple Gaussian data streams. We propose a novel extension of the window-limited CuSum (WL-CuSum) test which utilizes the James-Stein estimator to improve detection performance. Compared to traditional maximum likelihood-based approaches, the proposed approach can considerably reduce the detection delay, especially when the number of streams is large. Our theoretical results indicate that the proposed test asymptotically optimal, and non-asymptotically a uniform improvement over its maximum likelihood alternative. The performance is improved for all values of the unknown post-change parameter, as long as the number of the data streams is greater than three. Overall, the results suggest that shrinkage estimators, such as the James-Stein estimator, can provide substantial performance improvement in change detection problems with unknown parameters.

The problem of quickest change detection is studied in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams. The James-Stein estimator is used in constructing detection schemes that exhibit strong detection performance both asymptotically and non-asymptotically. Our results indicate that utilizing the James-Stein estimator in the recently developed window-limited CuSum test constitutes a uniform improvement over its typical maximum likelihood variant. That is, the proposed James-Stein version achieves a smaller detection delay simultaneously for all possible post-change parameter values and every false alarm rate constraint, as long as the number of parallel data streams is greater than three. Additionally, an alternative detection procedure that utilizes the James-Stein estimator is shown to have asymptotic detection delay properties that compare favorably to existing tests. The second-order asymptotic detection delay term is reduced in a predefined low-dimensional subspace of the parameter space, while second-order asymptotic minimaxity is preserved. The results are verified in simulations, where the proposed schemes are shown to achieve smaller detection delays compared to existing alternatives, especially when the number of data streams is large.

This paper considers resource allocation problems for integrated sensing and communications (ISAC) systems operating in dynamic shared spectrum scenarios. Specifically, the paper proposes a new Model-Based Online Learning (MBOL) method that accounts for partial observability caused by noisy observations. First, the approach converts the partially observable Markov decision process (POMDP) to the equivalent belief state Markov decision process (MDP). Then, the state prediction model is learned from the sensor observations. A loss correction approach is introduced to solve the model learning problem under partial observability. The proposed approach is evaluated in allocating subcarriers and their powers to communications and sensing tasks in multicarrier ISAC systems. The simulations demonstrate improved performance in partially observable settings.

We consider a collaborative decision-making frame-work where heterogeneous agents receive streaming and partially informative observations. We consider two asynchronous scenarios that differ based on the agents' participation patterns and the fusion center's policies. By using hypothetical interventions on individual agents to conduct credit assignment, we attribute causal impact scores to each agent for the joint decision. By further employing these scores in a guided theoretical analysis, we compare the fusion center's two policies by evaluating their vulnerability to adversarial attacks, robustness against moderate deviations, and fairness.

We study communication-constrained secret key generation, where two legitimate parties would like to generate a secret key using communication subject to a rate constraint. The problem is studied in the finite-blocklength regime. In this regime, the use of auxiliary random variables subject to Markov chain conditions in the corresponding asymptotic bounds has proven to make most existing proof techniques insufficient. However, two recently proposed proof techniques – one for the achievability side based on Poisson matching, and another for the converse side based on reverse hypercontractivity – allow us to overcome these issues to some extent. Based on these techniques, novel one-shot and second-order achievability and converse bounds are derived for the problem. While the second-order bounds do not coincide, leaving a precise second-order characterization of the problem an open issue, they improve upon the previously known tightest bounds. The second-order bounds are demonstrated for two simple sources: the binary symmetric source and the Gaussian symmetric source. For the binary source, we find that the gap between the two bounds is mainly due to an unwanted constant in the converse bound, and the non-convexity of the achievability bound.

A wireless sensor network performs spatial inference on a physical phenomenon of interest. The areas in which this phenomenon exhibits interesting or anomalous behavior are identified whilst controlling false positives. We expand our previous work based on multiple hypothesis testing (MHT) and local false discovery rates to save energy and reduce spectrum use. The number of transmissions from sensors producing uninformative statistics are reduced by introducing censoring for MHT that imposes a communication rate constraint while maintaining the desired performance. Two novel methods are proposed. As our numerical experiments demonstrate, both approaches reduce the number of transmissions while maintaining false discovery rate control. In addition, one method allows to either define a fixed number of total transmissions or to trade the number of transmissions off against the achieved detection power.

This paper considers waveform optimization problems for managing and mitigating interference in integrated sensing and communications (ISAC) systems. In particular, we consider dynamic shared spectrum scenarios where channel and interference statistics are nonstationary. The focus is on allocating frequency and power resources in multicarrier ISAC systems. A data-efficient Model-Free Online Learning (MFOL) algorithm is proposed as an alternative to the previously proposed Model-Based Online Learning (MBOL) approach. Empirical results show that the MFOL method learns slower than the MBOL method but can perform better when a large number of training samples are available.

Integrated Sensing and Communication Systems (ISAC) that are capable of functioning both as radars and communication systems have a tremendous potential to provide significant performance gains and cost savings and facilitate the sharing of the same energy, spectral, and hardware resources. Managing interference in frequency and spatial domains is a crucial task in ISAC. We consider a radar-centric scenario where a radar system is able to do beamforming and transmit communications data on the side. We propose an improved method allowing good control of the transmit beampattern power resulting in lower communication error level. Furthermore, we also propose straightforward method for phase coding of information in radar signals.

A spatial signal is monitored by a large-scale sensor network. We propose a novel method to identify areas where the signal behaves interestingly, anomalously, or simply differently from what is expected. The sensors pre-process their measurements locally and transmit a local summary statistic to a fusion center or a cloud. This saves bandwidth and energy. The fusion center or cloud computes a spatially varying empirical Bayes prior on the signal’s spatial behavior. The spatial domain is modeled as a fine discrete grid. The contextual local false discovery rate is computed for each grid point. A decision on the local state of the signal is made for each grid point, hence, many decisions are made simultaneously. A multiple hypothesis testing approach with false discovery rate control is used. The proposed procedure estimates the areas of interesting signal behavior with higher precision than existing methods. No tuning parameters have to be defined by the user.

The ever-increasing congestion in the radio spectrum has made coexistence and co-design for radar and communication systems an important problem to address. The radio spectrum is a rapidly time-frequency-space varying resource, and learning is required to use the spectrum and mitigate the interference. This paper proposes a model-based online learning (MBOL) framework to enable a structured way to formulate efficient online learning algorithms for resource sharing in joint radar-communication (JRC) systems. As an example, we apply the MBOL framework for allocating frequency resources in non-cooperative shared spectrum scenarios. The proposed MBOL algorithm learns a predictive model using online convex optimization (OCO) and chooses the best frequency channels in uncertain interference environments. The algorithm outperforms the considered baseline algorithms in terms of regret that quantifies the cost of learning.

We employ a recent technique based on a semigroup application of the method of types to improve on a second-order converse for the common randomness (CR) generation problem. The previously known bound lead to a correct second-order asymptotic rate, but incorrect sign on the second-order term for error rates below 1/2. The new bound has both the correct scaling and sign of the second-order term for small enough error rates.

Detection of multiple spatial events in parallel is of wide interest in many modern applications, such as Internet of Things, environmental monitoring, and wireless communication. Sensor networks can be used for acquiring data and performing inference. In this paper, we take a Bayesian approach and model the detection of spatial events as a Bayesian multiple change point detection problem. The sensor network is assumed to be divided into distinct known clusters. In each cluster, a point source generates a spatial event that propagates omnidirectionally. The event causes a change in the local environment, which changes the distribution of observations at sensors located within the realm of this event. We propose a method for performing sequential multiple change-point detection under the Bayesian paradigm. It is shown analytically that the proposed procedure controls the false discovery rate (FDR), which is an appropriate criterion for statistically controlling the prevalence of false alarms in a setting where multiple decisions are made in parallel. It is numerically shown that exploiting spatial information decreases the average detection delay compared to procedures that do not properly use this information.

This paper investigates the problem of secret key generation from correlated Gaussian random variables in the short block-length regime. Inspired by the state-of-the-art performance provided by polar codes in the short blocklength regime for channel coding, we propose an explicit protocol based on polar codes for generating the secret keys. This protocol differs from previously proposed key generation protocols based on polar coding in two main ways: (i) we consider a Gaussian source for the key generation; (ii) we focus on the short block-length regime. Simulation results show that the proposed protocol performs well even for very short blocklengths, especially if one can relax the BER requirements for the generated keys. They also demonstrate that the polar code based protocol outperforms a similar one using LDPC codes in place of polar codes, and that this advantage grows the shorter the blocklength becomes.

We propose a novel three-stage delay-Doppler-angle estimation algorithm for a MIMO-OFDM radar in the presence of inter-carrier interference (ICI). First, leveraging the observation that spatial co-variance matrix is independent of target delays and Dopplers, we perform angle estimation via the MUSIC algorithm. For each estimated angle, we next formulate the radar delay-Doppler estimation as a joint carrier frequency offset (CFO) and channel estimation problem via an APES (amplitude and phase estimation) spatial filtering approach by transforming the delay-Doppler parameterized radar channel into an unstructured form. In the final stage, delay and Doppler of each target can be recovered from target-specific channel estimates over time and frequency. Simulation results illustrate the superior performance of the proposed algorithm in high-mobility scenarios.

In this paper the problem of recognizing waveform and modulation is addressed in radar-communications coexistence and shared spectrum scenarios. We propose a deep learning method for waveform classification. A hierarchical recognition approach is employed. The received complex-valued signal is first classified to single carrier radar, communication or multicarrier waveforms. Fourier synchrosqueezing transformation (FSST) time-frequency representation is computed and used as an input to a convolutional neural network (CNN). For multicarrier signals, key waveform parameters including the cyclic prefix (CP) duration, number of subcarriers and subcarrier spacing are estimated. The modulation type used for subcarriers is recognized. Independent component analysis (ICA) is used to enforce independence of I- and Q-components, and consequently significantly improving the classification performance. Simulation results demonstrate the high classification performance of the proposed method even for orthogonal frequency division multiplexing (OFDM) signals with high-order quadrature amplitude modulation (QAM).

Several modern applications involve large-scale sensor networks for statistical inference. For example, such sensor networks are of significant interest for Internet of Things applications. In this paper, we consider Bayesian multiple changepoint detection using a sensor network in which a fusion center can receive a data stream from each sensor. Due to communication limitations, the fusion center monitors only a subset of the data streams at each time slot. We propose a detection procedure that handles these limitations by monitoring the sensors with the highest posterior probabilities of change points having occurred. It is shown that the proposed procedure attains an average detection delay that does not increase with the number of sensors, while controlling the false discovery rate. The proposed procedure is also shown to be useful for unveiling the tradeoff between reducing the average detection delay and reducing the average number of observations drawn until discovery.

We consider the problem of secret key generation from correlated Gaussian random variables in the finite blocklength regime. Such keys could be used to encrypt communication in IoT networks, and have provable secrecy guarantees in contrast to classic cryptographic approaches. We investigate the performance of polar coding schemes for generating the secret key over short blocklengths. Our simulation results show that the proposed scheme achieves close to theoretical upper bounds at short blocklengths.

Sparse arrays can resolve vastly more scatterers than the number of sensors in tasks such as coherent source localization. This entails significant cost reductions compared to conventional arrays with uniformly spaced elements. In this paper, we introduce a parametric sparse linear array configuration called the Kløve array (KA). The KA has a contiguous sum and difference co-array, making it suitable for both active and passive sensing. We show that KAs of any size can have both low redundancy, and few closely spaced elements. This may improve robustness in the face of mutual coupling.1

RF convergence where the same transceiver is used for communications and sensing purposes is taking place. In this paper, a dual-use radar-communications multicarrier waveform is proposed, where different subcarriers are assigned to different subsystems. Two algorithms for subcarrier assignment and optimal power allocation for the radar and communications subsystems are developed. A compound mutual information (MI) based objective function is used for optimizing the power allocation of each subsystem in both design algorithms. The first proposed design algorithm assumes priority for the radar subsystem and it is called radar selfish design. The second proposed design algorithm is called cooperative design, in which both subsystems are jointly optimized by maximizing a compound MI based objective function.

In this paper we propose a genie-aided strategy to optimize the use of renewable energy (RE) in a community of households with shared access to storage and RE generation facilities. The households are spread over a limited geographical area, and are subject to different time-varying power consumption profiles, and energy prices. We consider a finite number of RE generators and energy storage devices (ESDs), which are deployed in specific locations. The proposed strategy seeks to minimize the energy cost incurred by the participating households by optimizing the rate at which RE is consumed over time. Our model takes into account the power loss incurred in the transmission of energy from the generators to the loads. The optimization problem is cast as a non-convex quadratically constrained quadratic program, which is simplified in order to derive an approximate solution. Numerical results show that transmission losses and differences across price and load can significantly affect the optimal RE allocation among the households. The proposed strategy offers valuable insights for energy planning purposes and can be used to devise real-time RE management algorithms by incorporating the necessary forecasting techniques.

Internet of Things technologies will enable smart energy planning, which in turn will expedite the adoption of renewable energy (RE). In this paper, we propose a mathematical framework to optimize the use of RE in a shared solar environment featuring households with access to several RE generators. We consider location and time-dependent electricity prices, and formulate an optimization problem to minimize the energy cost incurred by the households over a finite planning horizon. The proposed framework accounts for transmission losses and battery inefficiencies. We then proposed two approaches to solve the formulated optimization problem. The first approach is based on quadratic programming, and is used to obtain a precision-controllable solution, requiring discretization in time and convex relaxation. The second approach is based on variational methods, which are used to tackle the problem directly in continuous time, thus obtaining a solution in closed form after introducing reasonable simplifications. To ensure full cooperation, we finally derive a fair energy allocation policy, which allocates RE to each household in proportion to its capital investment. The obtained analytical results allow us to evaluate the relationship between achievable performance, RE production, transmission losses, and price variability. Extensive simulations are used to verify the derived analytical results, illustrate the characteristics of the proposed strategies and compare their achievable performance.

In this work, a distributed Kalman filtering and clustering framework for sensor networks tasked with tracking multiple state vector sequences is developed. This is achieved through recursively updating the likelihood of a state vector estimation from one agent offering valid information about the state vector of its neighbors, given the available observation data. These likelihoods then form the diffusion coefficients, used for information fusion over the sensor network. For rigour, the mean and mean square behavior of the developed Kalman filtering and clustering framework is analyzed, convergence criteria are established, and the performance of the developed framework is demonstrated in a simulation example.

Sparse sensor arrays offer a cost effective alternative to uniform arrays. By utilizing the co-array , a sparse array can match the performance of a filled array, despite having significantly fewer sensors. However, even sparse arrays can have many closely spaced elements, which may deteriorate the array performance in the presence of mutual coupling. This letter proposes a novel sparse planar array configuration with few unit inter-element spacings. This concentric rectangular array (CRA) is designed for active sensing tasks, such as microwave or ultrasound imaging, in which the same elements are used for both transmission and reception. The properties of the CRA are compared to two well-known sparse geometries: the boundary array and the minimum-redundancy array (MRA). Numerical searches reveal that the CRA is the MRA with the fewest unit element displacements for certain array dimensions.

Noise power uncertainty is a major issue in energy-based spectrum sensors. Any uncertainty in the noise power leads to significant reduction in the detection performance of the energy detector and also results in a performance limitation in the form of SNR walls. In this paper, we propose an evidence theory (also called Dempster-Shafer theory (DST)) based cooperative energy detection (CED) for spectrum sensing. The noise variance is modeled as a random variable with a known distribution. The analyzed system model is similar to a distributed parallel detection network where each secondary user (SU) evaluates the energy from its received signal samples and sends it to a fusion center (FC), which makes the final decision. However, in the proposed DST-based method, the SUs sends computed belief-values instead of actual energy value to the FC. The uncertainty in the noise variance is accounted for by discounting the belief values based on the amount of uncertainty associated with each SU. Finally, the discounted belief values are combined using Dempster rule to reach at a global decision. Simulation results indicate that the proposed DST scheme significantly improves the detection probability under low average signal-to-noise ratio(ASNR) compared to the traditional sum fusion rule in the presence of noise uncertainty.

In this paper we propose a novel coalitional game theory based optimization method for minimizing the cost of the electricity consumed from the power grid by a community of smart households. A smart household may own both a renewable energy source and an energy storage system (ESS), or only an ESS. We propose an optimization model in which all the members of the community jointly share their renewable resources and storage systems. We show that the proposed coalitional optimization method reduces the consumption costs both at community level and at the individual level when compared to the case in which the households would individually optimize their costs. The monetary revenues gained by the coalition are divided among the members of the coalition according to the Shapley value. Simulation examples show that the proposed coalitional optimization method may reduce the electricity costs for the community by roughly 18%.

Geometrical maps of the indoor environment are vital to many applications such as indoor localization and robot navigation. In this paper, a method for three-dimensional indoor mapping using multipath delay and direction estimates is developed. Required high-resolution estimates of multipath propagation path parameters are obtained using radio frequency measurements between two antenna arrays at multiple locations. A ray-tracing algorithm is developed for detecting specular propagation paths of radio signals and corresponding reflection points. A novel method is proposed to extract walls and other planar structures from the cloud of reflection points. The empirical results show an improved precision and enhanced geometric information compared to previous experiments.

Learning-based sensing policies for multi-band flexible spectrum use, in particular cognitive radios operating in non-stationary radio environments are proposed. The proposed policies stem from the stochastic non-stationary restless multi-armed bandit formulation of opportunistic spectrum access. The non-stationary radio environment assumed in this paper is an appropriate model for a realistic cognitive radio systems, where the obtainable data rates depend on many unknown time-varying factors. These are e.g. mobility, fading and primary user activity. The developed policies are index policies, where the index of a frequency band depends on the discounted average reward of the band and a recency-based exploration bonus. The exploration bonus encourages sensing frequency bands that have not been explored for a long time. However, there is a maximum number of time instances when any band can remain unexplored. These index policies are computationally simple making them attractive for mobile cognitive radios. In our simulation examples, we demonstrate that the proposed policies can often provide higher cumulative data rate than other existing state-of-the-art policies.

The widely used fixed-point FastICA algorithm has been derived and motivated as being an approximate Newton-Raphson (NR) algorithm. In the original derivation, the Lagrangian multiplier is treated as a constant and an ad hoc approximation is used for Jacobian matrix in the NR update. In this letter, we provide an alternative derivation of the FastICA algorithm without approximation. We show that any solution to the FastICA algorithm is a solution to the exact NR algorithm as well. In addition, we propose a novel power iteration algorithm for FastICA which is remarkably more stable than the fixed-point algorithm, when the sample size is not orders of magnitudes larger than the dimension. Our proposed algorithm can be run on parallel computing nodes.

In this paper, we address the prospects and key enabling technologies for highly efficient and accurate device positioning and tracking in fifth generation (5G) radio access networks. Building on the premises of ultra-dense networks as well as on the adoption of multicarrier waveforms and antenna arrays in the access nodes (ANs), we first formulate extended Kalman filter (EKF)-based solutions for computationally efficient joint estimation and tracking of the time of arrival (ToA) and direction of arrival (DoA) of the user nodes (UNs) using uplink reference signals. Then, a second EKF stage is proposed in order to fuse the individual DoA and ToA estimates from one or several ANs into a UN position estimate. Since all the processing takes place at the network side, the computing complexity and energy consumption at the UN side are kept to a minimum. The cascaded EKFs proposed in this article also take into account the unavoidable relative clock offsets between UNs and ANs, such that reliable clock synchronization of the access-link is obtained as a valuable by-product. The proposed cascaded EKF scheme is then revised and extended to more general and challenging scenarios where not only the UNs have clock offsets against the network time, but also the ANs themselves are not mutually synchronized in time. Finally, comprehensive performance evaluations of the proposed solutions on a realistic 5G network setup, building on the METIS project based outdoor Madrid map model together with complete ray tracing based propagation modeling, are provided. The obtained results clearly demonstrate that by using the developed methods, sub-meter scale positioning and tracking accuracy of moving devices is indeed technically feasible in future 5G radio access networks operating at sub-6 GHz frequencies, despite the realistic assumptions related to clock offsets and potentially even under unsynchronized network elements.

MIMO radars use multiple waveforms in order to resolve more targets and achieve gains in target detection, parameter estimation and recognition, for example. In this paper, we propose a method for optimizing multiple waveforms with low peak sidelobe and peak cross-correlation levels for MIMO radar. The optimization method relaxes the original quartic problem into a quadratic one and iterates the relaxed problem to improve the solution. The numerical examples demonstrate that good waveforms are obtained with the proposed method.

A joint radar/communication system is considered, where the radar adaptively designs the transmitted waveform such that the interference caused to the cellular systems is strictly controlled. In this paper, different Mutual Information based criteria for radar waveform optimization are proposed and the corresponding waveform optimization problems are formulated and solved analytically. Radar performance trade-offs for the considered Mutual Information based criteria are presented and, using simulation results, it is shown that a larger maximized Mutual Information does not guarantee an optimal detection performance. It is also emphasized the importance of exploiting the communication signals scattered off the target for the detection task when dealing with weak radar returns.

In this paper a novel algorithm is proposed for joint synchronization and localization in ad hoc networks. The proposed algorithm is based on broadcast messaging, with number of messages linear to the number of nodes, versus quadratic for techniques based on two-way message exchange. The identifiability of network synchronization problem is improved by introducing localization constraints. Hence, the proposed algorithm does not require a full set of measurements. Numerical results are provided using a model based on wireless LAN specifications. In scenarios with missing data, the proposed algorithm significantly improves synchronization and localization performance compared to commonly used techniques.

In blind equalization (BE) a cost function based on the fit between the equalizer outputs and the signaling constellation is generally defined. To minimize such a cost function, standard gradient descent learning is commonly used. We exploit the idea of relative gradient (RG) learning to modify such standard Bussgang-type algorithms. Instead of one output each time, our method uses a sliding block of outputs. Our RG-based block Bussgang algorithms have faster convergence than corresponding Bussgang algorithms based on the standard gradient.

Radar waveforms are often optimized to achieve minimal sidelobes in the ambiguity function. We show that sampling rate can affect the optimality of the sidelobe level, so the sampling rate should be considered already at the optimization phase. We develop a theorem showing that for narrowband waveforms with amplitude and phase coding, the peaks of the ambiguity function cannot increase due to oversampling. Nevertheless, it is shown that it is possible for oversampling to cause an increased sidelobe level. Numerical examples demonstrating the validity of the results are provided.

The ever increasing demand for spectrum, due to services with data rate requirements and ongoing exponential increase in the number of wireless devices, has pushed for new methods that allow for a flexible and shared use of spectrum among different wireless and radar systems. Different systems need to sense the spectrum and adaptively design their transmitted waveforms in a manner such that they do not cause harmful interference to other systems. In this paper we consider a scenario where radar and wireless communication systems are operated jointly. The opportunistic radar constantly senses the spectrum and adapts its waveform based on the occupancy and maximum allowed power. A radar waveform is optimized for the target detection task such that it does not cause significant performance loss to the communication system. We show that the waveform optimized based on the Neyman-Pearson detector provides a very similar detection performance with the one optimized based on Mutual Information maximization. We also demonstrate that the detection performance improves if, at the radar receiver, the reflections off the target due to the communication signals are considered.

Radar systems commonly require use of waveforms with low sidelobes and also low cross-correlation if multiple waveforms are being used. It is possible to decrease the apparent peak sidelobe and cross-correlation levels at the receiver by employing a mismatched filter. In this paper, we propose mismatched filter design method that minimizes the peak sidelobe and cross-correlation levels for all Doppler frequencies. The proposed design method is formulated as an optimization problem employing sum of squares representation of nonnegative polynomials and solved using semidefinite relaxation.

This paper proposes a new method for scheduling the charging of plug-in electric vehicle's (PEV) battery. The method is employed in the demand side management of smart grids and has the goal of reducing the cost of charging over a long time horizon. The problem of scheduling the PEV battery charging is modeled as a Markov decision process with unknown transition probabilities. A fitted Qiteration batch reinforcement learning algorithm with kernel-based approximation of the value iteration is proposed for learning the transition dynamics and solving the charging problem. The solution is obtained based on the knowledge of the true day-ahead electricity prices and predicted prices for the second day ahead. Simulation results using true pricing data demonstrate cost savings of 8%-40% for the consumer.

In indoor wireless localization, navigation and communications, knowledge of the floor plan is valuable side information and provides more reliable performance. Such information may not be available. Estimating indoor maps using sensor networks and time delay measurements, i.e., without angular information, is a challenging task. In this paper, a novel algorithm is developed to solve the problem of mapping and measurement clustering. The algorithm is applicable to wireless and acoustic networks with high resolution time delay measurements.

MIMO radars transmit multiple waveforms simultaneously. As the number of waveforms used increases, the cross-correlation between the waveforms also tends to increase if the transmission time or bandwidth is not increased. By using a bank of mismatched filters at the receivers, it is possible to decrease the peak cross-correlation and autocorrelation side-lobe levels of the used waveforms. Furthermore, interference power can also be significantly reduced at the same time. We propose a filterbank design for the MIMO radar receiver based on minimizing the interference power at the receiver while controlling peak sidelobe and cross-correlation values, resulting in a convex optimization problem.

Independent component analysis (ICA) is a widely used technique for extracting latent (unobserved) source signals from observed multidimensional measurements. In this paper we construct a fast and robust bootstrap (FRB) method for testing hypotheses on elements of the mixing matrix in the ICA model. The FRB method can be devised for estimators which are solutions to fixed-point (FP) equations. In this paper we develop FRB test for the widely popular FastICA estimator. The developed test can be used in real-world ICA analysis of high-dimensional data sets seen e.g. in big data analysis, as it avoids the common obstacles of conventional bootstrap such as immense computational cost and lack of robustness. Moreover, instability and convergence problems of the Fast ICA algorithm when applied to bootstrap data are prevented. Simulations and examples illustrate the usefulness and validity of the developed test.

This paper presents cepstral analysis of OFDM signals. Cepstrum can reveal periodicities in a signal and has been widely used in audio and speech processing applications. In this work, the focus is on cepstrum based detection and classification of OFDM signals for cognitive radio applications such as flexible spectrum reuse and coexistence of heterogeneous networks. Two cepstrum based sensing schemes formulated as hypothesis testing are proposed. The distributions of the test statistics are derived under the null hypothesis so that the thresholds for the Neyman-Pearson detectors can be computed analytically. These cepstrum based schemes are compared to the traditional energy detector. First scheme is robust to noise uncertainty which is a clear benefit when compared to the energy detector. On the other hand, the second cepstrum based scheme has performance similar to the energy detection. Later, it is shown that the cepstral analysis can be used to estimate parameters of OFDM waveforms such as number of samples in data and cyclic prefix (CP) parts of an OFDM symbol. These features can be used to distinguish among different OFDM waveforms, which is not possible with energy detection.

An ambiguity function (AF) for the multiple-input multiple-output (MIMO) radar with correlated waveforms is derived. It serves as a generalized AF for which the phased-array and the traditional MIMO radar AFs are important special cases. A simplified expression for the AF for the case of far-field targets and narrow-band waveforms is also derived. We establish relationships between the generalized MIMO radar AF metric and the previous works on AF including the Woodward's AF and the AF defined for the traditional colocated MIMO radar. Moreover, we compare the AF of the MIMO radar with correlated waveforms with the squared-summation-form AF definition. Simulation results show that the generalized MIMO radar AF achieves lower relative sidelobe level with proper design of the waveform correlation matrix or, equivalently, the transmit beamspace matrix.

In his paper, we propose to model the energy consumption of smart grid households with energy storage systems (ESS) as an intertemporal trading economy. Intertemporal trade refers to transaction of goods across time when an agent, a any time, is faced with the option of consuming and/or saving with the aim of using the savings in the future and/or spending the savings from the past. Smart homes define optimal consumption as balancing/leveling their consumption profile such that the utility company is presented with a more uniform demand. Due to the varying nature of energy requirements of household and market energy prices over different time periods in a day, households face a trade-off between consuming to meet their current energy requirements and/or sorting energy for future consumption and/or spending energy stored in the past. These trade-offs or consumption preferences of the household are modeled as a Cobb-Douglas utility function using consumer theory. This utility function is maximized subject to budge and storage constrains to solve for the optimal consumption profile. We graphically illustrate the process of computing the optimal consumption point when a day is divided into two or three time periods. For higher dimensional multi-period models, we formulae the optimization problem as a geometric program (GP). Simulation results show that the proposed approach is able to achieve a uniform consumption profile with extremely low peak to average ratio (PAR) close to 1 in addition to reducing consumption costs for the household by about 6%.

This letter considers the problem of estimating the directional probability distribution of wavefields observed by sensor arrays. In particular, the angular distributions of wavefields are assumed to be mixtures of von-Mises distributions. Mixture models facilitate estimating multimodal and skewed angular distributions. The von-Mises distribution is fully defined with two parameters, namely the mean direction (circular mean) and the concentration parameter. The widely-employed Gaussian distribution is not appropriate in directional statistics since its support is the entire real-line instead of the$[- \pi,\pi)$angular domain. A covariance-matching based estimator is proposed for the parameters of a mixture of von-Mises distributions and the corresponding Cramér-Rao lower bound is derived. A closed-form expression for the covariance matrix of the array response due to scattering is also derived based on the wavefield modeling principle. These results remain valid even for real-world conformal arrays with nonidealities including mutual coupling, mounting platform reflections, and array elements with individual directional beampatterns.

This letter proposes robust nonparametric cyclic detectors based on the spatial sign and magnitude rank concepts. The proposed detectors are single-cycle detectors exploiting the known (conjugate) cyclic autocorrelation of the signal of interest. Cyclostationarity allows distinguishing among different signals and emitters that exhibit distinct cyclostationary properties. The asymptotic distributions of the proposed cyclic detectors are established under the null hypothesis when only noise is present. Simulation results demonstrate the robust performance of the proposed detection algorithms in both Gaussian and heavy-tailed non-Gaussian noise environments.

A spatial coding of the transmitted waveforms in a distributed MIMO radar system is proposed for reducing the impact of noise and interference on the channel matrix estimate. The channel matrix is needed in target parameter estimation as well as transmitter resource allocation and target recognition, for example. It is shown that when noise or interference are correlated after filtering at the receiver, it is possible decrease the error of the channel coefficient estimates by using the proposed coding method. Numerical results shown here demonstrate the benefits of the method in practical scenarios.

Multi-linear techniques using tensor decompositions provide a unifying framework for the high-dimensional data analysis. Sparsity in tensor decompositions clearly improves the analysis and inference of multi-dimensional data. Other than non-negative tensor factorizations, the literature on tensor estimation using sparsity is limited. In this paper, we introduce sparse regularization methods for tensor decompositions which are useful for dimensionality reduction, feature selection as well as signal recovery. One major challenge in most of the tensor decomposition algorithms is their heavy dependence on good initializations. To alleviate such a critical problem we propose a reliable method based on the ridge regression to provide good starting values taking advantage of sparsity. Combined with such initializations our sparse regularization methods show highly improved performance over the conventional methods in the demonstrated simulation studies.

Demand-side management will play a crucial role in balancing the energy generation and demand in future smart grids. In this paper, game-theoretic demand-side management algorithms are proposed for energy consumption scheduling under load uncertainty. The demand-side optimization and scheduling problem is formulated as a noncooperative cost minimization game among the endusers and an iterative algorithm that averages over the load uncertainty is proposed for solving it. The proposed algorithm is proven to converge to a Nash equilibrium. Simulation results show that taking into account the uncertainty in the load reduces significantly the load peak-to-average ratio and the hourly variation of the aggregate load profile.

In this paper we introduce a novel method for synchronization and range estimation in wireless networks, that can also be applied to other broadcast-based networks. The method is based on broadcasting messages by the nodes in a single neighborhood, and estimating their time of arrival at every node. Timing errors and pairwise distances are estimated simultaneously. The number of messages needed in our method is linear to the number of nodes, versus quadratic for commonly used techniques. The algorithm is analyzed by simulation, showing equal performance compared to the state of the art at significantly lower complexity in communication.

Cooperative sensing (CS) is important for efficiently acquiring spectrum awareness in cognitive radio systems. The main focus of this paper is on the BEP (bit error probability) walls for soft decision (SD) based CS in cognitive radios. The BEP wall is a performance limitation for CS caused by imperfect reporting channels. In this paper, a distributed detection system using parallel sensing topology and a fusion center (FC) is considered. Each secondary user (SU) sends energy-based multibit SD to the FC over a reporting channel with a certain BEP. The maximum output entropy (MOE) quantization is considered for quantizing the estimated energy. For the considered case, it is established that the BEP wall values for SD based CS with MOE quantization are identical for arbitrary number of bits for quantization. Moreover, the BEP wall values for SD based CS with MOE quantization are proven to be the same as the BEP wall values for the Chair-Varshney fusion rule, which is an optimal fusion rule for one-bit hard decision based CS. Later relation between the BEP wall values of the SD based CS and the K-out-of-N fusion rules is also established.

In this paper, we propose estimating the velocity of a target using a widely distributed multiple-input multiple-output radar that employs multiple pulse repetition frequencies. In a MIMO radar, it is possible to use different PRFs in different transmitters without added complexity. This allows one to increase the number of pulses for estimation without decreasing the unambiguous range or increasing the time the target needs to be illuminated. We derive a maximum likelihood estimator for the velocity of the target under the assumptions that the scattering is independent and noise spatially and temporally white.

In this paper a reinforcement learning-based distributed sensing policy is proposed for cognitive radio networks. The proposed sensing policy is controlled by a fusion center that employs action-value learning to focus the search for idle frequencies to those parts of the spectrum that persistently provide a high data rate. The fusion center learns the local sensing performances of the secondary users and attempts to minimize the number of assigned users for sensing under a constraint on the global detection probability. A heuristic polynomial time algorithm iteratively employing the Hungarian method is proposed for finding a feasible assignment that minimizes the number of active sensors. Simulation results show that the proposed algorithm is able to find near-optimal solutions in practise significantly faster than an exact branch-and-bound search.

The focus of this paper is on performance limitations for cooperative spectrum sensing in cognitive radios caused by reporting channel errors. In this paper, hard decision (HD) based cooperative sensing (CS) is considered. Each secondary user (SU) detecting a primary user (PU) sends a one-bit local decision to a fusion center (FC). The reporting channel errors may cause bit errors which may be non-identically distributed. The reporting channels are modeled as binary symmetric channels with certain bit error probability (BEP). The limiting performances of the Chair-Varshney and K-out-of-N fusion rules at the FC are analyzed in the presence of reporting channel errors and later numerical results are presented. Earlier works in the literature have shown the existence of a BEP wall in the presence of reporting channel errors for CS under the constraints on the probabilities of missed detection and false alarm. In this paper, the BEP wall phenomenon for HD based CS is studied in a Bayesian formulation such that there is a constraint on the average probability of error.

The compound-Gaussian (CG) distributions have been successfully used for modelling the non-Gaussian clutter measured by high-resolution radars. Within the CG class, the complexK-distribution and the complext-distribution have been used for modelling sea clutter which is often heavy-tailed or spiky in nature. In this paper, a heavy-tailed CG model with an inverse Gaussian texture distribution is proposed and its distributional properties such as closed-form expressions for its probability density function (p.d.f.) as well as its amplitude p.d.f., amplitude cumulative distribution function and its kurtosis parameter are derived. Experimental validation of its usefulness for modelling measured real-world radar lake-clutter is provided where it is shown to yield better fits than its widely used competitors.

We address diversity schemes for synchronization signal transmission in MIMO systems. We provide both analytical and numerical evaluation of different diversity schemes in different scenarios in terms of signal-to-noise ratio, spatial correlation and maximum Doppler frequency. We first derive an expression for probability of detection in presence of transmit, receive and time diversity. We establish statistical properties of optimum spatial diversity transmission schemes and analytically characterize also the performance of more practical diversity schemes. Analytical results are verified with simulations. Finally we provide extensive results on both optimum schemes as well as the more practical open-loop schemes in different diversity scenarios. The results of the paper can be used to facilitate practical design and implementation of synchronization in multi-antenna wireless systems.

This paper analyzes the performance of multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) technology through the ergodic capacity. The capacity is represented based on the mean of the effective signal-to-interference-and-noise ratio (SINR) values. The asymptotic distribution of the effective SINR in the case of independent and m-dependent quality measures, i.e., post-processed SINRs, is established analytically. The asymptotic distribution is applicable for the size of post-processed SINRs of at least 1000 samples or more and m = 10. The mean value of the effective SINR based on the moment generating function of post-processed SINR is derived. Additionally, the impact of mobility on the system performance is characterized through the ergodic capacity and a system level factor which measures user mobility. The performance of MIMO OFDM system is validated by fully dynamic 3GPP Long Term Evolution network simulations in downlink under realistic mobility scenarios with low (3 km/h), medium (30 km/h) and high (120 km/h) user speeds. The simulations verify that the derived asymptotic distributions of the effective SINR for the independent and m-dependent cases are very accurate in all mobility scenarios. The simulated ergodic capacity show clear loss in the average MIMO spectral efficiency especially in high mobility scenarios.

In a widely distributed MIMO radar, the transmitters and the receivers are distributed so that they see a target from different aspects. The scattering from the target is therefore different for each transmitter-receiver pair. It is commonly assumed that a set of orthogonal waveforms are transmitted and the scattered waveforms are then separated using a matched filter to achieve diversity. In this paper, we propose a beamforming method for the widely distributed MIMO radar. Orthogonal waveforms are used initially for probing the target, i.e. to obtain information about the the target and the channel and a single waveform is then transmitted so that the SNR in the receivers is increased. Numerical simulations demonstrate that this will increase the probability of detecting the target.

The main focus of this paper is to present a performance limitation of collaborative spectrum sensing in cognitive radios with imperfect reporting channels. We consider hard decision (HD) based cooperative sensing (CS), in which each SU sends a one-bit binary decision corresponding to the absence or the presence of primary user (PU) to a fusion center (FC). Each SU sends the hard decision over a reporting channel that may cause bit errors. The effect of reporting channel errors is modeled through the widely used bit error probability (BEP). The FC fuses the local binary decisions from all the SUs to make a final decision. Counting rule or K-out-of-N fusion rule is considered for CS and its performance is studied using analytical tools and simulations. Under the constraints on the error probabilities of false alarm and missed detection, a performance limitation in the form of a BEP wall is shown to exist for the counting rule. If the BEP of the reporting channel is above the BEP wall value, then constraints on the cooperative detection performance cannot be met at the FC irrespective of the received signal quality on the listening channel or the sensing time at the SUs. Expressions for the BEP walls are presented for K-out-of-N fusion rules in terms of the error probabilities at the FC and the number of SUs collaborating. The BEP wall values are shown to be sufficiently low to be of practical importance.

Recent research has revealed that circularity (or, propriety) of complex random signals can be exploited in developing optimal signal processors. In this paper, a robust estimator of circularity is pro posed. The estimate is found by solving M-estimation equations and employing a novel weighting scheme. A simple iterative algorithm for its computation is introduced. A robust circularity detector stemming from the large sample properties of the estimator is proposed. It is shown to be valid detector under the broad class of complex elliptically symmetric (CES) distributions. An illustrative example demonstrating the reliable performance of the detector in a practical signal processing application is provided.

The main focus of this paper is on the performance limitations for cooperative spectrum sensing in cognitive radios caused by the reporting channel errors. In this paper, we consider hard decision (HD) based cooperative sensing (CS), where each secondary user (SU) detecting a primary user (PU) sends a one-bit local decision to the fusion center (FC). The reporting channel errors may cause bit errors which may be non-identically distributed. The effect of reporting channel errors is incorporated in the analysis through Bit Error Probability (BEP). The detection performance at the fusion center is studied for the counting rule or K-out-of-N fusion rule using analytical tools and simulations. For CS, a BEP wall exists under the imposed constraints on the false alarm probability and missed detection probability. In this paper, we specifically study the BEP wall phenomenon for the counting rule in a general scenario, where the reporting channels are independent but may or may not be identically distributed.

This paper addresses the problem of spectrum sharing in cognitive radios where secondary users (SUs) cooperatively sense the spectrum for identifying and accessing unoccupied spectrum bands. It is shown that spectrum sensing and sharing scenario can be modeled as a transferable utility (TU) cooperative game and that Vickrey-Clarke-Groves (VCG) auction mechanism can be used to allocate spectrum resources fairly to each user. SUs form coalitions to jointly sense the spectrum. The worth of each SU is calculated according to the work done for the coalition in terms of the information obtained about primary user (PU) activity from sensing the spectrum. The resulting games are balanced and superadditive and each SU gets a pay-off according to her worth in the coalition. Depending upon their spectrum needs, SUs use this pay-off to bid for unoccupied bands of spectrum through an VCG auction. VCG auction mechanism provides SUs with an incentive to bid truthfully according to their demand and is socially optimal. The concepts and results are illustrated using a simple example.

Mobile broadcasting MIMO systems differ in several essential ways from conventional MIMO applications, especially when they are operating in single-frequency networks. There are certain channel features, like the imbalance of received average powers, which should be taken into account in system design. In this paper, space-time coding that allows reduced complexity maximum likelihood decoding of the received signal in a single-frequency network is introduced. A novel optimization criterion for fast-decodable 4×2 structures is proposed and the performance in single-frequency networks is studied in different scenarios through simulations. It is noticed that the reduced complexity codes suffer only a fraction of a decibel performance loss compared to an earlier proposed alternative for digital video broadcasting while achieving significant savings in computational complexity when maximum likelihood decoding is applied.

In this work, the sum-rate performance of joint opportunistic scheduling and receiver design (JOSRD) is analyzed for multiuser multiple-input-multiple output (MIMO) space-division multiple access (SDMA) downlink systems. In particular, we study linear rake receivers with selective combining, maximum ratio combining and optimal combining in which signals received from all antennas of each mobile terminal (MT) are linearly combined to improve the effective signal-to-interference-plus-noise ratios (SINRs). By exploiting limited feedback on the effective SINRs, the base station (BS) schedules simultaneous data transmission on multiple beams to the MTs with the largest effective SINRs. Using extreme value theory, the average sum-rates and their scaling laws for JOSRD are derived. In particular, it is shown that the limiting distribution of the effective signal-to-interference (SIR) is of the Frechet-type whereas that of the effective SINR converges to the Gumbel-type. Furthermore, the SIR-based sum-rate scaling laws are found to follow ε log K with 0<;ε<;1, which stands in contrast to the SINR-based scaling laws governed by the conventional log log K form. Both analytical and simulation results confirm that significant performance improvement can be achieved by incorporating low-complexity linear combining techniques into the design of scheduling schemes in MIMO-SDMA downlink systems.

Cognitive radios and flexible spectrum use (FSU) provide an efficient way to exploit underutilized radio spectrum by allowing secondary users to access licensed frequencies in an agile manner with the constraint that the licensed user will not be interfered. In order to identify such spectral opportunities, spectrum sensing is needed by the secondary users. In this paper a cooperative spectrum sensing policy employed by spatially displaced multiple cognitive radios is proposed. It enables sensing of multiple potentially discontinuous frequency bands simultaneously and facilitates mitigating the effects of shadowing and fading through spatial diversity.

In this paper the performance of multiple-input multiple-output (MIMO) system in the UTRAN Long Term Evolution (LTE) standard is evaluated by means of ergodic system capacity in low (3 km/h), medium (30 km/h) and high (120 km/h) mobility scenarios. The impact of adaptive modulation as well as Hybrid ARQ (HARQ) with Chase Combining to the distribution of effective SINR is established analytically and validated by simulations. A model for ergodic system capacity employing adaptive modulation and HARQ is developed. The simulation results show that adaptive modulation combined with HARQ increases the MIMO system performance significantly especially in low mobility case, and smaller reduction of rate is experienced in high mobility scenarios.

In this paper we propose azimuth and elevation angle of arrival estimation algorithms for arbitrary array configurations. The proposed algorithms extend the Polynomial Rooting Intersection for Multidimensional Estimation (PRIME) and statistically efficient Modified Variable Projection (MVP) algorithms to arbitrary sensor array configurations without explicit knowledge of the steering vector. The proposed algorithms exploit the concept of Manifold Separation Technique (MST). Thus, the data are processed in the element-space domain and are not subject to mapping errors. Moreover, closed-form derivatives of the Weighted Subspace Fitting (WSF) cost function are obtained, even for real-world arrays with imperfections, making the proposed MVP computationally attractive. The obtained estimates for both elevation and azimuth show an error variance close to the Cramer-Rao Lower Bound (CRLB).

Complex random signals play an increasingly important role in array, communications, and biomedical signal processing and related fields. However, the mathematical foundations of complex-valued signals and tools developed for handling them are scattered in literature. There appears to be a need for a concise, unified, and rigorous treatment of such topics. In this paper such a treatment is provided. Moreover, we establish connections between seemingly unrelated objects such as real differentiability and circularity. In addition, a novel complex-valued extension of Taylor series is presented and a measure for circularity is proposed.

This paper proposes selective update and cooperation strategies for parameter estimation in distributed adaptive sensor networks. A set-membership filtering approach is employed that results in reduced complexity for updating parameter estimates at each network node, a significant reduction in information exchange between cooperating nodes, and an optimal strategy to obtain consensus estimates. The proposed strategies and the estimation algorithm offer a new way to explore cooperation in adaptive distributed sensor networks.

New radio access technologies are being developed under the scope of e.g. IMT-Advanced that provide high data rate local area wireless access with reduced infrastructure costs compared to traditional cellular technologies. One challenge in such a scenario is the adjacent channel interference that arises between uncoordinated cellular communication network deployments. For example, the adjacent channel leakage from a wide-band base station (BS) transmission may block the access from user equipment (UE) in the vicinity. We present a novel transmission scheme that optimizes the own link capacity by tuning the power spectral density (PSD) of an OFDM signal under general constraints on adjacent channel leakage. In a possible use case the proposed scheme would allow access for closeby adjacent channel UEs at a minimum penalty on the inband capacity.

An underlaying direct Device-to-Device (D2D) communication mode in future cellular networks, such as IMT-Advanced, is expected to provide spectrally efficient and low latency support of e.g. rich multi-media local services. Enabling D2D links in a cellular network presents a challenge in transceiver design due to the potentially severe interference between the cellular network and D2D radios. In this paper we propose MIMO transmission schemes for cellular downlink that avoid generating interference to a D2D receiver operating on the same time-frequency resource. System simulations demonstrate that substantial gains in D2D SINR of up to 15 dB and around 10% total cell capacity gains can be obtained by using the proposed scheme.

We study impacts of frequency and time offsets on cooperative multi-user MIMO-OFDM systems. In such systems, frequency offsets cause multi-user interference in addition to the inter-carrier interference effects typically seen in traditional MIMO-OFDM systems. Also, the impact of time offsets is more severe since the time offsets are larger due to transmitter synchronization imperfections and different propagation delays from the transmitters to the receivers. We derive an expression for the SINR seen at the receiver, showing especially how frequency offsets rotate the equivalent channel, thereby causing precoding imperfections. We simulate the interference impacts in the context of LTE-Advanced with realistic assumptions. Simulation results clearly show that the impacts of time and frequency offsets are more severe in cooperative MIMO-OFDM systems than in traditional MIMO-OFDM systems.

Future cellular networks such as IMT-Advanced are expected to allow underlaying direct Device-to-Device (D2D) communication for spectrally efficient support of e.g. rich multimedia local services. Enabling D2D links in a cellular network presents a challenge in radio resource management due to the potentially severe interference it may cause to the cellular network. We propose a practical and efficient scheme for generating local awareness of the interference between the cellular and D2D terminals at the base station, which then exploits the multiuser diversity inherent in the cellular network to minimize the interference. System simulations demonstrate that substantial gains in cellular and D2D performance can be obtained using the proposed scheme.

The increasing user density and higher data rate demands of future wireless networks are to be met with new technologies under the scope of IMT-advanced. The required high data rates can be provided by wide transmission bandwidths and a high density of access points in local area scenarios. Carefully coordinated network deployment and high performance RF front-ends are envisioned infeasible due to implied high costs. A major design challenge is then to handle the potentially severe adjacent channel interference arising among operators serving the same geographical area. This paper investigates the types of interference that form the major bottlenecks to the performance of time division duplex systems in such a scenario. This provides valuable input to system design pointing out the most detrimental interference types to be mitigated.

We analyze MIMO diversity transmission of synchronization signals in a slot synchronization scenario typical in modern wireless communication systems. Assuming a threshold-based correlation detector with noncoherent combining of diversity branches at the receiver, we derive general analytical expressions for probabilities of false alarm, detection and missed detection for a frequency-selective MIMO channel, and study the effects of diversity and channel correlation to these quantities. We apply the theoretical analysis for the usual SIMO case, cyclic delay diversity, time-switched transmit diversity, orthogonal transmit diversity and the precoding vector/matrix switching techniques. We verify the theoretical analysis through simulations in a practical 3GPP LTE context. Finally, we evaluate performance of the diversity schemes in different scenarios using the derived theoretical expressions.

In this paper we propose practical algorithms for optimization under unitary matrix constraint. This type of constrained optimization is needed in many signal processing applications. Steepest descent and conjugate gradient algorithms on the Lie group of unitary matrices are introduced. They exploit the Lie group properties in order to reduce the computational cost. Simulation examples on signal separation in MIMO systems demonstrate the fast convergence and the ability to satisfy the constraint with high fidelity.

In many signal processing algorithms the estimation of signal co-variance matrices is a key task. In many applications using tensor representation for the signals provides significant benefits in deriving new algorithms and revealing interesting signal properties. It is natural to model many signals in MIMO communications, physics, principal component analysis, or medical imaging using tensors. It is of high interest to develop signal processing algorithms for such problems. For some tensor-valued signals the covariance matrix may be approximated by a structured covariance with a Kronecker-product structure. This type of signals are referred to as separable. When the observed signals are contaminated by additive Gaussian noise, the separability property is lost and one ends up with shifted Kronecker-structured covariance matrices. In this paper, an iterative Maximum Likelihood (ML) estimator for covariance matrices of tensor-valued signals where covariance matrices have a shifted Kronecker-structure is proposed. The proposed algorithm is applied to wideband MIMO channel sounding measurements needed in realistic MIMO channel modeling.

This paper proposes a clustering approach to parameter estimation in distributed sensor networks. The proposed approach is an alternative to the conventional centralized and decentralized approaches. This is made possible by the unique adaptive estimation architecture, U-SHAPE, stemming from set-membership adaptive filtering. At the expense of a slightly degraded mean-square error performance (comparing to the least-squares approach), the proposed approach offers improved data processing flexibility in a distributed sensor network, reduced signal processing hardware and reduced communication bandwidth and power requirements.

Opportunistic scheduling (OS) schemes have been proposed previously by the authors for multiuser MIMO-SDMA downlink systems with linear combining. In particular, it has been demonstrated that significant performance improvement can be achieved by incorporating low-complexity linear combining techniques into the design of OS schemes for MIMO-SDMA. However, this previous analysis was performed based on the effective signal-to-interference ratio (SIR), assuming an interference- limited scenario, which is typically a valid assumption in SDMA-based systems. It was shown that the limiting distribution of the effective SIR is of the Frechet type. Surprisingly, the corresponding scaling laws were found to follow isin log K with 0 < isin < 1, rather than the conventional log log K form. Inspired by this difference between the scaling law forms, in this paper a systematic approach is developed to derive asymptotic throughput and scaling laws based on signal-to- interference-noise ratio (SINR) by utilizing extreme value theory. The convergence of the limiting distribution of the effective SINR to the Gumbel type is established. The resulting scaling law is found to be governed by the conventional log log K form. These novel results are validated by simulation results. The comparison of SIR and SINR-based analysis suggests that the SIR-based analysis is more computationally efficient for SDMA-based systems and it captures the asymptotic system performance with higher fidelity.

MIMO radar is a new concept in which radar employs multiple waveforms to improve its performance. Previously, a transmit beamforming method was proposed for MIMO radars. This method allows optimization of the beampattern by altering the cross-correlation matrix of the transmitted waveforms. The optimization is based on minimization of a cost function, but the use of numerical methods in the algorithm leads to high computational complexity. Here we propose a new cost function for the beampattern optimization. For linear arrays and typical beampatterns, this cost function can be evaluated in closed form, thus reducing the computational complexity considerably. Simulation examples demonstrate that the proposed cost function also leads to faster convergence and lower approximation error.

This paper addresses the problem of estimating a common modulation from a group of intercepted radar pulses. Estimated modulation profile operates as the basis for specific emitter identification (SEI). A robust M-estimation technique using scaled conjugate gradient algorithm for improving the frequency alignment of the pulses is proposed. In addition, postprocessing of the estimated modulation profiles for identification is considered. Simulation experiments are conducted in order to compare the performance with previously proposed methods. Results show that the proposed robust M-estimation technique provides improved performance at low signal-to-noise ratio regime due to better frequency alignment of the intercepted pulses.

In this paper, we introduce a novel subspace-based approach for carrier frequency offset (CFO) estimation in OFDM. The proposed estimator exploits both scattered and continual pilots commonly used in mobile television systems such as DVB-H. Rapid channel estimation and CFO compensation is necessary in order to deal with high mobility, time-slicing and potential handovers during the receiver switch-off time. The proposed method achieves frequency synchronization within a single OFDM block. No extensive time averaging is needed, which makes the approach very attractive for time and frequency selective channels where the CFO may be time varying. It is particularly suitable to burst type of transmission used, for example in DVB-H. Simulation examples are provided within the framework of mobile DVB-H systems.

Opportunistic scheduling and beamforming schemes are proposed for multiuser MIMO-SDMA downlink systems with linear combining in this work. Signals received from all antennas of each mobile terminal (MT) are linearly combined to improve theeffectivesignal-to-noise-interference ratios (SINRs). By exploiting limited feedback on the effective SINRs, the base station (BS) schedules simultaneous data transmission on multiple beams to the MTs with the largest effective SINRs. Utilizing the extreme value theory, we derive the asymptotic system throughputs and scaling laws for the proposed scheduling and beamforming schemes with different linear combining techniques. Computer simulations confirm that the proposed schemes can substantially improve the system throughput.

Multiple carrier-frequency offsets (CFO) arise in a distributed antenna system, where data are transmitted simultaneously from multiple antennas. In such systems the received signal contains multiple CFOs due to mismatch between the local oscillators of transmitters and receiver. This results in a time-varying rotation of the data constellation, which needs to be compensated for at the receiver before symbol recovery. This paper proposes a new approach for blind CFO estimation and symbol recovery. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual multiple-input multiple-output (MIMO) problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently transform the multiple CFOs estimation problem into many independent single CFO estimation problems. Furthermore, an initial estimate of the CFO is obtained from the phase of the MIMO system response. The Cramer-Rao lower bound is also derived, and the large sample performance of the proposed estimator is compared to the bound.

In this paper we introduce a method for modelling the steering vector of an arbitrary array such that its steering vector can be expressed as the product of a characteristic matrix of the array itself and a vector with a Vandermonde structure containing the unknown parameter. We call this technique manifold separation. By exploiting this concept, we developed a novel version of the root-MUSIC algorithm for direction of arrival (DoA) estimation of sources. It can be applied to arbitrary 2-D array configurations. The proposed algorithm processes the data in element-space domain and does not require any transformation or array interpolation. The novel algorithm, named element-space root-MUSIC, provides computationally low complexity (search-free) DoA estimation and has close to CRB performance already at low SNRs

In some signal processing tasks involving complex-valued multichannel measurements, classical whitening approaches do not completely remove the second-order statistical dependencies of the data. This paper describes adaptive procedures for estimating the strong uncorrelating transform for jointly diagonalizing the covariance and pseudo-covariance matrices of multidimensional signals. Novel algorithms are derived that extend and combine the power method and orthogonal iterations with ordinary fixed and iterative whitening procedures. Finally, we show how to combine our procedures with orthogonal PAST algorithms to perform subspace tracking and source signal clustering based on non-circularity

This paper proposes a combined frequency and time domain channel estimation method for MIMO OFDM systems. Initial channel estimation is performed by first estimating the channel response in frequency domain, exploiting a set of dedicated pilot carriers, followed by an interpolation step. In order to reduce the interpolation error and improve the bit error rate performance, we propose to refine the channel estimates in time domain using the equalized signal from the frequency domain processing. Simulations have been carried out using the spatial channel model proposed under the 3GPP framework. The proposed method has been tested in a wide range of mobile speeds in conjunction with several standard MIMO equalizers. The results show that the proposed estimator outperforms widely used time and frequency domain channel estimation approaches

Multiple scattering propagation channel is a physically motivated generic model whose special cases include Rayleigh, Rice, double-Rayleigh and "leaky keyhole" channels. Estimation of the parameters of its amplitude distribution is still largely an unexplored problem. In this paper, several novel estimators based on the empirical characteristic (ECF) function are derived. The mathematical form of the considered signal model makes the ECF approach ideally suited for the estimation problem at hand, whereas the maximum-likelihood (ME) estimator is analytically and computationally intractable. Furthermore, it can be easily extended to other similar signal models. By simulations it is shown that the derived ECF estimators have at least as small mean square error as the previously proposed moment-based approaches

In MIMO systems the interference from the same cell transmit (TX) antennas causes severe interference. Moreover, if the channel is frequency selective, also inter-chip interference is present. Canceling both inter-antenna and inter-chip interference is a challenging task, especially when the same codes are reused across the TX antennas. In this paper we propose a hybrid receiver combining minimum mean square error (MMSE) equalizer and chip level inter-antenna interference canceler. The performance is studied via simulations carried out in high speed downlink packet access (HSDPA) system with ITU channel

The development of future wireless communication systems requires modeling of the radio propagation environment. These models need the estimation of the model parameters from channel sounding measurements. In this paper, we build a state-space model, and estimate the propagation parameters with the Extended Kalman Filter in order to capture the dynamics of the channel parameters in time. The model also includes the effect of distributed diffuse scattering in radio channels. The issue of varying state variable dimension, i.e., the number of propagation paths to track, is investigated. For this purpose, we rely also on maximum likelihood based estimation techniques. The proposed algorithm is investigated using both simulated and measured data.

In this paper, the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA problems to complex-valued models. Relevant properties of complex random vectors are described in order to extend the Darmois-Skitovich theorem for complex-valued models. This theorem is used to construct a proof of a theorem for each of the above ICA model concepts. Both circular and noncircular complex random vectors are covered. Examples clarifying the above concepts are presented

In this paper, we characterize the error introduced by the beamspace transform when it is applied to a uniform circular array (UCA). Several algorithms for direction of arrival (DoA) estimation employ this modal transform. In particular, we focus on the UCA unitary root-MUSIC algorithm. The performance of such an estimator is degraded and bias occurs especially if the array has a small number of elements. Here we propose a novel technique for reducing the bias. This leads to practically bias-free DoA estimates.

For the development of future wireless systems, it is crucial to create accurate channel models. Channel sounding using antenna arrays and consequently propagation parameter estimation are key tasks in creating such models. In this paper we present an estimator for the angular distribution of the diffuse scattering component that is observed in channel sounding measurements. The angular distribution is modeled as a mixture of Von Mises distributions, which correspond to scatterer clusters. The parameters of the individual distributions as well as the mixture proportions are estimated. The large sample performance of the estimator is studied by deriving the Cramer-Rao lower bound and comparing the variance of the estimates to it. The simulations show that the the proposed estimator has asymptotically optimal performance since it attains the Cramer-Rao lower bound for relatively small sample sizes.

In this paper, we propose a novel subspace based approach for blind carrier frequency offset estimation in OFDM. Correlation in the squared spectrum of the channel is exploited and a low rank signal model is thereby obtained without virtual subcarriers. The proposed estimator accomplishes frequency synchronization with a single OFDM block. No extensive time averaging is needed, which makes the approach very attractive for time and frequency selective channels where the offset may be time varying. The method is statistically very efficient since close to optimal performance is achieved with respect to the Cramer-Rao bound with a single block.

In this paper we propose a low complexity frequency-domain method for finding the minimum mean square error (MMSE) equalizer. Special properties of circulant matrices are exploited in the method. Simulations show that only a minor performance loss is experienced compared to time-domain processing. We also compare joint space-time processing to decoupled equalization and spatial combining. The complexity reduction due to the decoupled processing is evident, while the performance loss remains small. Consequently, the proposed low complexity frequency-domain method can also be used with multiple receive antennas with tolerable performance loss compared to joint space time equalization. Additionally, different MMSE equalizer definitions for multiple receive antennas are considered, and their performance is studied in simulation using estimated channels. Simulations are carried out in high data rate WCDMA system model.

In this paper we derive an estimator for both time-delay and angular channel propagation parameters of the diffuse scattering component that is frequently observed in channel sounding measurements. The joint angular-delay model leads to correlation matrix with high dimensionality, which prevents direct implementation of a maximum-likelihood (ML) estimator using finite precision arithmetics and finite memory resources. We derive low complexity methods for computing the ML estimates that exploit the structure of the covariance matrices. The estimator is based on a two step procedure: first, the parameters of the power delay profile are estimated, as well as measurement noise power. Then, using the estimated time-delay parameters, the parameters of the angular distributions are estimated. We present simulation results and compare the estimated time-delay and angular distributions to the actual distributions, showing that high precision estimates are obtained.

This letter addresses the blind signal estimation problem in the so-called conjugate signal model, where the observed signal is a linear combination of the desired signal and its complex conjugate. It will be shown that blind signal recovery in this kind of signal model is feasible using only the second-order statistics of the observed signal, under the assumption of circular or proper complex signals. Furthermore, one practical example application in the field of communications receiver signal processing will be given, where the image signal interference caused by amplitude and phase mismatches of the receiver analog branches is digitally attenuated. In addition to the analytical results and practical implementation algorithms, the efficiency of the proposed estimation concepts in the digital image rejection application is evaluated using computer simulations, showing impressive performance results.

In this paper, we address the problem of blind carrier frequency offset (CFO) estimation in OFDM systems, in the case of frequency selective channels. By assuming real constellations, the proposed blind method enforces a diagonal structure for signal pseudo covariance matrices in the frequency domain. The power of non-diagonal elements is minimized. A closed-form solution is derived which leads to accurate and computationally efficient CFO estimation in multipath fading channels. Moreover, in the case of complex circularly symmetric noise, the theoretical performance does not depend on the SNR. Simulation results are presented using realistic channel models in typical urban scenarios.

We will derive a stochastic maximum likelihood method for estimating spatio-temporal channel parameters. Such estimators are needed in propagation studies where extensive channel measurements and sounding are required. These are seminal tasks in the process of developing advanced channel models. The proposed method employs angular Von Mises distribution model which is appropriate for directional data typically observed in channel measurement campaigns. The signal model is stochastic. The performance of the proposed method is compared to SAGE algorithm where the signal model is deterministic. The computational complexity of the proposed method is lower and channel parameters are estimated with higher fidelity because the underlying distribution model is well-suited for directional data.

In this letter, we give the conditions for identifiability, separability and uniqueness of linear real valued independent component analysis (ICA) models. A theorem is formulated and a proof is provided for each of the above concepts. These results extend the conditions for solving ICA problems, originally established by Comon , to wider class of mixing models and source distributions. Examples clarifying the above concepts are presented as well.

In this paper we address the problem of channel estimation for multiple-input multiple-output OFDM systems for mobile users. A channel tracking and equalization method stemming from Kalman filtering is proposed for time-frequency selective channels. Tracking of the MIMO channel matrix is performed in the time-domain and equalization in the frequency domain. The computational complexity is significantly reduced by applying the matrix inversion lemma. Simulation results are presented using a realistic channel model in typical urban scenarios.

In this paper we address the problem of channel estimation for multiple-input multiple-output OFDM systems for mobile users. Channel tracking and equalization method stemming from Kalman filtering is proposed for time-frequency selective channels. Tracking of MIMO channel matrix is performed in time-domain and equalization in frequency domain. Applying the matrix inversion lemma significantly reduces computational complexity. Simulation results are presented using realistic channel model in typical urban scenarios.

This paper addresses the problem of antenna array processing in nonGaussian noise and interference conditions. Such conditions arise due to man-made interference in indoor and outdoor mobile communication channels as well as in military communications. In this paper M-estimators of the array (pseudo-)covariance matrix based upon complex data set are introduced. Estimates of the noise and signal subspaces based on M-estimators are then used to robustify the subspace direction of arrival (DOA) estimation methods. In addition, eigenvalues based on M-estimators are used in MDL criterion, thus yielding a robust signal detection method. The reliable performance of the proposed methods are shown by simulations.

In this paper we address the problem of channel and frequency offset estimation for multiple-input multiple-output OFDM systems for mobile users. The proposed method stems from extended Kalman filtering. It is suitable for time and frequency selective channels. The algorithm performs channel and offset tracking in time-domain followed by equalization in frequency domain. Simulation results demonstrating high fidelity tracking capability are presented using realistic channel model in typical urban scenarios.

This paper addresses the problem of channel estimation and tracking for space-time block coding. Channel tracking performance is investigated using several recursive algorithms. In the simulations it is shown that different channel tracking procedures can be used in several scenarios. As a performance criterion the orthogonality property of the decoding matrix is considered. A realistic channel model developed in COST 207 project is used in our examples.

This article addresses the problem of blind source separation from time-varying noisy mixtures using a state variable model and recursive estimation. An estimate of each source signal is produced real time at the arrival of new observed mixture vector. The goal is to perform the separation and attenuate noise simultaneously, as well as to adapt to changes that occur in the mixing system. The observed data are projected along the eigenvectors in signal subspace. The subspace is tracked real time. Source signals are modeled using low-order AR (autoregressive) models, and noise is attenuated by trading off between the model and the information provided by measurements. The type of zero-memory nonlinearity needed in separation is determined on-line. Predictor-corrector filter structures are proposed, and their performance is investigated in simulation using biomedical and communications signals at different noise levels and a time-varying mixing system. In quantitative comparison to other widely used methods, significant improvement in output signal-to-noise ratio is achieved.

Blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences. Blind equalizers may be implemented with linear prediction-error filters (PEFs). For many practical channel types, a suitable delay at the output of the equalizer allows for achieving a small estimation error. The delay cannot be controlled with one-step predictors. Consequently, multistep PEF-based algorithms have been suggested as a solution to the problem. The derivation of the existing algorithms is based on the assumption of a noiseless channel, which results in zero-forcing equalization. We consider the effects of additive noise at the output of the multistep PEF. Analytical error bounds for two PEF-based blind equalizers in the presence of noise are derived. The obtained results are verified with simulations. The effect of energy concentration in the channel impulse response on the error bound is also addressed.

In quadrature receivers, unavoidable imbalances in the analog front-end between the I- and Q-branches result in finite and usually insufficient rejection of the image frequency band. This causes the image signal to appear as interference on top of the desired signal. Both analog and digital techniques to compensate the effects of I/Q imbalance have been presented in the literature. In this paper, we carry out a detailed performance analysis of the interference cancellation based imbalance compensation structure utilizing baseband digital signal processing. Also simulation results are provided for comparison. The results indicate that the interference canceller based solution can offer adequate performance for most communication applications.

Blind equalization of a communication channel using a prediction-based lattice blind equalizer (LBE) is considered. Second order cyclostationary statistics and a single-input multiple-output model arising from fractional sampling of the received data are used. The performance of the LBE algorithm is studied in extensive simulations where commonly used example channels are employed. Convergence in the mean square error (MSE) and symbol error rate (SER) as well as the number of symbols required to open the eye are studied at different SNRs. Robustness in the face of channel order mismatch and channels with common subchannel zeros is considered. The simulation results are compared to the results obtained by the fractionally spaced constant modulus algorithm, the cyclic-RLS algorithm and the subspace method by Moulines et al. (see IEEE Trans. Signal Proc., vol.43, no.2, p.516-25, 1995).

Nonlinear multichannel filters have successfully been applied to biomedical signals, multichannel images as well as processing of vector fields. In multichannel signals, component variances and correlations among components may be unequal and time-varying. Such changes can be expressed as an affine transformation of the input signal. In this paper, we investigate how the performance and statistical properties of multichannel filters stemming from order statistics (OS) change under affine transformations. An affine equivariant multichannel filter is introduced and the use of the affine equivariant performance metric replacing the mean square error is proposed. Advantages of affine equivariance are demonstrated in simulation, and filtering examples using real data are given.

In this paper, covariance estimation and consequently reduced ordering in multivariate order statistic (OS) filters are studied. The robustness of covariance estimators is characterized by plotting the sensitivity surfaces that describe the change caused by outliers in the condition number of the covariance matrix. The efficiency of the estimators under nominal noise distribution is studied. The estimation of correlations and component variances are addressed separately through eigendecomposition of the covariance matrix. The results indicate that correlations and ratios of component variances are estimated rather accurately using robust estimators whereas a constant correction factor is often necessary to get consistent estimates, The minimum volume ellipsoid (MVE) and minimum covariance determinant (MCD) algorithms based on random sampling do not perform reliably for small sampled or when too few elemental subsets are drawn. The qualitative comparison is performed in a RGB color image filtering task. The filter employing the iterative minimum covariance determinant (IMCD) estimate preserves the edges the best whereas the M-estimator smooths out noise effectively on homogeneous regions. The robustness of the IMCD filter and the efficiency of an M-estimator can be combined using a final refinement step as in the case of S-IMCD filters.

An orthogonal fitting technique for spline approximation is introduced. The technique takes into account the fact that there is uncertainty in both sides of the input-output relationship. In least squares (LS) spline approximation a computationally costly iterative process is required to refine the parameterization such that the error is orthogonal to the signal. This process may be avoided by using the total LS (TLS) fitting in case the nature of the error in parameterization is random instead of systematic. A lower rank approximation of the signal may be used as an input to the spline fitting process. In particular, if adaptive parameterization based on distances among observations is used a more reliable parameterization can be obtained. The TLS technique yields a lower bias than LS fitting whereas the LS has a lower variance. However, the difference in variance is not significant.

In this paper, the problem of constructing geometric models from data provided by 3-D imaging sensors is addressed. Such techniques allow for rapid modeling of sculptured free-form shapes and generation of geometric models for existing parts. In order for a complete data set to be obtained, multiple images, each from a different viewpoint, have to be merged. A technique stemming from the Iterative Closest Point (ICP) method for estimating the relative transformations among the viewpoints is developed. Computational solutions are provided for estimating shape from noisy sensory measurements using representations that conform with commonly used representations from Computer Aided Geometric Design (CAGD). In particular, NURBS and triangular surface representations are applied in shape estimation. The surface approximations are refined by the algorithms to meet a user-defined tolerance value.

A class of nonlinear filters for multivariate data is introduced. A robust error criterion is minimized. Approximate algorithms for computing the filter output are developed. A polynomial signal model is used in applications where the signal amplitude has to be retained with high fidelity. Simulated data and RGB color image data are used in experiments.

The modified trimmed mean (MTM) filters are known to possess desirable robustness and detail preservation properties. They combine the averaging operation with the median operation which implies that the filters also attenuate noise efficiently. We investigate multivariate extensions of the MTM filters. In the multivariate case, there is no unique way to define the MTM filters and hence there are several design options. A few of the most promising definitions for these filters and various design options are studied. The robustness of multivariate MTM filters is analyzed using the influence function approach. Filtering examples are also given using RGB color images.

A class of nonlinear regression filters based on robust estimation theory is introduced. The goal of the filtering is to recover a high-quality image from degraded observations. Models for desired image structures and contaminating processes are employed, but deviations from strict assumptions are allowed since the assumptions on signal and noise are typically only approximately true. The robustness of filters is usually addressed only in a distributional sense, i.e., the actual error distribution deviates from the nominal one. In this paper, the robustness is considered in a broad sense since the outliers may also be due to inappropriate signal model, or there may be more than one statistical population present in the processing window, causing biased estimates. Two filtering algorithms minimizing a least trimmed squares criterion are provided. The design of the filters is simple since no scale parameters or context-dependent threshold values are required. Experimental results using both real and simulated data are presented. The filters effectively attenuate both impulsive and nonimpulsive noise while recovering the signal structure and preserving interesting details.

This paper addresses the problem of attenuating noise from vector-valued image data. A class of nonlinear filters stemming from robust estimation is introduced. An exact algorithm requires extensive computation. Therefore, approximate algorithms for computing the filter output are developed. The filters produce reliable results even if the assumptions on noise process are only approximately true. The performance of the techniques is studied using simulated data and data from range imaging sensor and in the case of additive multivariate noise with equal component variances, unequal component variances, correlated noise components, and in the presence of outliers.>

This paper addresses the problems of image enhancement and restoration in the case of multivariate image data. Multivariate generalizations of median filtering are studied. The robustness properties of two such techniques are investigated using the influence function approach. Robust polynomial filters are introduced for applications where the original image has to be restored with high fidelity. Filtering examples are given using multivariate noise processes with equal component variances, unequal component variances, correlated noise components, and in the presence of outliers. Both simulated data and multivariate data from a range imaging sensor are used.>

In previous work (Koivunen and Pietikainen, 1991) the authors presented a segmentation method that combines useful properties of edge and region-based segmentation. The least squares estimation used gives good results when pixels in the neighborhood are from one statistical population, and the noise is Gaussian distributed. To be able to deal with very deviant pixel values, the authors applied an iterative reweighting least squares method and a least trimmed squares method for surface description. This paper presents the improvements on the robustness of the surface description, and a quantitative analysis of the quality of the description. The validity of the assumptions used is also evaluated quantitatively. Both synthetic and real range images are used for test images.>