Goal-oriented semantic communications and signal processing are foreseen to play a key role in advancing future communication networks. Leveraging recent advances in machine learning (ML) techniques and artificial intelligence (AI), research is shifting towards intelligent end-to-end systems that can extract relevant semantic information and transmit only when necessary. It was recently proposed that graph languages representing semantic information can be modeled using a hidden semi-Markov model (HSMM) for smoothing, learning, and fusion algorithms. This paper aims to build upon this HSMM framework for multi-sensor goal-oriented semantic communications and proposes an expectation-maximization (EM) algorithm to learn the underlying semantic model by incorporating multi-sensor observations and handling missing data. The results show that the proposed algorithm learns the semantic model by utilizing the set of observations and effectively mitigates the effects of missing observations.

We propose novel fusion algorithms based on hidden semi-Markov models (HSMMs) for robust goal-oriented signal processing in wireless sensor networks with noisy and missing data. We extend the prior work that models the temporal evolution of semantic information as an HSMM to handle practical challenges encountered in massive machine-type communication (mMTC) scenarios. Our first contribution is to introduce a method to statistically model missing observations by adjusting the emission probabilities of the HSMM, enabling the system to continue functioning even in the event of sensor failure. Secondly, by integrating signals from multiple sensors whose observations are conditionally independent given the semantic state and using their joint likelihoods, we develop HSMM-based fusion solutions using the Viterbi and forward-backward algorithms. The effectiveness of the proposed approach is validated by extensive simulation results, demonstrating notable improvements in hidden semantic state estimation even with high sensor error and missing data rates. These findings highlight the potential of HSMM-based fusion for enhancing robustness in semantic communication systems for 6G and beyond.

Considering the demanding requirements of 6G integrated sensing and communication (ISAC) applications [1], we propose a radar-centric ISAC system design methodology. This approach is enabled by semantic downlink communication within the goal-oriented semantic signal processing framework [2] and incorporates an improved monopulse direction-finding (MDF) technique for accurate direction-finding. In addition, the computational complexity analysis of the proposed MDF method is also provided. The proposed scheme employs frequency-modulated continuous wave radar signals and differential phase-shift keying. In a case study, we demonstrate an example ISAC system design and show that the proposed MDF technique outperforms the state-of-the-art. Furthermore, we demonstrate the communication performance of the proposed scheme under 3GPP tapped delay line and clustered delay line channel models [3] and show that the communication performance is robust to the choice of radar waveform.

In future wireless communication, an exponential increase in connected devices and the need for safety-critical and data-intensive applications like Autonomous Vehicles (AVs) and eXtended Reality (XR) will render large-scale intelligent agent deployments infeasible. To address this, we propose a novel framework where a centralized Smart Service Provider (SSP) transmits actions to agents, balancing effectiveness and transmission costs. Our approach leverages the observation that both semantic information extraction from raw sensor data and action generation from semantic states are many-to-one mappings. We model action decisions using stochastic policies from Reinforcement Learning (RL) literature. A key novelty is our focus on when to transmit. Namely, the SSP, observing what an agent observes, estimates the agent’s likely action. Based on the weighted statistical distance between the SSP’s policy and the agent’s estimated policy, the SSP decides whether an "action innovation" has occurred, and if so, transmits an action to the agent. Simulations demonstrate that transmitting only 10% of the time is sufficient to satisfy goals with up to 1% deviation, and compression rates up to 8,108:1 are achievable compared to existing standards. This "effective communication" scheme significantly reduces transmission overhead while maintaining high performance.

Semantic signal processing and communications are poised to play a central part in developing the next generation of sensor devices and networks. A crucial component of a semantic system is the extraction of semantic signals from the raw input signals, which has become increasingly tractable with the recent advances in machine learning (ML) and artificial intelligence (AI) techniques. The accurate extraction of semantic signals using the aforementioned ML and AI methods, and the detection of semantic innovation for scheduling transmission and/or storage events are critical tasks for reliable semantic signal processing and communications. In this work, we propose a reliable semantic information extraction framework based on our previous work on semantic signal representations in a hierarchical graph-based structure. The proposed framework includes a time integration method to increase fidelity of ML outputs in a class-aware manner, a graph-edit-distance based metric to detect innovation events at the graph-level and filter out sporadic errors, and a Hidden Markov Model (HMM) to produce smooth and reliable graph signals. The proposed methods within the framework are demonstrated individually and collectively through simulations and case studies based on real-world computer vision examples.

Ionogram scaling is the process of reconstructing electron density with respect to height by using the measurements of a remote sensing instrument known as ionosonde. In this study, a novel two-stage ionogram scaling technique, ionogram scaling and electron density (ISED), is proposed. In the first stage, hidden Markov models (HMMs) are used to identify the actual ionospheric reflections in the ionosonde measurements. In the second stage, an International Reference Ionosphere extended to plasmasphere (IRI-Plas) model-based optimization problem is solved to obtain the vertical profile that generates the best least-squares fit to the reflections identified in the first stage. To show the performance of ISED in a global scale, experiments are conducted on 14812 ionograms recorded at the three different stations that are Pruhonice in Czech Republic, Eielson in USA, and São Luis in Brazil. Application of ISED to raw ionograms indicates 97.6% of the cases, and ISED provides accurate electron density reconstructions, which is an improvement about 8.7% over automatic real-time ionogram scaler with true height (ARTIST), most commonly used ionogram scaling technique.

Specific Emitter Identification (SEI) is the process of specifically identifying mobile transmitters by extracting unique features from the precise measurements of their emitted signals. A novel signal processing scheme with two stages is proposed for the identification of specific radar emitters. In the first stage, the received radar pulses are accurately time aligned and coherently integrated in order to increase the Signal-to-Noise (SNR) ratio. Using this technique, measurements with SNR improvements of more than 25 dB are obtained, enabling detection of subtle differences between different emitters. In the second step, Variational Mode Decomposition (VMD) is used to decompose both the envelope and the instantaneous frequency of the received signal into a set of modes. Then, these mode signals are characterized by using a group of features for identification. We demonstrate highly successful identification performance with the proposed method on real radar datasets.

We propose a novel randomized linear least squares solver which is an improvement of Iterative Hessian Sketch and randomized preconditioning. In the proposed Momentum-IHS technique (M-IHS), Heavy Ball Method is used to accelerate the convergence of iterations. It is shown that for any full rank data matrix, rate of convergence depends on the ratio between the feature size and the sketch size. Unlike the Conjugate Gradient technique, the rate of convergence is unaffected by either the condition number or the eigenvalue spectrum of the data matrix. As demonstrated over many examples, the proposed M-IHS provides compatible performance with the state of the art randomized preconditioning methods such as LSRN or Blendenpik and yet, it provides a completely different perspective in the area of iterative solvers which can pave the way for future developments.

Visible light positioning (VLP) systems based on light emitting diodes can facilitate high accuracy localization services for indoor scenarios. In this paper, direct and two-step positioning approaches are investigated for both synchronous and asynchronous VLP systems. First, the Cramér-Rao lower bound (CRLB) and the direct positioning-based maximum likelihood estimator are derived for 3-D localization of a visible light communication receiver in a synchronous scenario by utilizing information from both time delay parameters and channel attenuation factors. Then, a two-step position estimator is designed for synchronous VLP systems by exploiting the asymptotic properties of time-of-arrival and received signal strength estimates. The proposed two-step estimator is shown to be asymptotically optimal, i.e., converges to the direct estimator at high signal-to-noise ratios. In addition, the CRLB and the direct and two-step estimators are obtained for positioning in asynchronous VLP systems. It is proved that the two-step position estimation is optimal in asynchronous VLP systems for practical pulse shapes. Various numerical examples are provided to illustrate the improved performance of the proposed estimators with respect to the current state-of-the-art and to investigate their robustness against model uncertainties in VLP systems.

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints in order to maximize the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple additive Gaussian noise channels. The optimal strategy is shown to perform channel switching either among at most three channels with full channel utilization (i.e., no idle periods), or between at most two channels with partial channel utilization. In addition, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for calculating the optimal strategy. For two-channel strategies, an upper bound in terms of the noise standard deviations of the employed channels is provided for the ratio between the optimal power levels. Furthermore, a simple condition depending solely on the systems parameters is derived, under which partial channel utilization cannot be optimal. Numerical examples are presented to demonstrate the validity of the theoretical results.

Kernel density estimation (KDE) is widely‐used for non‐parametric estimation of an underlying density from data. The performance of KDE is mainly dependent on the bandwidth parameter of the kernel. This study presents an alternative method of estimating the bandwidth by incorporating sparsity priors in the Fourier transform domain. By using cross‐validation (CV) together with an l 1 constraint, the proposed method significantly reduces the under‐smoothing effect of traditional CV methods. A solution for all free parameters in the minimisation is proposed, such that the algorithm does not need any additional parameter tuning. Simulation results indicate that the new approach is able to outperform classical and more recent approaches over a set of distributions of interest.

Synthetic Aperture Radar (SAR) has significant importance in many remote sensing applications. Errors due to the platform motion or measurement model uncertainties can cause degradations in the constructed SAR images. Most of the methods deal with the phase errors which cause defocusing on the image. For efficient processing of the measurements, they discretize the fast time-slow time plane and then employ autofocus algorithms on this discrete grid. However, the reflectors which are not placed exactly on the grid degrade the image quality considerably. This is the most probable case in the practical SAR operation and it causes blur or spark like affects on the image. This is called the off-grid target problem. In this work, a Compressed Sensing based technique is developed which constructs spotlight mode SAR image, handles the off-grid target problem and makes autofocus simultaneously. A gradient descent type iterative solution is used.

Optimal channel switching that provides the highest performance over a set of Gaussian channels with variable utilization costs is investigated in the presence of average power and average cost constraints. First, generic cost functions are considered, and it is shown that the optimal channel switching strategy performs channel switching (time sharing) among at most three different channels and always operates at the average power and average cost limits. Also, for channel switching between two channels, relations between the optimal power levels are obtained depending on the average power limit, and it is proved that the ratio of the optimal power levels is upper bounded by the ratio of the larger noise variance to the smaller one. In addition, for logarithmic cost functions, the convexity properties of the error probability are investigated as a function of power and cost, and the optimal channel switching strategy is shown to employ at most two channels, which can easily be determined based on specific formulas, when the average power limit is larger than a certain threshold. Numerical examples are presented to provide illustrations of the theoretical results.

In this study, we consider performance improvement of an array of fixed estimators by using stochastic design techniques. The optimal design is investigated both in the absence and presence of an average power constraint. Two different performance criteria are considered; the average Bayes risk and the maximum Bayes risk. It is shown that the optimal stochastic parameter design results in a randomization between different numbers of parameter values depending on the type of the performance criterion.

In this paper, lossless polar compression of q-ary memoryless sources in the noiseless setting is investigated. Polar compression scheme for binary memoryless sources, introduced by Cronie and Korada, is generalized to sources over prime-size alphabets. In order to reduce the average codeword length, a compression scheme based on successive cancellation list decoding is proposed. Also, a specific configuration for the compression of correlated sources is considered, and it is shown that the introduced polar compression schemes achieve the corner point of the admissible rate region. Based on this result, proposed compression schemes are extended to arbitrary finite source alphabets by using a layered approach.

Optimal detector randomization is studied for the downlink of a multiuser communications system, in which users can perform time-sharing among multiple detectors. A formulation is provided to obtain optimal signal amplitudes, detectors, and detector randomization factors. It is shown that the solution of this joint optimization problem can be calculated in two steps, resulting in significant reduction in computational complexity. It is proved that the optimal solution is achieved via randomization among at most min{K,Nd} detector sets, where K is the number of users and \Nd is the number of detectors at each receiver. Lower and upper bounds are derived on the performance of optimal detector randomization, and it is proved that the optimal detector randomization approach can reduce the worst-case average probability of error of the optimal approach that employs a single detector for each user by up to K times. Various sufficient conditions are obtained for the improvability and nonimprovability via detector randomization. In the special case of equal crosscorrelations and noise powers, a simple solution is developed for the optimal detector randomization problem, and necessary and sufficient conditions are presented for the uniqueness of that solution. Numerical examples are provided to illustrate the improvements achieved via detector randomization.

In this study, the jointly optimal power control with signal constellation randomization is proposed for the downlink of a multiuser communications system. Unlike a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with signal constellation randomization involves randomization/time-sharing among different signal constellations for each user. A formulation is obtained for the problem of optimal power control with signal constellation randomization, and it is shown that the optimal solution can be represented by a randomization among (K+1) or fewer distinct signal constellations for each user, where K denotes the number of users. In addition to the original nonconvex formulation, an approximate solution based on convex relaxation is derived. Then, detailed performance analysis is presented when the receivers employ symmetric signaling and sign detectors. Specifically, the maximum asymptotical improvement ratio is shown to be equal to the number of users, and the conditions under which the maximum and minimum asymptotical improvement ratios are achieved are derived. Numerical examples are presented to investigate the theoretical results, and to illustrate performance improvements achieved via the proposed approach.

A novel expectation maximization based matching pursuit (EMMP) algorithm is presented. The method uses the measurements as the incomplete data and obtain the complete data which corresponds to the sparse solution using an iterative EM based framework. In standard greedy methods such as matching pursuit or orthogonal matching pursuit a selected atom can not be changed during the course of the algorithm even if the signal doesn't have a support on that atom. The proposed EMMP algorithm is also flexible in that sense. The results show that the proposed method has lower reconstruction errors compared to other greedy algorithms using the same conditions.

In this paper, stochastic signaling is studied for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, it is shown that, for a given decision rule at the receiver, stochastic signaling based on the available CSI at the transmitter results in a randomization between at most two different signal levels for each symbol. Then, the performance of stochastic signaling and conventional deterministic signaling is compared, and sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Finally a numerical example is presented to explore the theoretical results.

We show that the exact recovery of sparse perturbations on the coefficient matrix in overdetermined Least Squares problems is possible for a large class of perturbation structures. The well established theory of Compressed Sensing enables us to prove that if the perturbation structure is sufficiently incoherent, then exact or stable recovery can be achieved using linear programming. We derive sufficiency conditions for both exact and stable recovery using known results of ℓ0/ℓ1equivalence. However the problem turns out to be more complicated than the usual setting used in various sparse reconstruction problems. We propose and solve an optimization criterion and its convex relaxation to recover the perturbation and the solution to the Least Squares problem simultaneously. Then we demonstrate with numerical examples that the proposed method is able to recover the perturbation and the unknown exactly with high probability. The performance of the proposed technique is compared in blind identification of sparse multipath channels.

In this paper, a new array signal processing technique by using particle swarm optimization (PSO) is proposed to identify multipath channel parameters. The proposed technique provides estimates to the channel parameters by finding a global minimum of an optimization problem. Since the optimization problem is formulated in the cross-ambiguity function (CAF) domain of the transmitted signal and the received array outputs, the proposed technique is called as PSO-CAF. The performance of the PSO-CAF is compared with the space alternating generalized expectation maximization (SAGE) technique and with another recently proposed PSO based technique for various SNR values. Simulation results indicate the superior performance of the PSO-CAF technique over mentioned techniques for all SNR values.

Optimal stochastic signaling is studied under second and fourth moment constraints for the detection of scalar-valued binary signals in additive noise channels. Sufficient conditions are obtained to specify when the use of stochastic signals instead of deterministic ones can or cannot improve the error performance of a given binary communications system. Also, statistical characterization of optimal signals is presented, and it is shown that an optimal stochastic signal can be represented by a randomization of at most three different signal levels. In addition, the power constraints achieved by optimal stochastic signals are specified under various conditions. Furthermore, two approaches for solving the optimal stochastic signaling problem are proposed; one based on particle swarm optimization (PSO) and the other based on convex relaxation of the original optimization problem. Finally, simulations are performed to investigate the theoretical results, and extensions of the results to M-ary communications systems and to other criteria than the average probability of error are discussed.

Localization of the sources of Event Related Potentials (ERP) is a challenging inverse problem, especially to resolve sources of neural activity occurring simultaneously. By using an effective dipole source model, we propose a new technique for accurate source localization of ERP signals. The parameters of the dipole ERP sources are optimally chosen by using Particle Swarm Optimization technique. Obtained results on synthetic data sets show that proposed method well localizes the dipoles on their actual locations. On real data sets, the fit error between the actual and reconstructed data is successfully reduced to noise level by localizing a few dipoles in the brain.

In many signal processing applications the core problem reduces to a linear system of equations. Coefficient matrix uncertainties create a significant challenge in obtaining reliable solutions. In this paper, we present a novel formulation for solving a system of noise contaminated linear equations while preserving the structure of the coefficient matrix. The proposed method has advantages over the known Structured Total Least Squares (STLS) techniques in utilizing additional information about the uncertainties and robustness in ill-posed problems. Numerical comparisons are given to illustrate these advantages in two applications: signal restoration problem with an uncertain model and frequency estimation of multiple sinusoids embedded in white noise.

Many real world problems which can be assigned to the machine learning domain are inverse problems. The available data is often noisy and may contain outliers, which requires the application of global optimization. Evolutionary Algorithms (EA's) are one class of possible global optimization methods for solving such problems. Within population based EA's, Differential Evolution (DE) is a widely used and successful algorithm. However, due to its differential update nature, given a current population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitnesses of the population. This paper presents a novel extension of DE called Randomized and Rank based Differential Evolution (R2DE) to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the fitnesses. In experiments including non-linear dimension reduction by autoencoders, it is shown that R2DE improves robustness and speed of global convergence.

By extending the time-bandwidth product concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is introduced. The GTBP provides a rotation independent measure for the support of the signals in time-frequency domain. A close form expression for the adaptive kernel of STFT that provides the minimum increase on the GTBP of a signal is derived. Also, a linear canonical decomposition of the obtained GTBP optimal STFT is presented to identify its relation to the rotationally invariant STFT analysis.

A novel approach is presented for the design of signals in Wigner Domain. In this method, the desired signal features in the time-frequency domain are specified in two stages. First the user specifies the spine curve around which the energy of the desired signal is distributed in the time-frequency plane. Then, the user specifies the spread of the desired signal energy around the spine. In addition to this fundamentally new way of defining the time-frequency features of the desired signal, the actual synthesis of the signal is performed in a warped fractional Fourier transform approach [1]. After obtaining the designed signal, it is transformed back to the original time domain providing the final result of the new signal synthesis technique. In contrast to the conventional algorithms, the proposed method provides very good results even if the inner cross-term structure of the desired signal is not specified.

A novel regularization technique which can combine signals from all GPS satellites for a given instant and given station, is developed to estimate the vertical total electron content values for the 24 hour period without missing any important feature in the temporal or spatial domain. The algorithm is based on the minimization of a cost function including a high pass penalty function. The developed regularized estimation algorithm is applied to GPS data for various locations for the solar maximum week of April 23 - April 28, 2001. It is observed that the new method is very successful in estimating TEC both for quiet and disturbed days.

A new algorithm is proposed to obtain very high-resolution time-frequency analysis of signal components with curved time-frequency supports. The proposed algorithm is based on the fractional Fourier domain warping concept introduced in this work. By integrating this warping concept to the recently developed directionally smoothed Wigner distribution algorithm (Ozdemir et al., 2000), the high performance of that algorithm on linear, chirp-like components is extended to signal components with curved time-frequency supports. The main advantage of the algorithm is its ability to suppress not only the cross-cross terms, but also the auto-cross terms in the Wigner distribution. For a signal with N samples duration, the computational complexity of the algorithm is O(NlogN) flops for each computed slice of the new time-frequency distribution.

An efficient algorithm is proposed to extract components of a composite signal. The proposed approach has two stages of processing in which the time-frequency supports of the individual signal components are identified and then the individual components are estimated by performing a simple time-frequency domain incision on the identified support of the component. The use of a previously developed time-frequency representation significantly improves the performance of the proposed approach by providing a very accurate description on the auto-Wigner terms of the composite signal. Then, simple fractional Fourier domain incision provides reliable estimates for each of the signal components in O(N log N) complexity for a composite signal of duration N.

A new algorithm is proposed for reliable communication over HF tropospheric links in the presence of rapid channel variations. In the proposed approach, using fractionally spaced channel outputs, sequential estimation of channel characteristics and input sequence is performed by utilizing subspace tracking and Kalman filtering. Simulation based comparisons with the existing algorithms show that the proposed approaches significantly improve the performance of the communication system and enable us to utilize HF communication in bad conditions.

A novel algorithm is proposed for efficiently smoothing the slices of the Wigner distribution by exploiting the developed relation between the Radon transform of the ambiguity function and the fractional Fourier transformation (Odzemir and Ankan, 1999). The main advantage of the new algorithm is its ability to suppress cross-term interference on chirp-like auto-components without any detrimental effect to the auto-components. For a signal with N samples, the computational complexity of the algorithm is O(N log N) flops for each smoothed slice of the Wigner distribution.

This paper considers the problem of interpolating a signal from one uniformly-spaced grid to another, where the grid spacings may be related by an arbitrary, irrational factor. Noting that interpolation is the digital equivalent of magnification, we begin by reviewing optical systems for magnification and "computation" of the chirp Fourier transform. This route suggests several analog schemes for magnification, which can be discretized to produce algorithms for interpolation. We then derive one of these algorithms from first principles, using a digital signal processing perspective. The result is an important, but forgotten, algorithm for interpolation first suggested as an application of the chirp-z transform by Rabiner, Schafer, and Rader (1969). Unlike the earlier derivation, our approach is direct-we do not make use of Bluestein's trick of completing the square. In addition, our approach identifies parameters under user control that can be optimized for best performance.

To take advantage of fast converging multi-channel recursive least squares algorithms, we propose an adaptive IIR system structure consisting of two parts: a two-channel FIR adaptive filter whose parameters are updated by the rotation-based multi-channel least squares lattice (QR-MLSL) algorithm, and an adaptive regressor which provides more reliable estimates to the original system output based on previous values of the adaptive system output and noisy observation of the original system output. Two different regressors are investigated and robust ways of adaptation of the regressor parameters are proposed. Based on extensive set of simulations, it is shown that the proposed algorithms converge faster to more reliable parameter estimates than LMS type algorithms.

It is possible to obtain either exact realizations or useful approximations of linear systems or matrix-vector products arising in many different applications, by synthesizing them in the form of repeated or multi-channel filtering operations in fractional Fourier domains, resulting in much more efficient implementations with acceptable reduction in accuracy. By varying the number and configuration of the filter blocks, which may take the form of arbitrary flow graphs, it is possible to trade off between accuracy and efficiency in the desired manner. The proposed scheme constitutes a systematic way of exploiting the information inherent in the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.

Printing color images on color printers, and displaying them on computer monitors requires a significant reduction of physically distinct colors, which causes degradation in image quality. An efficient method to improve the display quality of a quantized image is error diffusion which works by distributing the previous quantization errors to neighboring pixels exploiting the eye's averaging of colors in the neighborhood of the point of interest. This creates the illusion of more colors. A new error diffusion method is presented in which the adaptive recursive least squares (RLS) algorithm is used rather than the deterministic approaches in literature. To improve the performance, a diagonal scan is used in processing the image.

We consider the application of an alternative imaging algorithm to the inversion of strip-mapping synthetic aperture radar (SAR) data. The algorithm was originally developed and successfully applied in the area of geophysics to estimate the conductivity distribution from wellbore induction measurements. The SAR measurement relation satisfies the same form of integral equation describing the wellbore problem. By exploiting the form of the measurement kernel, we derive a SAR image formation algorithm involving deconvolution-backprojection. Unlike correlation-based SAR image formation, our approach is more general, without simplifying assumptions on the range function, and is robust to measurement noise, at the expense of increased computational complexity. Simulation results are presented that demonstrate the effectiveness of the proposed algorithm.

A large class of physical phenomenon observed in practice exhibit non-Gaussian behavior. In this paper, /spl alpha/-stable distributions, which have heavier tails than Gaussian distribution, are considered to model non-Gaussian signals. Adaptive signal processing in the presence of such kind of noise is a requirement of many practical problems. Since, direct application of commonly used adaptation techniques fail in these applications, new approaches for adaptive filtering for /spl alpha/-stable random processes are introduced.

The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum mean square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.

The performance of a commonly employed linear array of sonar sensors is assessed for point-obstacle localization intended for robotics applications. Two different methods of combining time-of-flight information from the sensors are described to estimate the range and azimuth of the obstacle: pairwise estimate method and the maximum likelihood estimator. The variances of the methods are compared to the Cramer-Rao lower bound, and their biases are investigated. Simulation studies indicate that in estimating range, both methods perform comparably; in estimating azimuth, maximum likelihood estimate is superior at a cost of extra computation. The results are useful for target localization in mobile robotics.

A constrained optimization method is used to reconstruct signals from their noisy linear transforms. In this approach the fit error energy is minimized over a set of signals whose first few normalized autocorrelation coefficients are larger than specified constraint values. This provides another method of introducing regularization to the least squares signal reconstruction. By choosing the constraint values larger more regularization can be obtained. Significant computational saving is gained by solving the corresponding dual optimization problem in the actual computation of the reconstruction. Comparison of the results of this and other approaches leads us to the conclusion that although the proposed approach requires more computation, it provides better reconstructions.>

A large class of physical phenomena observed in practice exhibit non-Gaussian behavior. In the letter /spl alpha/-stable distributions, which have heavier tails than Gaussian distributions, are considered to model non-Gaussian signals. Adaptive signal processing in the presence of such a noise is a requirement of many practical problems. Since direct application of commonly used adaptation techniques fail in these applications, new algorithms for adaptive filtering for /spl alpha/-stable random processes are introduced.>

An algorithm was proposed for computer-aided tomography and spotlight-mode synthetic aperture radar in a recent work by W. Lawton (IEEE Trans. Acoust., Speech, and Signal Process, vol.36, p.933-971, June 1988). This processing scheme assumes that Fourier transform samples of the projections obtained lie on a concentric-squares polar grid. The spatial-domain image is produced through a series of convolutions and DFTs (discrete Fourier transforms), all performed using FFTs (fast Fourier transforms). The algorithm requires O(N/sup 2/logN) operations to produce an N*N image and is made possible by the geometry of the concentric-squares polar grid. The present authors more completely describe the Lawton algorithm and derive a closed-form, approximate expression for its impulse response for the case of spotlight-mode synthetic aperture radar. A formula is given for the exact number of multiplications required by the algorithm, and a set of simulated point target responses is given to help assess the image quality provided by the algorithm.>