This paper investigates the positioning of the pilot symbols, as well as the power distribution between the pilot and the communication symbols for the orthogonal time frequency space (OTFS) modulation scheme. We analyze the pilot placements that minimize the mean squared error (MSE) in estimating the channel taps. This allows us to identify two new pilot allocations for OTFS that save approximately 50% of the pilot overhead compared to existing allocations. In addition, we optimize the average channel capacity by adjusting the power distribution. We show that this leads to a significant increase in average capacity. The results provide valuable guidance for designing the OTFS parameters to achieve maximum capacity. Numerical simulations are performed to validate the findings.

This paper addresses graph topology identification for applications where the underlying structure of systems like brain and social networks is not directly observable. Traditional approaches based on signal matching and spectral templates have limitations, particularly in handling scale issues and sparsity assumptions. We introduce a novel covariance matching methodology that efficiently reconstructs the graph topology using observable data. For the structural equation model (SEM) using an undirected graph, we demonstrate that our method can converge to the correct result under relatively soft conditions. Furthermore, we extend our methodology to polynomial models and any known distribution of latent variables, broadening its applicability and utility in diverse graph-based systems.

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise estimates, our method accounts for dynamic changes in the network structure over time. We model the network at each timestep as the state of the SSM, and use observations to update beliefs that quantify the probability of the network being in a particular state. Then, by considering the dynamics of transition and observation models through the update and prediction steps, respectively, the proposed method can incorporate the information of real-time graph signals into the beliefs. These beliefs provide a probability distribution of the network at each timestep, being able to provide both an estimate for the network and the uncertainty it entails. Our approach is evaluated through experiments with synthetic and real-world networks. The results demonstrate that our method effectively estimates network states and accounts for the uncertainty in the data, outperforming traditional techniques such as recursive least squares.

This paper investigates jointly optimal array geometry and waveform designs for active sensing. Specifically, we focus on minimizing the Cramér-Rao lower bound (CRB) of the angle of a single target in white Gaussian noise. We first find that several array-waveform pairs can yield the same CRB by virtue of sequences with equal sums of squares, i.e., solutions to certain Diophantine equations. Furthermore, we show that under physical aperture and sensor number constraints, the CRB-minimizing receive array geometry is unique, whereas the transmit array can be chosen flexibly. We leverage this freedom to design a novel sparse array geometry that not only minimizes the single-target CRB given an optimal waveform, but also has a nonredundant and contiguous sum co-array—a desirable property when launching independent waveforms, with relevance also to the multi-target case.

In this paper, we propose an analytical solution for recovering a low-rank positive semi-definite (PSD) matrix from its rank-one measurements. We show that by utilizing a set of structured measurement vectors, we can analytically determine the null space of this low-rank PSD matrix. Based on the result, the PSD matrix can be efficiently recovered. Our analysis shows that the proposed method only requires$(N-K)(2K+1) + K^{2}$measurements to guarantee exact recovery of the PSD matrix, where$N$and$K$respectively denote the dimension and the rank of the PSD matrix. Numerical results show that the proposed method achieves a considerable improvement over existing state-of-the-art methods in terms of both sample complexity and computational efficiency. Specifically, the proposed method helps improve the computational efficiency by an order of magnitude as compared with existing methods.

CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a massive MIMO system, as the receiver generally sums the components from different paths or users. To achieve accurate and low-latency channel estimation, good and fast CP decomposition (CPD) algorithms are desired. The CP alternating least squares (CPALS) is the workhorse algorithm for calculating the CPD. However, its performance depends on the initializations, and good starting values can lead to more efficient solutions. Existing initialization strategies are decoupled from the CPALS and are not necessarily favorable for solving the CPD. This paper proposes a deep-learning-aided CPALS (DL-CPALS) method that uses a deep neural network (DNN) to generate favorable initializations. The proposed DL-CPALS integrates the DNN and CPALS to a model-based deep learning paradigm, where it trains the DNN to generate an initialization that facilitates fast and accurate CPD. Moreover, benefiting from the CP low-rankness, the proposed method is trained using noisy data and does not require paired clean data. The proposed DL-CPALS is applied to millimeter wave MIMO-OFDM channel estimation. Experimental results demonstrate the significant improvements of the proposed method in terms of both speed and accuracy for CPD and channel estimation.

Graphs are widely used to represent complex information and signal domains with irregular support. Typically, the underlying graph topology is unknown and must be estimated from the available data. Common approaches assume pairwise node interactions and infer the graph topology based on this premise. In contrast, our novel method not only unveils the graph topology but also identifies three-node interactions, referred to in the literature as second-order simplicial complexes (SCs). We model signals using a graph autoregressive Volterra framework, enhancing it with structured graph Volterra kernels to learn SCs. We propose a mathematical formulation for graph and SC inference, solving it through convex optimization involving group norms and mask matrices. Experimental results on synthetic and real-world data showcase a superior performance for our approach compared to existing methods.

In this work, we deal with the problem of reconstructing a complete bandlimited graph signal from partially sampled noisy measurements. For a known graph structure, an efficient greedy algorithm is presented to partition the graph nodes into disjoint subsets such that sampling the graph signal from any subset leads to a sufficiently accurate reconstruction. Furthermore, we consider a scenario where the graph is massive and data processing centrally is no longer practical. To overcome this issue, a distributed framework is proposed that allows us to implement partitioning algorithms in a parallelized fashion. Finally, we provide numerical simulation results on synthetic and real-world data to show that our proposals outperform the state-of-the-art.

In this paper, we show the mathematical equivalence of two popular modulation schemes: OSDM and OTFS. The former is mainly used in underwater acoustic communications, while the latter scheme is a promising modulation technique in radio-frequency communications. Although literature suggests a link between the two modulation schemes by connecting them to related modulation schemes like V-OFDM and A-OFDM, to the best of the authors’ knowledge, a direct mathematical comparison between the schemes has not been presented yet. The main purpose of this paper is therefore to show the mathematical equivalence of the two schemes. In addition, by combining the knowledge of acoustic and radio-frequency communications, we give insight in the performance of OSDM/OTFS in terms of intersymbol interference (ISI) and intercarrier interference (ICI) by analyzing its signal structure.

Hearing impairment is a prevalent problem with daily challenges like impaired speech intelligibility and sound localisation. One of the shortcomings of spatial filtering in hearing aids is that speech intelligibility is often not optimised directly, meaning that different auditory processes contributing to intelligibility are often not considered. One example is the perceptual phenomenon known as spatial release from masking (SRM). This paper develops a signal model that explicitly considers SRM in the beamforming design, achieved by transforming the binaural intelligibility prediction model (BSIM) into a signal processing framework. The resulting extended signal model is used to analyse the performance of reference beamformers and design a novel beamformer that more closely considers how the auditory system perceives binaural sound. It can be shown that the binaural minimum variance distortionless response (BMVDR) beamformer is also an optimal solution for the extended, perceived model, suggesting that SRM does not play a significant role in intelligibility enhancement after optimal beamforming. However, the optimal beamformer is no longer unique in the extended signal model. The additional secondary degrees of freedom can be used to preserve binaural cues of interfering sources while still achieving the same perceived performance of the BMVDR beamformer, though with a possible high sensitivity to intelligibility model mismatch errors.

Sensor selection is a useful method to help reduce data throughput, as well as computational, power, and hardware requirements, while still maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown source models. In this work, we propose to tackle the sensor selection problem for angle of arrival estimation using the worst-case Cramér-Rao bound of two uncorrelated sources. To do so, we cast the problem as a convex semi-definite program and retrieve the binary selection by randomized rounding. Through numerical examples related to a linear array, we illustrate the proposed method and show that it leads to the natural selection of elements at the edges plus the center of the linear array. This contrasts with the typical solutions obtained from minimizing the single-target Cramér-Rao bound.

Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose an algorithmic approach to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.

This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.

Mobile base stations on board unmanned aerial vehicles (UAVs) promise to deliver connectivity to those areas where the terrestrial infrastructure is overloaded, damaged, or absent. A fundamental problem in this context involves determining a minimal set of locations in 3D space where such aerial base stations (ABSs) must be deployed to provide coverage to a set of users. While nearly all existing approaches rely on average characterizations of the propagation medium, this work develops a scheme where the actual channel information is exploited by means of a radio tomographic map. A convex optimization approach is presented to minimize the number of required ABSs while ensuring that the UAVs do not enter no-fly regions. A simulation study reveals that the proposed algorithm markedly outperforms its competitors.

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks like graph signal reconstruction, graph or node classifications, and link prediction. However, these methods are only suitable for data defined on the nodes of a graph. In this paper, we propose a simplicial convolutional neural network (SCNN) architecture to learn from data defined on simplices, e.g., nodes, edges, triangles, etc. We study the SCNN permutation and orientation equivariance, complexity, and spectral analysis. Finally, we test the SCNN performance for imputing citations on a coauthorship complex.

This paper proposes an efficient direction of departure (DOD) and direction of arrival (DOA) estimation method for multi-input multi-output (MIMO) systems. For uncorrelated scenarios, the redundancy of the covariance matrix is first exploited by establishing its concise representation through redundancy reduction, which transforms the original large-size covariance matrix into a smaller-size matrix without loss of useful angle information. Then, the resulting transformed matrix, which retains a salient structure, permits efficient two-dimensional (2D) angle estimators working on a reduced-size problem for DOD and DOA estimation. Compared with conventional subspace-based methods, the proposed method incorporating an appropriate 2D angle estimator is more computationally efficient and can achieve higher estimation accuracy for small numbers of snapshots and low signal-to-noise ratios, which are verified by simulation results.

To deal with high-dimensional data, graph filters have shown their power in both graph signal processing and data science. However, graph filters process signals exploiting only pairwise interactions between the nodes, and they are not able to exploit more complicated topological structures. Graph Volterra models, on the other hand, are also able to exploit relations between triplets, quadruplets and so on. However, they have only been exploited for topology identification and are only based on one-hop relations. In this paper, we first review graph filters and graph Volterra models and then merge the two concepts resulting in so-called topological Volterra filters (TVFs). TVFs process signals over multiple hops of higher-level topological structures. First-level TVFs are basically similar to traditional graph filters, yet higher-level TVFs provide a more general processing framework. We apply TVFs to inverse filtering and recommender systems.

Signal processing and machine learning algorithms for data sup-ported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the topology has to be learned from data. Topology identification is a challenging task, as the problem is often ill-posed, and becomes even harder when the graph structure is time-varying. In this paper, we address the problem of dynamic topology identification by building on recent results from time-varying optimization, devising a general-purpose online algorithm operating in non-stationary environments. Because of its iteration-constrained nature, the proposed approach exhibits an intrinsic temporal-regularization of the graph topology without explicitly enforcing it. As a case-study, we specialize our method to the Gaussian graphical model (GGM) problem and corroborate its performance.

Link prediction is one of the core problems in network and data science with widespread applications. While predicting pairwise nodal interactions (links) in network data has been investigated extensively, predicting higher-order interactions (higher-order links) is still not fully understood. Several approaches have been advocated to predict such higher-order interactions, but no principled method has been put forth to tackle this challenge so far. Cross-fertilizing ideas from Volterra series and linear structural equation models, the present paper introduces self-driven graph Volterra models that can capture higher-order interactions among nodal observables available in networked data. The novel model is validated for the higher-order link prediction task using real interaction data from social networks.

Diffusion-based semi-supervised learning on graphs consists of diffusing labeled information of a few nodes to infer the labels on the remaining ones. The performance of these methods heavily relies on the initial labeled set, which is either generated randomly or using heuristics. The first sometimes leads to unsatisfactory results because random labeling has no guarantees to label all classes while heuristic methods only yield a good performance when multiple recursive training stages are possible. In this paper, we put forth a new paradigm for one-shot active semi-supervised learning for graph diffusions. We rephrase active learning as the problem of selecting the output labels from a label propagation model. Subsequently, we develop two methods to solve this problem and label the nodes. The first method assumes there are only a few starting labels and relies on projected compressive sensing to build the label set. The second method drops the assumption of a few starting labels and builds on sparse sensing techniques to label a few nodes. Both methods have solid mathematical grounds in signal processing and require a single training phase. Numerical results on three scenarios corroborate our findings and showcase the improved performance compared with the state of the art.

The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series carries a vector of quantities rather than a scalar one. To tackle this issue, we devise a new framework and propose new methodologies based on the graph vector autoregressive model. More explicitly, we leverage product graphs to model the high-dimensional graph data and develop multidimensional graph-based vector autoregressive models to forecast future trends with a number of parameters that is independent of the number of time series and a linear computational complexity. Numerical results demonstrating the prediction of moving point clouds corroborate our findings.

A novel class of k-space trajectories for magnetic resonance imaging (MRI) sampling using space filling curves (SFCs) is presented here. More specifically, Peano, Hilbert and Sierpinski curves are used. We propose 1-shot and 4-shot variable density SFCs by utilizing the space coverage provided by SFCs in different iterations. The proposed trajectories are compared with state-of-the-art echo planar imaging (EPI) trajectories for 128 × 128 and 256 × 256 phantom and brain images. The simulation results show that the readout time is reduced by up to 45% for the 128 × 128 image with little compromise in reconstruction quality. Also, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index are improved by 2.32 dB and 0.1009, respectively, with an 18% shorter readout time using the 4-shot Hilbert SFC trajectory for reconstructing a 256 × 256 brain MRI image.

The development of compressed sensing (CS) techniques for magnetic resonance imaging (MRI) is enabling a speedup of MRI scanning. To increase the incoherence in the sampling, a random selection of points on the k-space is deployed and a continuous trajectory is obtained by solving a traveling salesman problem (TSP) through these points. A feasible trajectory satisfying the gradient constraints is then obtained by parameterizing it using state-of-the-art methods. In this paper, a constrained convex optimization based method to obtain feasible trajectories is proposed. The method is motivated by the fact that the readout time is proportional to the number of sample points and includes the lengths of the segments of the trajectory in the cost function to obtain variable length trajectories. The proposed method provides a reduction in readout time by more than 50% for random-like trajectories with an improvement of about 1.5 dB in peak signal-to-noise ratio (PSNR) and 0.0762 in structural similarity (SSIM) index on average for a realistic brain phantom MRI image adopting single-shot trajectories.

This paper concerns wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs). We rely on the assumption that the power spectrum of the wideband sources is the same up to a scaling factor, which could in theory allow us to resolve not only more sources than the number of antennas but also more sources than the number of degrees of freedom (DoF) of the difference co-array of the SLA. We resort to the Jacobi-Anger approximation to transform the coarray response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. Based on the obtained model, two super-resolution DoA estimation approaches based on atomic norm minimization (ANM) are proposed, one with and one without prior knowledge of the power spectrum. Simulation results show that our proposed methods outperform the state of the art and are indeed capable of resolving more sources than the number of DoF of the difference co-array.

This paper develops an enhanced low-rank structured covariance reconstruction (LRSCR) method based on the decoupled atomic norm minimization (D-ANM), for super-resolution two-dimensional (2D) harmonic retrieval with multiple measurement vectors. This LRSCR-D-ANM approach exploits a potential structure hidden in the covariance by transferring the basic LRSCR to an efficient D-ANM formulation, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. The new LRSCR-D-ANM method builds upon the existence of a generalized Vandermonde decomposition of its solution, which otherwise cannot be guaranteed by the basic LRSCR unless a very conservative condition holds. Further, a low-complexity solution of the LRSCR-D-ANM is provided for fast implementation with negligible performance loss. Simulation results verify the advantages of the proposed LRSCR-D-ANM over the basic LRSCR, in terms of the wider applicability and the lower complexity.

To perform any meaningful optimization task, distribution grid operators need to know the topology of their grids. Although power grid topology identification and verification has been recently studied, discovering instantaneous interplay among subsets of buses, also known as higher-order interactions in recent literature, has not yet been addressed. The system operator can benefit from having this knowledge when re-configuring the grid in real time, to minimize power losses, balance loads, alleviate faults, or for scheduled maintenance. Establishing a connection between the celebrated exact distribution flow equations and the so-called self-driven graph Volterra model, this paper puts forth a nonlinear topology identification algorithm, that is able to reveal both the edge connections as well as their higher-order interactions. Preliminary numerical tests using real data on a 47-bus distribution grid showcase the merits of the proposed scheme relative to existing alternatives.

Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to challenging dynamic, time-varying, and even huge-size settings. This is driven by technological transformations that converted infrastructural and social platforms into complex and dynamic networked systems with even pervasive sensing and computing capabilities. This article reviews a broad class of state-of-the-art algorithms for time-varying optimization, with an eye to performing both algorithmic development and performance analysis. It offers a comprehensive overview of available tools and methods and unveils open challenges in application domains of broad range of interest. The real-world examples presented include smart power systems, robotics, machine learning, and data analytics, highlighting domain-specific issues and solutions. The ultimate goal is to exemplify wide engineering relevance of analytical tools and pertinent theoretical foundations.

A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.

For swarm systems, distributed processing is of paramount importance and Bayesian methods are preferred for their robustness. Existing distributed sparse Bayesian learning (SBL) methods rely on the automatic relevance determination (ARD), which involves a computationally complex reweighted l1-norm optimization, or they use loopy belief propagation, which is not guaranteed to converge. Hence, this paper looks into the fast marginal likelihood maximization (FMLM) method to develop a faster distributed SBL version. The proposed method has a low communication overhead, and can be distributed by simple consensus methods. The performed simulations indicate a better performance compared with the distributed ARD version, yet the same performance as the FMLM.

This paper aims at accurate channel estimation for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under practical limitations, including an arbitrary array geometry and a hybrid hardware structure. Taking on an angle-based approach, this work adopts a generalized array manifold separation approach via the Jacobi-Anger approximation, which transforms a non-ideal, non-uniform array manifold into a virtual array domain with a desired uniform geometric structure to facilitate super-resolution angle estimation and channel acquisition. Accordingly, structure-based optimization techniques are developed to estimate the channel parameters within a short sensing time. In particular, the difference in time-variation of path angles and path gains is capitalized to design a two-step scheme that can quickly sense fading channels. Theoretical results are provided on the fundamental limits of the proposed technique in terms of sample efficiency. Simulations testify the effectiveness of the proposed approaches.

This paper develops efficient super-resolution spatial channel covariance estimation techniques for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under the hybrid precoding constraint. Two structure-based optimization techniques including low-rank structured covariance reconstruction and dynamic atomic norm minimization are proposed to accurately estimate the channel covariance matrix. For computational efficiency, a fast iterative algorithm is developed via the alternating direction method of multipliers. The extension of this work to the higher-dimensional cases is also discussed. Simulation results verify the effectiveness of the proposed methods in hybrid mmWave massive MIMO systems.

Graph neural networks (GNNs) regularize classical neural networks by exploiting the underlying irregular structure supporting graph data, extending its application to broader data domains. The aggregation GNN presented here is a novel GNN that exploits the fact that the data collected at a single node by means of successive local exchanges with neighbors exhibits a regular structure. Thus, regular convolution and regular pooling yield an appropriately regularized GNN. To address some scalability issues that arise when collecting all the information at a single node, we propose a multi-node aggregation GNN that constructs regional features that are later aggregated into more global features and so on. We show superior performance in a source localization problem on synthetic graphs and on the authorship attribution problem.

In this paper, the focus is on the gain and phase calibration of sparse sensor arrays to localize more sources than the number of physical sensors. The proposed technique is a blind calibration method as it does not require any calibrator sources. Joint estimation of the gain errors, phase errors, and source directions is a complicated non-convex optimization problem, which is transformed into a convex optimization problem by exploiting the underlying algebraic structure. It is shown that the developed solver is suitable for analog as well as one-bit measurements. Numerical experiments based on sparse rulers are provided to illustrate the developed theory.

Autonomous unmanned aerial vehicles (UAVs) with on-board base station equipment can potentially provide connectivity in areas where the terrestrial infrastructure is overloaded, damaged, or absent. Use cases comprise emergency response, wildfire suppression, surveillance, and cellular communications in crowded events to name a few. A central problem to enable this technology is to place such aerial base stations (AirBSs) in locations that approximately optimize the relevant communication metrics. To alleviate the limitations of existing algorithms, which require intensive and reliable communications among AirBSs or between the AirBSs and a central controller, this paper leverages stochastic optimization and machine learning techniques to put forth an adaptive and decentralized algorithm for AirBS placement without inter-AirBS cooperation or communication. The approach relies on a smart design of the network utility function and on a stochastic gradient ascent iteration that can be evaluated with information available in practical scenarios. To complement the theoretical convergence properties, a simulation study corroborates the effectiveness of the proposed scheme.

An analytical algebraic approach for distributed network identification is presented in this paper. The information propagation in the network is modeled using a state-space representation. Using the observations recorded at a single node and a known excitation signal, we present algorithms to compute the eigenfrequencies and eigenmodes of the graph in a distributed manner. The eigenfrequencies of the graph may be computed using a generalized eigenvalue algorithm, while the eigenmodes can be computed using an eigenvalue decomposition. The developed theory is demonstrated using numerical experiments.

In this paper the focus is on sampling and reconstruction of signals supported on nodes of arbitrary graphs or arbitrary signals that may be represented using graphs, where we extend concepts from generalized sampling theory to the graph setting. To recover such signals from a given set of samples, we develop algorithms that incorporate prior knowledge on the original signal when available such as smoothness or subspace priors related to the underlying graph. For reconstructing arbitrary signals, we constrain the reconstruction to the graph, and provide a consistent reconstruction method, in which both the reconstructed signal and the input yield exactly the same measurements. Given a set of graph frequency domain samples, the sampling and interpolation operations may be efficiently implemented using linear shift-invariant graph filters.

In this work, we introduce subset selection strategies for signal reconstruction based on kernel methods, particularly for the case of kernel-ridge regression. Typically, these methods are employed for exploiting known prior information about the structure of the signal of interest. We use the mean squared error and a scalar function of the covariance matrix of the kernel regressors to establish metrics for the subset selection problem. Despite the NP-hard nature of the problem, we introduce efficient algorithms for finding approximate solutions for the proposed metrics. Finally, numerical experiments demonstrate the applicability of the proposed strategies.

In this work, we jointly exploit tools from graph signal processing and control theory to drive a bandlimited graph signal that is being diffused on a random time-varying graph from a subset of nodes. As our main contribution, we rely only on the statistics of the graph to introduce the concept of controllability in the mean, and therefore drive the signal on the expected graph to a desired bandlimited state. A mean-square error (MSE) analysis is performed for two main tasks: i) to highlight the role played by the signal bandwidth and the control nodes to the deviation from the mean signal of a particular realization; and ii) to select the control nodes and design the control signal that minimize this MSE. Numerical results validate the introduced controllability in the mean framework and show its ability to cope with time-varying topologies.

The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), leading to stochastic maximum likelihood (ML) DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. Simulations demonstrate that taking the heteroscedastic noise into account improves DOA estimation.

In processing spatially distributed data, multi-agent robotic platforms equipped with sensors and computing capabilities are gaining interest for applications in inhospitable environments. In this work an algorithm for a distributed realization of sparse bayesian learning (SBL) is discussed for learning a static spatial process with the splitting-over-features approach over a network of interconnected agents. The observed process is modeled as a superposition of weighted kernel functions, or features as we call it, centered at the agent's measurement locations. SBL is then used to determine which feature is relevant for representing the spatial process. Using upper bounding convex functions, the SBL parameter estimation is formulated as ℓ1-norm constrained optimization, which is solved distributively using alternating direction method of multipliers (ADMM) and averaged consensus. The performance of the method is demonstrated by processing real magnetic field data collected in a laboratory.

In this paper, we present a calibration algorithm for acoustic vector sensors arranged in a uniform linear array configuration. To do so, we do not use a calibrator source, instead we leverage the Toeplitz blocks present in the data covariance matrix. We develop linear estimators for estimating sensor gains and phases. Further, we discuss the differences of the presented blind calibration approach for acoustic vector sensor arrays in comparison with the approach for acoustic pressure sensor arrays. In order to validate the proposed blind calibration algorithm, simulation results for direction-of-arrival (DOA) estimation with an uncalibrated and calibrated uniform linear array based on minimum variance distortion less response and multiple signal classification algorithms are presented. The calibration performance is analyzed using the Cramér-Rao lower bound of the DOA estimates.

This letter investigates methods to detect graph topological changes without making any assumption on the nature of the change itself. To accomplish this, we merge recently developed tools in graph signal processing with matched subspace detection theory and propose two blind topology change detectors. The first detector exploits the prior information that the observed signal is sparse w.r.t. the graph Fourier transform of the nominal graph, while the second makes use of the smoothness prior w.r.t. the nominal graph to detect topological changes. Both detectors are compared with their respective nonblind counterparts in a synthetic scenario that mimics brain networks. The absence of information about the alternative graph, in some cases, might heavily influence the blind detector's performance. However, in cases where the observed signal deviates slightly from the nonblind model, the information about the alternative graph turns out to be not useful.

In this paper, we are interested in learning the underlying graph structure behind training data. Solving this basic problem is essential to carry out any graph signal processing or machine learning task. To realize this, we assume that the data is smooth with respect to the graph topology, and we parameterize the graph topology using an edge sampling function. That is, the graph Laplacian is expressed in terms of a sparse edge selection vector, which provides an explicit handle to control the sparsity level of the graph. We solve the sparse graph learning problem given some training data in both the noiseless and noisy settings. Given the true smooth data, the posed sparse graph learning problem can be solved optimally and is based on simple rank ordering. Given the noisy data, we show that the joint sparse graph learning and denoising problem can be simplified to designing only the sparse edge selection vector, which can be solved using convex optimization.

Generally in distributed signal processing, and specifically in distributed graph filters, reducing the communication and computational complexity plays a key role in the network lifetime. In this work we present a novel algorithm to sparsify the graph filtering operation in a random way, where each node decides locally with a certain probability with which of its neighbors to communicate. We show that, if the filter coefficients are changed accordingly, the first and second order moment of the stochastic output are identical to the deterministic filter output and bounded, respectively. We apply our idea on the tasks of signal denoising and diffusion. Numerical results show that the distributed implementation costs of the filter can be reduced up to 95% with a variance of 10-3from the deterministic output.

We present a novel implementation strategy for distributed autoregressive moving average (ARMA) graph filters. Differently from the state of the art implementation, the proposed approach has the following benefits: (i) the designed filter coefficients come with stability guarantees, (ii) the linear convergence time can now be controlled by the filter coefficients, and (iii) the stable filter coefficients that approximate a desired frequency response are optimal in a least squares sense. Numerical results show that the proposed implementation outperforms the state of the art distributed infinite impulse response (IIR) graph filters. Further, even at fixed distributed costs, compared with the popular finite impulse response (FIR) filters, at high orders our method achieves tighter low-pass responses, suggesting that it should be preferable in accuracy-demanding applications.

We study the sensor selection problem for field estimation, where a best subset of sensors is activated to monitor a spatially correlated random field. Different from most commonly used centralized selection algorithms, we propose a decentralized architecture where sensor selection can be carried out in a distributed way and by the sensors themselves. A decentralized approach is essential since each sensor has access only to the information (e.g., correlation) in its neighborhood. To make distributed optimization possible, we decompose the global cost function into local cost functions that require only the information in local neighborhoods of sensors. We then employ the alternating direction method of multipliers (ADMM) to solve the proposed sensor selection problem. In our algorithm, each sensor solves small-scale optimization problems, and communicates directly only with its immediate neighbors. Numerical results are provided to show the effectiveness of our approach.

Advancing a holistic theory of networks and network processes requires the extension of existing results in the processing of time-varying signals to signals supported on graphs. This paper focuses on the definition of stationarity and power spectral density for random graph signals, generalizes the concepts of autoregressive and moving average random processes to the graph domain, and investigates their parametric spectral estimation. Theoretical and algorithmic results are complemented with numerical tests on synthetic and real-world graphs.

The combination of baseband and analog precoding for multiple-input multiple-output (MIMO) systems is considered in this paper which is referred to as hybrid precoding. The system capacity, as a design criterion, is maximized subject to unit modulus constraints on the elements of the analog precoder (phase shifters), and a total power constraint. This is a non-convex problem due to the product of the analog and baseband precoder variables. The proposed technique suggests computing non-trivial complex derivatives of the objective and constraints, analytically, in order to develop an iterative gradient-based sequential optimization algorithm to solve the non-convex problem. Promising simulation results show that the solution of the proposed algorithm is sufficiently close to the optimal (full-baseband) precoder solution, regardless of the channel characteristics.

Massive MIMO systems achieve high sum spectral efficiency by simultaneously serving large numbers of users. In time division duplexing systems, however, the reuse of uplink training pilots among cells results in channel estimation errors, which causes downlink inter-cell interference. Handling this interference is challenging due to the large channel dimensionality and the high complexity associated with implementing large precoding/combining matrices. In this paper, we propose multi-layer precoding to enable efficient and low-complexity operation in full-dimensional massive MIMO, where a large number of antennas are used in two dimensions. In multi-layer precoding, the precoding matrix of each base station is written as a product of a number of precoding matrices. Multi-layer precoding: 1) leverages the directional characteristics of large-scale MIMO channels to manage inter-cell interference with low channel knowledge requirements and 2) allows for an efficient implementation using hybrid analog/digital architectures. We present and analyze a specific multi-layer precoding design for full-dimensional massive MIMO systems. The asymptotic optimality of the proposed design is then proved for some special yet important channels. Numerical simulations verify the analytical results and illustrate the potential gains of multi-layer precoding compared with other multi-cell precoding solutions.

In this paper, a new direction of arrival (DOA) estimation approach is devised using concepts from information geometry (IG). The proposed method uses geodesic distances in the statistical manifold of probability distributions parametrized by their covariance matrix to estimate the direction of arrival of several sources. In order to obtain a practical method, the DOA estimation is treated as a single-variable optimization problem, for which the DOA solutions are found by means of a line search. The relation between the proposed method and MVDR beamformer is elucidated. An evaluation of its performance is carried out by means of Monte Carlo simulations and it is shown that the proposed method provides improved resolution capabilities at low SNR with respect to MUSIC and MVDR.

The path-loss exponent (PLE) is a key parameter in wireless propagation channels. Therefore, obtaining the knowledge of the PLE is rather significant for assisting wireless communications and networking to achieve a better performance. Most existing methods for estimating the PLE not only require nodes with known locations but also assume an omni-directional PLE. However, the location information might be unavailable or unreliable and, in practice, the PLE might change with the direction. In this paper, we are the first to introduce two directional maximum likelihood (ML) self-estimators for the PLE in wireless networks. They can individually estimate the PLE in any direction merely by locally collecting the related received signal strength (RSS) measurements. The corresponding Cramér-Rao lower bound (CRLB) is also obtained. Simulation results show that the performance of the proposed estimators is very close to the CRLB. Additionally, also for the first time, the RSSs based on only a geometric path loss are found to follow a truncated Pareto distribution in wireless random networks. This might be of great help in the analysis of wireless communications and networking.

In this paper we focus on the relative position and orientation estimation between rigid bodies in an anchorless scenario. Several sensor units are installed on the rigid platforms, and the sensor placement on the rigid bodies is known beforehand (i.e., relative locations of the sensors on the rigid body are known). However, the absolute position of the rigid bodies is not known. We show that the relative localization of rigid bodies amounts to the estimation of a rotation matrix and the relative distance between the centroids of the rigid bodies. We measure all the unknown pairwise distances between the sensors, which we use in a constrained least squares estimator. Furthermore, we also allow missing links between the sensors. The simulations support the developed theory.

A novel scheme for sampling graph signals is proposed. Space-shift sampling can be understood as a hybrid scheme that combines selection sampling -- observing the signal values on a subset of nodes - and aggregation sampling - observing the signal values at a single node after successive aggregation of local data. Under the assumption of bandlimitedness, we state conditions and propose strategies for signal recovery in different settings. Being a more general procedure, space-shift sampling achieves smaller reconstruction errors than current schemes, as we illustrate through the reconstruction of the industrial activity in a graph of the U.S. economy.

Since the global positioning system (GPS) is not applicable underwater, source localization using wireless sensor networks (WSNs) is gaining popularity in oceanographic applications. Unlike terrestrial WSNs (TWSNs) which uses electromagnetic signaling, underwater WSNs (UWSNs) require underwater acoustic (UWA) signaling. Received signal strength (RSS)-based source localization is considered in this paper due to its practical simplicity and the constraint of low-cost sensor devices, but this area received little attention so far because of the complicated UWA transmission loss (TL) phenomena. In this paper, we address this issue and propose two novel semidefinite programming (SDP) approaches which can be solved more efficiently. The numerical results validate our proposed SDP solvers in underwater environments, and indicate that the placement of the anchor nodes influences the RSS-based localization accuracy similarly as in the terrestrial counterpart. We also highlight that adopting traditional terrestrial RSS-based localization methods will fail in underwater scenarios.

Partial FFT demodulation is a newly-emerging technique to mitigate the inter-carrier interference (ICI) of orthogonal frequency division multiplexing (OFDM) systems over time-varying underwater acoustic channels. In this letter, we extend the partial FFT demodulation method for a single-input single-output (SISO) configuration to the multiple-input multiple-output (MIMO) case. By assuming no channel knowledge, we design an adaptive algorithm which performs sliding-window channel estimation, partial FFT combining and data detection across subcarriers iteratively. Furthermore, a new parameter “residual ICI span” is introduced to counteract the post-combining ICI and provide a better system performance.

Millimeter wave (mmWave) systems will likely employ directional beamforming with large antenna arrays at both the transmitters and receivers. Acquiring channel knowledge to design these beamformers, however, is challenging due to the large antenna arrays and small signal-to-noise ratio before beamforming. In this paper, we propose and evaluate a downlink system operation for multi-user mmWave systems based on compressed sensing channel estimation and conjugate analog beamforming. Adopting the achievable sum-rate as a performance metric, we show how many compressed sensing measurements are needed to approach the perfect channel knowledge performance. The results illustrate that the proposed algorithm requires an order of magnitude less training overhead compared with traditional lower-frequency solutions, while employing mmWave-suitable hardware. They also show that the number of measurements need to be optimized to handle the trade-off between the channel estimate quality and the training overhead.

An offline sampling design problem for Gaussian detection is considered in this paper. The sensing operation ismodeled by a selection vector, whose sparsity order is determined by the prescribed global error probability. Since the numerical optimization of the error probability is difficult, equivalent simpler costs, viz., the Kullback-Liebler distance and Bhattacharyya distance are optimized. The sensing problem is formulated and solved sub-optimally using convex optimization techniques. It is shown that the sensing problem can be solved optimally for conditionally independent Gaussian observations. Further, we show that for non-identical sensor observations, the number of sensors required to achieve a certain detection performance decreases as the sensors become more correlated.

Covariance estimation from compressive samples has become particularly attractive for two main reasons. First, many applications do not require the signal itself, and second-order statistics are oftentimes sufficient. The resulting requirement on the sampling rate of the original signal can therefore be reduced. Second, signal recovery from compressive samples leads to underdetermined systems which require additional constraints, such as the popular sparsity assumption. In contrast, covariance estimation can yield overdetermined problems, even from compressive samples, so that the additional constraints on the signal can be dropped. In this paper, we provide a unified framework for deriving lower bounds on the sampling rate required for covariance estimation of stationary signals, by deriving the lower Beurling density of the difference set associated with the original sampling set. A general sampling scheme is first considered, followed by the analysis of multicoset sampling. We prove that, in both cases, the sampling rate can be arbitrarily low, as was remarked extensively in the literature.

In this work, we propose a generalized framework for designing optimal sensor constellations for spatio-temporally correlated field estimation using wireless sensor networks. The accuracy of the field intensity estimate in every point of a given service area strongly depends upon the number and the constellation of the sensors along with the spatio-temporal statistics of the field. We formulate and solve a sparsity-enforcing optimization problem to select the best sensor locations that achieve some desired estimation performance. The sparsity-enforcing iterative selection algorithm is aware of the non-separable space-time covariance structure of the field.

Medium access control (MAC) determines how sensor nodes share the channel for packet exchanging. To obtain the maximum network efficiency for accomplishing a specific task, the network has to adapt its parameters accordingly. In other words, different MAC protocols are required for different tasks. Localization is a crucial task of an underwater acoustic sensor network (UASN) which requires multiple packet exchanges. This article concerns the problem of designing a MAC protocol for a UASN which efficiently schedules the localization packets of the anchors. Knowing the relative positions of the anchors and their maximum transmission range, the scheduling protocol takes advantage of the long propagation delay of underwater communications to minimize the duration of the localization task. First, we formulate the concept of collision-free packet transmission for localization, and we show how the optimum solution can be obtained. Furthermore, we model the problem as a mixed integer linear program both in single-channel and multi-channel scenarios. Then, we propose two low-complexity algorithms, and through comprehensive simulations we compare their performances with the optimal solution as well as with other existing methods. Numerical results show that the proposed algorithms perform near optimum and better than alternative solutions.

Existing solutions to the sensor placement problem are based on sensor selection, in which the best subset of available sampling locations is chosen such that a desired estimation accuracy is achieved. However, the achievable estimation accuracy of sensor placement via sensor selection is limited to the initial set of sampling locations, which are typically obtained by gridding the continuous sampling domain. To circumvent this issue, we propose a framework of continuous sensor placement. A continuous variable is augmented to the grid-based model, which allows for off-the-grid sensor placement. The proposed offline design problem can be solved using readily available convex optimization solvers.

We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher order ARMA filters in the time domain.

The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived-the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations. This kind of vectors arises naturally when sampling wide-sense stationary random processes and features a number of applications in signal and array processing. Explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and nonperiodic fashion are provided by considering two of the most common linear compression schemes, which we classify as dense or sparse. It is seen that the maximum compression ratios depend on the structure of the HT subspace containing the covariance matrix of the uncompressed observations. Compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure. Universal samplers are also proposed to compress unknown HT subspaces.

Antenna arrays will be an important ingredient in millimeter-wave (mmWave) cellular systems. A natural application of antenna arrays is simultaneous transmission to multiple users. Unfortunately, the hardware constraints in mmWave systems make it difficult to apply conventional lower frequency multiuser MIMO precoding techniques at mmWave. This paper develops low-complexity hybrid analog/digital precoding for downlink multiuser mmWave systems. Hybrid precoding involves a combination of analog and digital processing that is inspired by the power consumption of complete radio frequency and mixed signal hardware. The proposed algorithm configures hybrid precoders at the transmitter and analog combiners at multiple receivers with a small training and feedback overhead. The performance of the proposed algorithm is analyzed in the large dimensional regime and in single-path channels. When the analog and digital precoding vectors are selected from quantized codebooks, the rate loss due to the joint quantization is characterized, and insights are given into the performance of hybrid precoding compared with analog-only beamforming solutions. Analytical and simulation results show that the proposed techniques offer higher sum rates compared with analog-only beamforming solutions, and approach the performance of the unconstrained digital beamforming with relatively small codebooks.

Distributed spectrum sensing improves the detection reliability of a cognitive radio network but generally comes at the price of a large power consumption. Since cognitive radios are generally low-power sensors with limited batteries, a combined censoring and sleeping scheme is considered as an energy-efficient algorithm for distributed spectrum sensing. Each sensor switches off its sensing module with a specific sleeping rate. When the sensor is on, a censoring policy is employed to send the sensing result to the fusion center. The result is only transmitted, if it is deemed to be informative. Hence, the energy consumption of each sensor, including the sensing and transmission energies, is reduced. The underlying sensing parameters are derived by minimizing the maximum average energy consumption per sensor subject to a lower-bound on the global probability of detection and an upper-bound on the global probability of false alarm. We analyze the problem for the OR and the AND rule and provide a performance analysis for a case study based on the IEEE 802.15.4/ZigBee standard. It is shown that the combined censoring and sleeping scheme achieves a significant energy saving compared to the case where no censoring or sleeping is taken into account.

This article considers the joint problem of packet scheduling and self-localization in an underwater acoustic sensor network with randomly distributed nodes. In terms of packet scheduling, our goal is to minimize the localization time, and to do so we consider two packet transmission schemes, namely a collision-free scheme (CFS), and a collision-tolerant scheme (CTS). The required localization time is formulated for these schemes, and through analytical results and numerical examples their performances are shown to be dependent on the circumstances. When the packet duration is short (as is the case for a localization packet), the operating area is large (above 3 km in at least one dimension), and the average probability of packet-loss is not close to zero, the collision-tolerant scheme is found to require a shorter localization time. At the same time, its implementation complexity is lower than that of the collision-free scheme, because in CTS, the anchors work independently. CTS consumes slightly more energy to make up for packet collisions, but it is shown to provide a better localization accuracy. An iterative Gauss-Newton algorithm is employed by each sensor node for self-localization, and the Cramér Rao lower bound is evaluated as a benchmark.

We introduce a new cyclic spectrum estimation method for wide-sense cyclostationary (WSCS) signals sampled at sub-Nyquist rate using non-uniform sampling. We exploit the block Toeplitz structure of the WSCS signal correlation matrix and write the linear relationship between this matrix and the correlations of the sub-Nyquist rate samples as an overdetermined system. We find the condition under which the system matrix has full column rank allowing for least-squares reconstruction of the WSCS signal correlation matrix from the correlations of the compressive measurements. We also evaluate the case when the support of the WSCS signal correlation is limited and look at a special case where each selection matrix is restricted to either an identity matrix or an empty matrix. In the latter case, we can connect the full column rank condition of the system matrix with a circular sparse ruler.

Wideband spectrum sensing improves the agility of spectrum sensing and spectrum hand-off in cognitive radio systems. In this paper, a distributed wideband spectrum sensing technique over adaptive diffusion networks is proposed. Considering unknown and different channels between the primary and the cognitive users, an averaged received power spectrum across all the cognitive users is estimated by each user using diffusion adaptation techniques. This averaged power spectrum estimate is reliable enough for the users to perform spectrum sensing and make a decision regarding the presence or the absence of the primary user. The simulation results show that the detection performance of the system improves with the number of iterations. Further, a satisfactory detection performance at low SNRs is achieved after a few iterations, which is a desired characteristic for cognitive radio systems. Finally, it is shown that the cooperative technique outperforms the non-cooperative one in terms of estimation accuracy and detection performance.

Sensor selection is an important design task in sensor networks. We consider the problem of adaptive sensor selection for applications in which the observations follow a non-linear model, e.g., target/bearing tracking. In adaptive sensor selection, based on the dynamical state model and the state estimate from the previous time step, the most informative sensors are selected to acquire the measurements for the next time step. This is done via the design of a sparse selection vector. Additionally, we model the evolution of the selection vector over time to ensure a smooth transition between the selected sensors of subsequent time steps. The original non-convex optimization problem is relaxed to a semi-definite programming problem that can be solved efficiently in polynomial time.

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via the group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion. We develop low-complexity solvers for our proposed formulations through the alternating direction method of multipliers.

Distributed spectrum sensing enhances the detection reliability of a cognitive radio network. However, this comes at the price of a higher energy consumption. To solve this problem, a combined censoring and sleeping scheme is considered where the cognitive radios switch off their sensing module with a specific sleeping rate in each sensing period. The awake cognitive radios send their local decisions to the fusion center only if it is deemed to be informative. The fusion center either employs the OR or the AND rule to make the final decision about the presence or absence of the primary user. This paper investigates which rule performs better in terms of energy efficiency under various conditions. The underlying sensing parameters are derived by minimizing the maximum average energy consumption per sensor subject to a constraint on the probabilities of false alarm and detection. This way, it can be ensured that the spectrum opportunities are utilized efficiently while the primary users are not interfered with. A case study based on IEEE 802.15.4/ZigBee is considered for performance evaluation. It is shown that significant energy savings can be obtained by employing combined censoring and sleeping.

The selection of the minimum number of sensors within a network to satisfy a certain estimation performance metric is an interesting problem with a plethora of applications. We explore the sparsity embedded within the problem and propose a relaxed sparsity-aware sensor selection approach which is equivalent to the unrelaxed problem under certain conditions. We also present a reasonably low-complexity and elegant distributed version of the centralized problem with convergence guarantees such that each sensor can decide itself whether it should contribute to the estimation or not. Our simulation results corroborate our claims and illustrate a promising performance for the proposed centralized and distributed algorithms.

Compressive sampling (CS) based multiple symbol differential detectors are proposed for impulse-radio ultra-wideband signaling, using the principles of generalized likelihood ratio tests. The CS based detectors correspond to two communication scenarios. One, where the signaling is fully synchronized at the receiver and the other, where there exists a symbol level synchronization only. With the help of CS, the sampling rates are reduced much below the Nyquist rate to save on the high power consumed by the analog-to-digital converters. In stark contrast to the usual compressive sampling practices, the proposed detectors work on the compressed samples directly, thereby avoiding a complicated reconstruction step and resulting in a reduction of the implementation complexity. To resolve the detection of multiple symbols, compressed sphere decoders are proposed as well, for both communication scenarios, which can further help to reduce the system complexity. Differential detection directly on the compressed symbols is generally marred by the requirement of an identical measurement process for every received symbol. Our proposed detectors are valid for scenarios where the measurement process is the same as well as where it is different for each received symbol.

Rigid body localization refers to a problem of estimating the position of a rigid body along with its orientation using anchors. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body is not known, but, the relative position of the sensors or the topology of the sensors on the rigid body is known. We express the absolute position of the sensors as an affine function of the Stiefel manifold and propose a simple least-squares (LS) estimator as well as a constrained total least-squares (CTLS) estimator to jointly estimate the orientation and the position of the rigid body. To account for the perturbations of the sensors, we also propose a constrained total least-squares (CTLS) estimator. Analytical closed-form solutions for the proposed estimators are provided. Simulations are used to corroborate and analyze the performance of the proposed estimators.

In this paper, we jointly solve the problem of transmit antenna selection and zero-forcing (ZF) precoding in a multiple input multiple output (MIMO) system. A new problem formulation is proposed which enables efficient semi-definite programming (SDP) to solve the originally non-convex problem of antenna selection. This has been accomplished by imposing the Group Lasso sparsity promoting term in the precoding design criterium as a convex relaxation of the ℓ0-norm operation. For the selected set of antennas, we then minimize the overall transmit power, subject to a constraint on the maximum achievable throughput. Simulation results reveal the power saving advantage of the proposed algorithm compared to a randomly selected subset of antennas.

The problem of source localization from time-difference-of-arrival (TDOA) measurements is in general a non-convex and complex problem due to its hyperbolic nature. This problem becomes even more complicated for the case of multi-source localization where TDOAs should be assigned to their respective sources. We simplify this problem to an ℓ1-norm minimization by introducing a novel TDOA fingerprinting model for a multi-source scenario. Moreover, we propose an innovative trick to enhance the performance of our proposed fingerprinting model in terms of the number of identifiable sources. An interesting by-product of this enhanced model is that under some conditions we can convert the given underdetermined problem to an overdetermined one and efficiently solve it using classical least squares (LS) approaches. Our simulation results illustrate a good performance for the introduced TDOA fingerprinting.

Wideband spectrum sensing provides a means to determine the occupancy of channels spanning a broad range of frequencies. Practical limitations impose that the acquisition should be accomplished at a low rate, much below the Nyquist lower bound. Dramatic rate reductions can be obtained by the observation that only a few parameters need to be estimated in typical spectrum sensing applications. This paper discusses the joint estimation of the power of a number of channels, whose power spectral density (PSD) is known up to a scale factor, using compressive measurements. First, relying on a Gaussian assumption, an efficient approximate maximum likelihood (ML) technique is presented. Next, a least-squares estimator is applied for the general non-Gaussian case.

The present paper introduces a novel online asset allocation strategy which accounts for the sensitivity of Markowitz-inspired portfolios to low-quality estimates of the mean and the correlation matrix of stock returns. The proposed methodology builds upon the total least-squares (TLS) criterion regularized with sparsity attributes, and the ability to incorporate additional convex constraints on the portfolio vector. To solve such an optimization task, the present paper draws from the rich family of splitting algorithms to construct a novel online splitting algorithm with computational complexity that scales linearly with the number of unknowns. Real-world financial data are utilized to demonstrate the potential of the proposed technique.

This article concerns the problem of scheduling the localization packets of the anchors in an underwater acoustic sensor network (UASN). Knowing the relative positions of the anchors and their maximum transmission range, we take advantage of the long propagation delay of underwater communication to minimize the duration of the localization task. First, we formulate the concept of collision-free packet transmission for localization, and we show how the optimum solution can be obtained. Furthermore, we propose two low-complexity algorithms, and through comprehensive simulations we compare their performances with the optimal solution as well as other existing methods. Numerical results show that the proposed algorithms perform near optimum and better than alternative solutions.

Reliable spectrum sensing is a key functionality of a cognitive radio network. Cooperative spectrum sensing improves the detection reliability of a cognitive radio system but also increases the system energy consumption which is a critical factor particularly for low-power wireless technologies. A censored truncated sequential spectrum sensing technique is considered as an energy-saving approach. To design the underlying sensing parameters, the maximum {average energy consumption per sensor} is minimized subject to a lower bounded global probability of detection and an upper bounded false alarm rate. This way both the interference to the primary user due to miss detection and the network throughput as a result of a low false alarm rate are controlled. {To solve this problem, it is assumed that the cognitive radios and fusion center are aware of their location and mutual channel properties.} We compare the performance of the proposed scheme with a fixed sample size censoring scheme under different scenarios and show that for low-power cognitive radios, censored truncated sequential sensing outperforms censoring. It is shown that as the sensing energy per sample of the cognitive radios increases, the energy efficiency of the censored truncated sequential approach grows significantly.

A fully asynchronous network with one sensor andManchors (nodes with known locations) is considered in this letter. We propose a novel asymmetrical time-stamping and passive listening (ATPL) protocol for joint clock synchronization and ranging. The ATPL protocol exploits broadcast to not only reduce the number of active transmissions between the nodes, but also to obtain more information. This is used in a simple estimator based on least-squares (LS) to jointly estimate all the unknown clock-skews, clock-offsets, and pairwise distances of the sensor to each anchor. The Cramér-Rao lower bound (CRLB) is derived for the considered problem. The proposed estimator is shown to be asymptotically efficient, meets the CRLB, and also performs better than the available clock synchronization algorithms.

We propose maximum a posteriori (MAP) based noncoherent differential detector for ultra-wideband (UWB) impulse radio (IR) signals, received at a sub-Nyquist sampling rate. We build our detector for a Laplacian distributed multipath channel, which models sparsity. Our MAP based detector outperforms differential detectors based on other state-of-the-art approaches from a practical point of view. Our work highlights the critical role of different measurement matrices for the compressed differential detectors in general and the MAP based compressed differential detectors in particular.

We extend one of our recently proposed anchorless mobile network localization algorithms (called PEST) to operate in a partially connected network. To this aim, we propose a geometric missing link reconstruction algorithm for noisy scenarios and repeat the proposed algorithm in a local-to-global fashion to reconstruct a complete distance matrix. This reconstructed matrix is then used in the PEST to localize the mobile network. We compare the computational complexity of the new link reconstruction algorithm with existing related algorithms and show that our proposed algorithm has the lowest complexity, and hence, is the best extension of the low complexity PEST. Simulation results further illustrate that the proposed link reconstruction algorithm leads to the lowest reconstruction error as well as the most accurate network localization performance.

We consider the problem of detecting a known signal with constant magnitude immersed in noise of unknown variance, when the propagation channel is frequency-flat and randomly time-varying within the observation window. A Basis Expansion Model with random coefficients is used for the channel, and a Generalized Likelihood Ratio approach is adopted in order to cope with deterministic nuisance parameters. The resulting scheme can be seen as a generalization of the wellknown Matched Filter detector, to which it reduces for time-invariant channels. Closed-form analytical expressions are provided for the distribution of the test statistic under both hypotheses, which allow to assess the detection performance.

In this paper, we propose a clock skew calibration method for ranging applications using an ultra-wideband (UWB) signal. The clock skew is one of the main error sources in time-of-arrival (TOA) based UWB ranging, since a long ranging signal is required to obtain a sufficiently high signal-to-noise ratio (SNR). Therefore, the clock skew calibration is essential for accurate TOA ranging. We propose to estimate the clock skew in the frequency domain to take full advantage of the periodic property of the ranging signal, which allows the proposed method to reach super-resolution. Simulation results corroborate the efficiency of the proposed method.

This paper deals with the distributed implementation of a recently proposed algorithm for the estimation of static fields. The algorithm combines wireless sensor network (WSN) field measurements with a physical field model in the form of a partial differential equation (PDE), such that the field can be estimated at locations different from the WSN sensor node locations. By discretizing the PDE using the finite element method (FEM), the physical field model reduces to a highly sparse linear system of equations. It is shown how this FEM-induced sparsity pattern can be exploited in the design of a distributed implementation such as to minimize the communication effort and data storage required in the WSN. Simulation results illustrate that a significant improvement in field estimation accuracy can be obtained, compared to the case when only WSN measurements (without a physical model) are used.

OFDM suffers from inter-carrier interferences in the presence of the time variation. This paper seeks to quantify the amount of interferences resulting from wideband channels which assumed to follow the multi-scale/multi-lag (MSML) model. Due to the fact that the mobility in wideband channels induces scale effects, Doppler is revealed in a manner distinct from the frequency shifts experienced in narrowband systems. The MSML channel model results in full channel matrices both in the frequency and time domains. However, banded approximations are still possible, leading to significant reduction in the equalization complexity. Herein, measures for determining whether time-domain or frequency-domain should be undertaken are provided based on the amount of the resulting interference.

In this paper, we analyze the problem of localizing and tracking a mobile node in an underwater environment with an isogradient sound speed profile (SSP). We will show that range-based localization algorithms are not so accurate in such an environment, and they should be replaced by time-based ones. Therefore, we relate the mobile node location to the travel time of a propagating sound wave from (to) an anchor node to (from) the mobile node. After obtaining sufficient time measurements, positioning can be achieved through multilateration. To accomplish this, we utilize the extended Kalman filter (EKF) for multilateration and tracking the mobile node's location in a recursive manner. Through several simulations, we will show that the proposed EKF algorithm performs superb in comparison with algorithms which assume a straight-line wave propagation in an underwater environment.

Two novel cooperative localization algorithms for mobile wireless networks are proposed. To continuously localize the mobile network, given the pairwise distance measurements between different wireless sensor nodes, we propose to use subspace tracking to track the variations in signal eigenvectors and corresponding eigenvalues of the double-centered distance matrix. We compare the computational complexity of the new algorithms with a recently developed algorithm exploiting the extended Kalman filter (EKF) and show that our proposed algorithms are computationally efficient, and hence, appropriate for practical implementations compared to the EKF. Simulation results further illustrate that the proposed algorithms are more accurate when the distance errors are small (low noise scenarios) in comparison with the EKF, while being more robust to the sampling period in high noise scenarios.

In this paper, we propose time-based localization approaches for asynchronous wireless sensor networks (WSNs), where not only clock skews but also clock offsets are present at all nodes. We first propose a joint synchronization and localization approach using the two-way ranging (TWR) protocol. Furthermore, a novel ranging protocol, namely asymmetric trip ranging (ATR), is employed and a two-step joint synchronization and localization approach is developed. As a result, we achieve efficient closed-form least-squares (LS) estimators. We compare these two proposed approaches. More over, simulation results corroborate the efficiency of our time-based localization schemes.

Block transmission of multi-scale orthogonal wavelet division multiplexing (OWDM) is proposed for signaling over wideband linear time-varying channels (LTV). Such channels are best modeled by multi-scale, multi-lag (MSML) models and the proposed OWDM designs are tailored to such channels. Given this signaling, the effective channel matrix for the received signal is banded, allowing for the modification of prior methods of equalization for orthogonal frequency division multiplexing over narrowband LTV channels. Performance of such equalizers and signaling is provided via simulation and shown to offer good performance coupled with high spectral efficiency over previously proposed designs.

Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. Weighted and structured generalizations of the TLS approach are further motivated in several signal processing and system identification related problems. On the other hand, modern compressive sampling and variable selection algorithms account for perturbations of the data vector, but not those affecting the regression matrix. The present paper addresses also the latter by introducing a weighted and structured sparse (S-) TLS formulation to exploit a priori knowledge on both types of perturbations, and on the sparsity of the unknown vector. The resultant novel approach is further able to cope with sparse, under-determined errors-in-variables models with structured and correlated perturbations, while allowing for efficient sub-optimum solvers. Simulated tests demonstrate the approach, and especially its ability to reliably recover the support of unknown sparse vectors.

In this paper, we analyze the performance of an IEEE 802.15.4 radio link in the 2360-2400 MHz band to support the ongoing Medical Body Area Network (MBAN) standardization activities in IEEE 802.15. There has been a lot of interest recently in opening the 2360-2400 MHz band for secondary allocations to promote MBAN innovations by providing a spectrum with less interference. In this work, we characterize the primary services in this band, focusing on Electronic News Gathering/Outside Broadcasting (ENG/OB) and Aeronautical Mobile Telemetry (AMT) systems. We study the performance in terms of the Packet Error Rate (PER) of an 802.15.4 MBAN radio link implemented on a Universal Software Radio Peripheral 2 (USRP2), in the presence of interference from these systems. A cognitive radio approach is proposed by implementing a spectrum sensing engine based on energy detection on USRP2. Our measurement results show an improvement in the performance of the radio along with primary user protection. In addition, an analytical expression for the packet error rate of the MBAN radio link with spectrum sensing is provided for a given Primary User (PU) activity, which matches well with the measured performance results.

Optimization of hard fusion spectrum sensing using the k-out-of-N rule is considered. Two different setups are used to derive the optimal k. A throughput optimization setup is defined by minimizing the probability of false alarm subject to a probability of detection constraint representing the interference of a cognitive radio with the primary user, and an interference management setup is considered by maximizing the probability of detection subject to a false alarm rate constraint. It is shown that the underlying problems can be simplified to equality constrained optimization problems and an algorithm to solve them is presented. We show the throughput optimization and interference management setups are dual. The simulation results show the majority rule is optimal or near optimal for the desirable range of false alarm and detection rates for a cognitive radio network. Furthermore, an energy efficient setup is considered where the number of cognitive radios is to be minimized for the AND and the OR rule and a certain probability of detection and false alarm constraint. The simulation results show that the OR rule outperforms the AND rule in terms of energy efficiency.

This paper investigates the issue of dynamic resource allocation (DRA) in the context of multi-user cognitive radio networks. We present a general framework adopting generalized signal expansion functions for representation of physical-layer radio resources as well as for synthesis of transmitter and receiver waveforms, which allow us to join DRA with waveform adaptation, two procedures that are currently carried out separately. Based on the signal expansion framework, we develop noncooperative games for distributed DRA, which seek to improve the spectrum utilization on a per-user basis under both transmit power and cognitive spectral mask constraints. The proposed DRA games can handle many radio platforms such as frequency, time or code division multiplexing (FDM, TDM, CDM), and even agile platforms with combinations of different types of expansion functions. To avoid the complications of having too many active expansion functions after optimization, we also propose to combine DRA with sparsity constraints. Generally, the sparsity-constrained DRA approach improves convergence of distributed games at little performance loss, since the effective resources required by a cognitive radio are in fact sparse. Finally, to acquire the channel and interference parameters needed for DRA, we develop compressed sensing techniques that capitalize on the sparse properties of the wideband signals to reduce the number of samples used for sensing and hence the sensing time.

Power spectrum blind sampling (PSBS) consists of a sampling procedure and a reconstruction method that is capable of perfectly reconstructing the unknown power spectrum of a signal from the obtained samples. In this letter, we propose a solution to the PSBS problem based on a periodic sampling procedure and a simple least squares (LS) reconstruction method. For this PSBS technique, we derive the lowest possible average sampling rate, which is much lower than the Nyquist rate of the signal. Note the difference with spectrum blind sampling (SBS) where the goal is to perfectly reconstruct the spectrum and not the power spectrum of the signal, in which case sub-Nyquist rate sampling is only possible if the spectrum is sparse. In the current work, we can perform sub-Nyquist rate sampling without making any constraints on the power spectrum, because we try to reconstruct the power spectrum and not the spectrum. In many applications, such as spectrum sensing for cognitive radio, the power spectrum is of interest and estimating the spectrum is basically overkill.

We propose a round-robin scheduling algorithm for orthogonal beamforming with a strict signal to interference-plus-noise ratio (SINR) constraint and limited feedback. The presented algorithm aims at scheduling the users at identical slots over different blocks, in order to reduce the necessary scheduling overhead, and to minimize the maximum delay between serving the same user. Thus, the presented algorithm is especially suited for real-time multimedia traffic. The algorithm allocates the users using orthogonal beamforming based on the quantized feedback provided by the users. The quantized feedback consists of the estimated power that is necessary to fulfill a predefined SINR constraint. Further, we propose an algorithm to design codebooks to quantize the estimated power. Using the feedback, the base station redistributes power from users with spare power to users that lack power so that they fulfill their SINR constraints. The performance of the algorithm is demonstrated through simulations.

In this paper, energy detectors are developed for wideband and ultra-wideband (UWB) pulse position modulation (PPM). Exact bit error probability (BEP) formulas are derived under different assumptions about the channel. More specifically, we present an expression for the instantaneous BEP for a specific channel realization, as well as an expression for the average BEP for a channel with independent and identically distributed zero-mean Gaussian coefficients. Simulation results corroborate the precision of the formulas.

Equalizer designs for digital communications over wireless channels exhibiting both multi-lag and multi-scale are investigated. Such channel models are well-suited for underwater acoustic communications and may have impact on the design of systems for vehicle-to-vehicle communications. First, the implications of the multi-scale, multi-lag model on equalizer design are highlighted. In particular, equalizers are time-varying as a function of symbol index. Three suboptimal, low complexity block equalizers (partial, truncated, and path combining) are compared to that of the full block equalizer and shown to offer a good tradeoff between complexity and performance. These four equalizers significantly outperform a simple matched filter which performs no equalization.

We consider a two-stage sensing scheme for cognitive radios where coarse sensing based on energy detection is performed in the first stage and, if required, fine sensing based on cyclostationary detection in the second stage. We design the detection threshold parameters in the two sensing stages so as to maximize the probability of detection, given constraints on the probability of false alarm. We compare this scheme with ones where only energy detection or cyclostationary detection is performed. The performance comparison is made based on the probability of detection, probability of false alarm and mean detection time.

We propose a sensor positioning scheme for a wireless sensor network consisting of beacons as well as collaborative anchors (CA) to help sensors within a prescribed service area to locate themselves. We assume a robust performance is achieved in the sense that a prescribed location accuracy requirement is fulfilled within the service area. Under the assumption that the time-of-arrival and location estimators adopted achieve the associated Cramér-Rao bound, the performance of the location scheme is derived and analyzed. A ranging energy optimization problem is proposed, and a practical algorithm is presented. The effectiveness of this algorithm is illustrated by numerical experiments.

In this paper, an Ultra-Wideband (UWB) receiver scheme with very low sampling rate is proposed for ranging in indoor multipath environments. The idea underlying the proposed scheme is that, instead of processing the whole UWB band, only partial sub-bands are considered at the receiver. The missing sub-bands are estimated by exploiting an estimate of the frequency correlation properties of the channel to reconstruct the signal over the whole UWB band. For the simulations, the IEEE UWB channel model is used and the range error using the proposed receiver scheme is obtained and compared to that of conventional UWB receivers which require very high sampling rates. Furthermore, a large number of UWB channel measurements in an office environment has been used to validate the accuracy of the obtained results. These results show that the range accuracy strongly depends on the number of received sub-bands and the spacing between them. For instance, using 1% of the total UWB bandwidth, an average range error of less than 10 cm is obtained. Furthermore, unlike conventional UWB receivers, the proposed technique performs better (in terms of range error) for low signal-to-noise ratios.

In this paper we focus on compressive sampling (CS) based ultra wideband (UWB) differential detection. We formulate an optimization problem to jointly recover the sparse received UWB signals as well as the differentially encoded data symbol. We utilize an alternating direction method of multipliers (ADMoM) to solve this joint optimization problem. Our proposed joint recovery method outperforms the straightforward separate recovery method, which recovers the sparse received UWB signals in a first step and then detects the differentially encoded symbol based on the recovered signals.

We consider the problem of node localization given partial pairwise distance measurements. Current solutions first complete the missing distances and then apply the classical multidimensional scaling (MDS) algorithm. Instead, we extend the classical MDS to a setup where the sensor network is composed of a fully connected group of nodes that communicate with each other (e.g., beacons), and a group of nodes that cannot communicate with each other, but each one of them communicates with each node in the first group. The positions of all nodes are unknown. We localize the fully connected nodes by exploiting their distance measurements to the disconnected nodes. At the same time, the positions of the disconnected nodes are obtained up to a translation relative to the positions of the connected nodes. Recovering this translation, can be obtained with an additional step. Simulation results show that the proposed algorithm outperforms current MDS-like solutions to the problem.

Single-carrier transmissions with frequency-domain equalization have gained much interest due to their comparable complexity and performance to OFDM, which conversely suffers from a high peak-to-average power ratio. In this paper, we develop a new frequency-domain block turbo equalizer for single-carrier (SC) transmissions over doubly-selective channels. The main feature of the proposed equalizer is its low complexity, which is only linear in the block length. A comparison between SC and OFDM systems with channel coding in doubly-selective channels is also given.

We present a compressive wide-band spectrum sensing scheme for cognitive radios. The received analog signal at the cognitive radio sensing receiver is transformed in to a digital signal using an analog-to-information converter. The autocorrelation of this compressed signal is then used to reconstruct an estimate of the signal spectrum. We evaluate the performance of this scheme in terms of the mean squared error of the power spectrum density estimate and the probability of detecting signal occupancy.

We are presenting an algorithm for scheduling users in a single-cell broadcast scenario. The presented algorithm aims to minimize the number of transmissions that are necessary to serve all the users in the cell a single time, while the different users still fulfill a strict SINR constraint. Depending on the individual channel characteristics, the algorithm adapts the number of users scheduled for transmission on the fly, and dynamically allocates the transmit power to the scheduled users. A high-performance and a low-complexity variant of the algorithm are presented and their performance is evaluated through simulations.

In this paper, we solve the problem of detecting the entries of a sparse finite-alphabet signal from a limited amount of data, for instance obtained by compressive sampling. While existing methods either rely on the sparsity property, the finite-alphabet property, or none of those properties to solve the under-determined system of linear equations, we capitalize on both the sparsity and the finite-alphabet features of the signal. The problem is first formulated in a Bayesian framework to incorporate the prior knowledge of sparsity, which is then shown to be solvable using sphere decoding (SD) or semi-definite relaxation (SDR) for efficient Boolean programming. A few toy simulations show how our method can outperform existing works.

We address ranging energy optimization for an unsynchronized localization system, which features robust sensor positioning, in the sense that specific accuracy requirements are fulfilled within a prescribed service area. Optimization problems related to the ranging energy of a sensor and beacons are proposed, after which a practical algorithm based on semidefinite programming is presented. The effectiveness of the algorithm is illustrated by a numerical experiment.

In this paper, we derive the Cramér-Rao bound (CRB) for range estimation, which does not only exploit the range information in the time delay, but also in the amplitude of the received signal. This new bound is lower than the conventional CRB that only makes use of the range information in the time delay. We investigate the new bound in an additive white Gaussian noise (AWGN) channel with attenuation by employing both narrowband (NB) signals and ultra-wideband (UWB) signals. For NB signals, the new bound can be 3dB lower than the conventional CRB under certain conditions. However, there is not much difference between the new bound and the conventional CRB for UWB signals. Further, shadowing effects are added into the data model. Several CRB-like bounds for range estimation are derived to take these shadowing effects into account.

In this paper, the performance of a time-division duplex ultra wideband system that has a transmitter/receiver pair of rake combining structures is optimized, where the total number of rake fingers to be deployed at the transmitter and the receiver is fixed. It is shown that there exists an optimum distribution of fingers between the two structures for systems with intersymbol interference, which maximizes the signal-to-interference plus noise ratio. Depending on the total number of rake fingers and/or post-rake fingers, i.e., those at the receiver, the optimum placement of post-rake fingers changes as the simulation results demonstrate.

This paper presents a flexible digital receiver for pulsed Ultra-Wideband (UWB) communications which is sampling below Nyquist rate. This receiver can trade demodulation performance for sampling rate, i.e. power consumption. The bit error rate for pulse amplitude and pulse position modulations is evaluated in AWGN and typical UWB channels. The performance of several types of equalizer is compared, taking into account their implementation complexity. A suboptimal but implementation efficient Minimum Mean-Square Error (MMSE) equalizer which reaches performances similar to the ideal MMSE equalizer is proposed. The impact of imperfect knowledge of the propagation channel and signal-to-noise ratio, due to the limited number of training symbols, on the performance of the receiver is assessed. Finally, the receiver architecture and implementation cost are discussed. The proposed subsampling receiver provides an attractive alternative to classical architectures based on correlation with a template.

We develop a new receiver for orthogonal frequency division multiplexing (OFDM) systems in time-varying channels by embedding channel estimation in a low-complexity block turbo equalizer. A linear minimummean squared error (MMSE) pilot-assisted channel estimator is presented, and the soft data estimates from the turbo equalizer are used to improve the quality of the channel estimates.

This paper discusses the issue of dynamic resource allocation (DRA) in the context of cognitive radio (CR) networks. We present a general framework adopting generalized transmitter and receiver signal-expansion functions, which allow us to join DRA with waveform adaptation, two procedures that are currently carried out separately. Moreover, the proposed DRA can handle many types of expansion functions or even combinations of different types of functions. An iterative game approach is adopted to perform multi-player DRA, and the best-response strategies of players are derived and characterized using convex optimization. To reduce the implementation costs of having too many active expansion functions after optimization, we also propose to combine DRA with sparsity constraints for dynamic function selection. Generally, it incurs little rate-performance loss since the effective resources required by a CR are in fact sparse.

A multiband OFDM transmitter and receiver are presented for underwater communications at low SNR. Compared with a single-band OFDM scheme, the multiband approach leads to a considerable reduction in the receiver complexity. The proposed system has been tested at sea with 16 subbands covering a total bandwidth of 3.6 kHz, at user data rates of 4.2 and 78 bit/s, and over ranges up to 52 km. At the lower rate, successful message recovery is achieved on a single hydrophone at SNRs down to -17 dB in a benign channel. In channels with a severe delay-Doppler spread the critical SNR rises by some 4 dB. At 78 bit/s the limits of the OFDM signaling scheme are clearly revealed, but at 4.2 bit/s the performance is limited by failure of signal detection and initial synchronization.

In this paper, we present a single-carrier transceiver for rapidly time-varying channels, where the equalization step is implemented in the frequency domain. When the channel abides with both fast fading and severe inter-block interference, our equalizer relies on a band approximation of the frequencydomain channel matrix to maintain low complexity. We will show that the band approximation error can be associated in the time domain to a critically-sampled complex exponential basis expansion modeling error. Based on this property, we propose a novel receiver architecture that extends the original data model by inserting zeros at the receiver. The resulting effective channel can be characterized by an oversampled complex exponential basis expansion model, which has a considerably reduced modeling error compared to the critically-sampled one. In other words, the band assumption that is essential to the equalizer will be made more accurate and thus the equalization performance can be improved.

We propose a low-complexity block turbo equalizer for orthogonal frequency-division multiplexing (OFDM) systems in time-varying channels. The complexity of the proposed algorithm is linear in the number of subcarriers by exploiting the band structure of the frequency-domain channel matrix. The presented block turbo equalizer is based on a soft minimum mean squared error (MMSE) block linear equalizer (BLE).

This paper presents two novel methods to optimally compress the feedback for spatial multiplexing with linear precoding. The methods exploit the time correlation of the channel and the knowledge of the previously fed back precoder matrices to estimate the conditional probabilities of the different possible feedback indices. These probabilities are then used to losslessly compress the actual feedback using variable-length codes. Two compression schemes are presented, one for a non-dedicated feedback channel and one for a dedicated feedback channel.

We consider a single-carrier transceiver, which abides with both fast channel fading and severe inter-block interference. To enable a low-complexity frequency-domain equalizer, it is desired that 1) the channel matrix be approximately banded; and 2) the inter-block interference be reduced. In this paper, we propose an extended data model, which incorporates a receiver window to enforce these two conditions.

Pilot-assisted channel estimation is considered in this letter, where the channel is assumed to be time-selective and can be accurately fit by a basis expansion model. The position and power of the pilots are crucial to the mean square error of the channel estimator. In this paper, we present nonlinear integer programming algorithms to optimize the position and power of the pilots. In comparison with the traditional equi-distant/powered pilot structure, the solution obtained from the proposed algorithms yields a better performance.

Spatial multiplexing with multi-mode precoding provides a means to achieve both high capacity and high reliability in multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. Multi-mode precoding uses linear transmit precoding that adapts the number of spatial multiplexing data streams or modes, according to the transmit channel state information (CSI). As such, it typically requires complete knowledge of the multi-mode precoding matrices for each subcarrier at the transmitter. In practical scenarios where the CSI is acquired at the receiver and fed back to the transmitter through a low-rate feedback link, this requirement may entail a prohibitive feedback overhead. In this paper, we propose to reduce the feedback requirement by combining codebook-based precoder quantization, to efficiently quantize and represent the optimal precoder on each subcarrier, and multi-mode precoder frequency down-sampling and interpolation, to efficiently reconstruct the precoding matrices on all subcarriers based on the feedback of the indexes of the quantized precoders only on a fraction of the subcarriers. To enable this efficient interpolation-based quantized multimode precoding solution, we introduce (1) a novel precoder codebook design that lends itself to precoder interpolation, across subcarriers, followed by mode selection, (2) a new precoder interpolator and, finally, (3) a clustered mode selection approach that significantly reduces the feedback overhead related to the mode information on each subcarrier. Monte-Carlo bit-error rate (BER) performance simulations demonstrate the effectiveness of the proposed quantized multi-mode precoding solution, at reasonable feedback overhead

We propose low-complexity equalizers for Alamouti space-time coded orthogonal frequency-division multiplexing (OFDM) systems in time- and frequency-selective channels, by extending the approach formerly proposed for single-antenna OFDM systems. The complexity of the proposed algorithm is linear in the number of subcarriers by exploiting the band structure of the frequency-domain channel matrix and a band LDLHfactorization. We design minimum mean squared error (MMSE) block linear equalizers (BLE) and block decision- feedback equalizers (BDFE) with and without windowing. We also develop a low-complexity algorithm that adaptively selects the useful bandwidth of the channel matrix. Simulation results show that the proposed algorithm produces a correct estimate of the bandwidth parameter.

Multicarrier systems are seriously affected by time-varying frequency-selective channels. Recently, windowing and decision-feedback equalization (DFE) have separately been proven to boost the performance of minimum mean-squared error (MMSE) block equalization, while maintaining a very low complexity by capitalizing on a band LDL factorization. This paper jointly considers receiver windowing and DFE, as well as the impact on the performance of a pilot-based frequency-domain channel estimation technique that relies on a basis expansion model (BEM) approach. We show that the combination of windowing and DFE still allows the use of a low-complexity band LDL factorization. Therefore, we can further improve the BER of OFDM systems affected by severe Doppler spread, while preserving linear complexity in the number of subcarriers

In this paper, we deal with channel estimation for Orthogonal Frequency-Division Multiplexing (OFDM) systems. The channels are assumed to be Time-Varying (TV) and approximated by a Basis Expansion Model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but can be approximated as banded. Based on this band approximation, we propose novel channel estimators to combat both the noise and the out-of-band interference. Our claims are supported by simulation results, which are obtained based on realistic TV channels with a fairly high Doppler spread.

This paper presents a low power pulsed UWB receiver sampling below Nyquist rate which can accomodate time-varying data rate and quality-of-service requirements for applications communicating via UWB. The performance of pulse amplitude and pulse position modulations is assessed in AWGN and dense multipath environments using the standard IEEE 802.15.3a channel models. The proposed subsampling receiver provides an attractive digital alternative to the classical approach based on analog correlations, and can reach data rates above 100 Mb/s.

A communication system based on transmit-reference (TR) ultra-wideband (UWB) is studied and further developed. Introduced by Hoctor and Tomlinson, the aim of the TR-UWB transceiver is to provide a straightforward impulse radio system, feasible to implement with current technology, and to achieve either high data rate transmissions at short distances or low data rate transmissions in typical office or industrial environments. The main contribution in this paper is the derivation of a signal processing model that takes into account the effects of the radio propagation channel, in particular, for the case where the two pulses in a doublet are closely spaced. Several receivers based on the code-division multiple-access-like properties of the proposed model are derived, and the performance of the algorithms is tested in a simulation.

This paper addresses some of the opportunities and the challenges in the design of multi-hop systems that utilize cooperation with one or two intermediate regenerative relays to provide high-quality communication between a source and a destination. We discuss the limitations of using a distributed Alamouti scheme in the relay channel and the additional complexity required to overcome its loss of diversity. As an alternative to the distributed Alamouti scheme, we propose and analyze two error aware distributed space-time (EADST) systems built around the Alamouti code. First, using a bit error rate based relay selection approach, we design an EADST system with one and two regenerative relays that rely on feedback from the destination and we show that the proposed system improves on the distributed Alamouti scheme. In addition, we prove that the proposed one relay EADST system collects the full diversity of the distributed MISO channel. Second, we introduce an EADST system without feedback in which the relaying energies depend on the error probabilities at the relays. Numerical results show that both EADST systems perform close to the error probability lower bound obtained by considering error-free reception at the relays

Transmit maximum-ratio combining (transmit MRC) is a popular antenna diversity technique that provides both spatial diversity and array gain in downlink multiple-input single-output (MISO) links. These gains, however, critically depend on the availability of the downlink channel state information (CSI). In time-division duplexing systems, channel reciprocity has been commonly put forth to justify the convenient use of the CSI already acquired from the uplink, in the calculation of the transmit-MRC weights. Recent work has questioned this practice, based on the non-reciprocity of multi-antenna RF transceivers, due to significant amplitude and phase mismatches across the antennas. Furthermore, expensive digital calibration solutions have been proposed to enforce the reciprocity of the multi-antenna RF transceivers. Both the impact of multi-antenna amplitude and phase mismatches and the performance of the proposed calibration approaches have only been assessed via simulations. In this contribution, we propose an alternative statistical analysis of the impact of these mismatches on transmit MRC. This analysis allows a faster and more reliable characterization as well as provides insight into the relative importance of these mismatches. Consequently, sufficient matching requirements can be extracted for the multi-antenna RF transceivers, for which simpler and cheaper calibration solutions can be devised.

In this paper, we discuss a semi-blind channel estimation algorithm for rapidly time-varying channels, relying on a complex exponential basis expansion model (CE-BEM) for the channel. However, whereas the original CE-BEM approach models a rectangularly windowed version of the channel, the proposed CE-BEM approach models a smoothly windowed version of the channel. This allows for a much better fit, and leads to better channel estimates. The obtained semi-blind channel estimates are subsequently used to construct a recently developed CE-BEM serial decision-feedback equalizer for CE-BEM channels. Simulations are carried out to validate the proposed ideas.

We present a low-complexity equalizer for multicarrier code-division multiple-access (MC-CDMA) downlink systems over time-varying (TV) multipath channels with non-negligible Doppler spread. The equalization algorithm, which is based on a block minimum mean-squared error (MMSE) approach, exploits the band structure of the frequency-domain channel matrix by means of a band LDL/sup H/ factorization. The complexity of the proposed block MMSE equalizer is linear in the number of subcarriers, and smaller with respect to a serial MMSE equalizer characterized by a similar performance.

A discrete-time equivalent system model is derived for differential and transmitted reference (TR) ultra-wideband (UWB) impulse radio (IR) systems, operating under heavy intersymbol-interference (ISI) caused by multipath propagation. In the systems discussed, data is transmitted using differential modulation on a frame-level, i.e., among UWB pulses. Multiple pulses (frames) are used to convey a single bit. Time hopping and amplitude codes are applied for multi user communications, employing a receiver front-end that consists of a bank of pulse-pair correlators. It is shown that these UWB systems are accurately modeled by second-order discrete-time Volterra systems. This proposed nonlinear equivalent system model is the basis for developing optimal and suboptimal receivers for differential UWB communications systems under ISI. As an example, we describe a maximum likelihood sequence detector with decision feedback, to be applied at the output of the receiver front-end sampled at symbol rate, and an adaptive inverse modeling equalizer. Both methods significantly increase the robustness in presence of multipath interference at tractable complexity.

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.

In this paper, we address the problem of identifying convolutive channels using a Gaussian maximum-likelihood (ML) approach when short training sequences (possibly shorter than the channel impulse-response length) are periodically inserted in the transmitted signal. We consider the case where the channel is quasi-static (i.e., the sampling period is several orders of magnitude smaller than the coherence time of the channel). Several training sequences can thus be used in order to produce the channel estimate. The proposed method can be classified as semiblind and exploits all channel-output samples containing contributions from the training sequences (including those containing contributions from the unknown surrounding data symbols). Experimental results show that the proposed method closely approaches the Cramer-Rao bound and outperforms existing training-based methods (which solely exploit the channel-output samples containing contributions from the training sequences only). Existing semiblind ML methods are tested as well and appear to be outperformed by the proposed method in the considered context. A major advantage of the proposed approach is its computational complexity, which is significantly lower than that of existing semiblind methods.

We discuss time-domain equalization of OFDM over doubly-selective channels. We consider the most general case, where the channel delay spread is larger than the cyclic prefix (CP), which results in inter-block interference (IBI). IBI, in conjunction with the Doppler effect, destroys the orthogonality between subcarriers and, hence, results in intercarrier interference (ICI). The time-domain equalizer (TEQ) is assumed to be a time-varying finite impulse response (TV FIR). The purpose of the TEQ is to convert the doubly-selective channel into a purely frequency-selective channel whose delay spread fits within the CP. In other words, the purpose of the TEQ is to restore orthogonality between subcarriers in the OFDM system.

The joint linear precoder and decoder minimum mean squared error (MMSE) design represents a low complexity yet powerful solution for spatial multiplexing MIMO systems. Its performance, however, critically depends on the availability of timely channel state information (CSI) at both transmitter and receiver. In practice, the latter assumption can be severely challenged, due to channel time variations that lead to outdated CSI at the transmitter. State-of-the-art designs mistakenly use the outdated CSI to design the linear precoder and rely on the receiver to reduce the induced degradation. In this paper, we propose a robust Bayesian joint linear precoder and decoder solution that takes into account the uncertainty of the true channel, given the outdated CSI at the transmitter. We finally assess the robustness of our design to channel time variations through Monte-Carlo analysis of the system's MMSE and average bit-error rate (BER) performance.

A new approach has recently been proposed to describe doubly selective channels (i.e., time- and frequency-selective channels) with a limited number of parameters; it is referred to as the basis expansion model (BEM). In the BEM, the true channel coefficients are approximated with a high accuracy using a limited number of complex exponentials. We propose a new method in order to identify the BEM coefficients of the transmission channel. We consider a transmission scheme where several short training sequences (i.e. their length is comparable to the channel order) are inserted in the stream of data symbols. We propose an iterative method that exploits all the received symbols that contain contributions from the training sequences and blindly filters out the contribution of the unknown surrounding data symbols. The proposed method has a low computational complexity and outperforms existing methods proposed in a similar context.

In a previous paper, we proposed a bitrate maximizing (BM) design criterion for the time-domain equalizer (TEQ) in a discrete multitone receiver. This BM-TEQ and the closely related BM per-group equalizers (PGEQ) get close to the performance of the so-called per-tone equalization (PTEQ). In this paper, we show that the BM-TEQ criterion, despite its nonlinear nature, is well suited for a recursive Levenberg-Marquardt (RLM) based design. This adaptive BM-TEQ also allows us to track slow variations of the transmission channel and the noise. This RLM-based design uses the same second-order statistics (SOS) as the earlier presented recursive least-squares (RLS) based adaptive PTEQ and opens up a complete range of adaptive BM equalizers: from the computationally efficient RLS-based PTEQ with largest memory cost, over the RLM-based BM-PGEQ with intermediate memory cost, towards an RLM-based BM-TEQ with considerably smaller memory cost, but larger equalizer updating complexity.

We propose a per-tone frequency-domain equalization approach for OFDM over doubly-selective channels. We consider the most general case, where the doubly-selective channel delay spread is larger than the cyclic prefix (CP), which results into inter-block interference (IBI). IBI in conjunction with the Doppler effect destroys the orthogonality between subcarriers and hence, results into severe intercarrier interference (ICI). In this paper, we propose a novel per-tone frequency-domain equalizer (PTFEQ) that is obtained through transferring a time-varying time-domain equalizer (TV-TEQ) to the frequency-domain. The purpose of the TV-TEQ is to restore orthogonality between subcarriers and eliminate ICI. We use the mean-square error criterion to design the PTFEQ. An efficient implementation of the proposed PTFEQ is also discussed. Finally, we show some simulation results of the proposed equalization technique.

Recently, serial linear equalizers (SLEs) and serial decision feedback equalizers (SDFEs) have been proposed to mitigate the doubly-selective channel effects. To design the SLE/SDFE and to model the doubly-selective channel, a so-called finite impulse response basis expansion model (FIR-BEM) is used. Initially, the FIR-BEM coefficients of the SLE/SDFE were designed based on the exact knowledge of the FIR-BEM coefficients of the doubly-selective channel. In practice, we can use a direct SLE/SDFE design procedure, which avoids an intermediate channel estimation step. In this paper, we describe this idea for the SLE and focus on direct semi-blind design of the FIR- BEM coefficients of the SLE. Simulation results demonstrate the validity of the proposed approach.

In this letter, we propose an interference-suppressing RAKE receiver for the code division multiple-access (CDMA) downlink. In the downlink, the received signal has a special structure that makes it possible for a RAKE receiver (which is a simple low-complexity linear receiver) with appropriately chosen weights to suppress interference efficiently. While there have been a few other interference-suppressing RAKE receivers proposed recently, our design is based on a different motivation, and we show that our approach significantly outperforms them especially when the number of active users in the cell is not large.

Frequency-selective channels can be converted to a set of flat-fading subchannels by employing orthogonal frequency-division multiplexing (OFDM). Conventional differential encoding on each subchannel, however, suffers from loss of multipath diversity, and a very high peak-to-average power ratio (PAPR), which causes undesirable nonlinear effects. To mitigate these effects, we design a block differential encoding scheme over the subchannels that preserves multipath diversity, and in addition, results in constant modulus transmitted symbols. This property is shown to ensure that the PAPR of the continuous-time transmitted waveform is reduced by a large factor. The maximum-likelihood decoder for the proposed scheme, conditioned on the current and previous received block, is shown to have linear complexity in the number of subcarriers. The constant modulus scheme will yield good bit-error rate performance with full rate only if short blocks are used. However, one may mitigate this problem by relaxing the constant modulus requirement. We show that in a practical OFDM system, we can group the subcarriers into shorter subblocks in a certain manner, and apply the constant modulus technique to each subblock. Thus, we improve diversity at a very low decoder complexity, and at the same time, we introduce an upper bound on the discrete-time PAPR, which, in turn, may lead to appreciable reduction in continuous-time PAPR, depending on the system parameters. Finally, in situations where we can sacrifice rate, additional complex field coding may be used to exploit the multipath diversity provided by channels longer than those the simple scheme can handle.

Frequency-shift keying (FSK) is a popular modulation scheme in power-limited communication links. This paper introduces space-time FSK (ST-FSK), which does not require any channel state information at the transmitter and the receiver, as in conventional noncoherent FSK. ST-FSK can be viewed as a special unitary ST modulation design. However, ST-FSK has a number of advantages over existing unitary ST modulation designs. ST-FSK is easier to design, and enjoys lower decoding complexity. Furthermore, ST-FSK guarantees full diversity. Finally, ST-FSK can be adopted in the digital as well as in the analog domain, and merges very naturally with frequency-hopping multiple access. As expected, all these advantages come at the cost of a decrease in spectral efficiency.

We construct unitary noncoherent space-time constellations, which can be considered as a concatenation of a training block with an orthogonal design. With a simple construction, our constellations are easy to design, enjoy full antenna diversity, allow for a simplified maximum-likelihood (ML) detector, and achieve error performance comparable to existing designs that rely on computer search. To exploit the constellation structures and improve coding gains, we further pursue a trellis-coded modulation (TCM) approach. Based on the sequence pairwise error analysis, we identify two simple parameters to quantify the asymptotic error performance, which enables us to compare among different TCM schemes or uncoded alternatives.

A so-termed chip-interleaved block-spread (CIBS) code division multiple access (CDMA) system has been introduced for cellular applications in the presence of frequency selective multipath channels. In both uplink and downlink operation, CIBS-CDMA achieves multiuser-interference (MUI) free reception within each cell. This paper focuses on the cellular downlink configuration and compares CIBS-CDMA against the conventional direct-sequence (DS) CDMA system, which relies on a chip equalizer to restore code orthogonality and, subsequently, suppresses MUI by despreading. We provide a unifying framework for both systems and investigate their performance in the presence of intercell interference and soft-handoff operation. Extensive comparisons from load, performance, complexity, and flexibility perspectives illustrate the merits, along with the disadvantages, of CIBS-CDMA over DS-CDMA, and reveal its potential for future wireless systems.

We propose a minimum mean-square error (MMSE) time-varying (TV) finite impulse response (FIR) decision feedback equalizer (DFE) for doubly-selective (time- and frequency-selective) channels. We use the basis expansion model (BEM) to approximate the doubly-selective channel and to design the TV FIR DFE. This allows us to turn a large design problem into an equivalent small design problem, containing only the BEM coefficients of the doubly-selective channel and the BEM coefficients of the TV FIR feedforward and feedback equalization filters. Through computer simulations we show that the performance of the proposed TV FIR DFE approaches the performance of the block DF equalizer, while the equalization and the design complexity are generally much lower.

The combination of space-time block coding (STBC) and direct-sequence code division multiple access (DS-CDMA) has the potential to increase the performance of multiple users in a cellular environment. However, if not carefully designed, the resulting communication scheme suffers from increased multi-user interference (MUI), which dramatically deteriorates the performance. To tackle this MUI problem in the downlink, we combine two specific CDMA and STBC techniques, namely single-carrier block-spread (SCBS) CDMA and time-reversal (TR) STBC. The resulting transceiver allows for deterministic maximum likelihood (ML) user separation through low-complexity code-matched filtering as well as deterministic transmit stream separation through linear processing. These properties guarantee maximum diversity gains of N/sub T/N/sub R/(L+1) for every user in the system, irrespective of the system load, where N/sub T/ is the number of transmit antennas, N/sub R/ the number of receive antennas and L the order of the underlying multipath channels. Moreover, it turns out that a low-complexity linear receiver based on frequency-domain equalization comes close to extracting the full diversity in reduced as well as full load settings.

In this paper, we address the general problem of identifying convolutive channels when several training sequences are inserted in the transmitted data symbols stream. We analyze the general situation where the training sequences differ from each other. We consider quasi-static channels (i.e. the sampling period is several orders of magnitude below the coherence time of the channel). There are no requirements on the length of the training sequence and all the received symbols that contain contributions from the training symbols are used for the identification. We first propose an iterative method that quickly converges to the maximum likelihood (ML) channel estimate. We also derive a simple closed form expression that approximates the ML channel estimate.

Multiple antennas at the receiver and transmitter are often used to combat the effects of fading in wireless communication systems. However, implementing multiple antennas at mobile stations is impractical for most wireless applications due to the limited size of the mobile unit. We emulate spatial diversity using mobile relay stations, which cooperate by retransmitting the information received from a mobile station to a destination station. We propose an Alamouti based cooperative system with two relay stations and we provide an approximate formula for the average symbol error probability of this system in a Rayleigh fading environment.

In this paper, we propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly-selective (time- and frequency-selective) channels. We use the basis expansion model (BEM) to approximate the doubly-selective channel and to design the TV FIR equalizer. This structure allows us to turn a large design problem into an equivalent small design problem, containing only the BEM coefficients of both the doubly-selective channel and the TV FIR equalizer. Focus is on the minimum mean-square error (MMSE) solution, but the zero-forcing (ZF) solution is also discussed. Comparisons with the linear block equalizer (LBE) are made. Through computer simulations we show that the performance of the MMSE TV FIR equalizer approaches that of the MMSE LBE, while the design as well as the implementation complexity are much lower.

In this paper we propose a zero forcing (ZF) time-varying (TV) finite-impulse response (FIR) equalizer for doubly-selective (time- and frequency-selective) channels. We use the basis expansion model (BEM) to approximate the doubly-selective channel and to design the TV FIR equalizer. This allows us to turn a large TV problem into an equivalent small-time invariant (TIV) problem, containing only the BEM coefficients of the doubly-selective channel and the TV FIR equalizer. It is shown that a ZF TV FIR equalizer only exists if there is more than one receive antenna. The ZF TV FIR equalizer approach we propose here unifies and extends many previously proposed serial equalization approaches. Through computer simulations we show that the performance of the ZF TV FIR equalizer approaches the one of the ZF block equalizer, while the equalization as well as the design complexity is much lower.

This paper focuses on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, where the MIMO channel order is larger than the length of the cyclic prefix (CP). By swapping the filtering operations of the MIMO channel and the fast Fourier transform (FFT), it is shown that each tone of a MIMO OFDM system can be viewed as a MIMO single-carrier (SC) system. As a result, the existing equalization approach for MIMO SC systems can be applied to each tone of MIMO OFDM systems. This so-called per-tone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative for recently developed time-domain equalization (TEQ) approach for MIMO OFDM systems. The main difference between the PTEQ and TEQ approach is that a per-tone equalizer equalizes a single tone on the symbol level (low rate), whereas a time-domain equalizer equalizes all tones together on the sample level (high rate). Next to some other advantages, this means that a per-tone equalizer can much more easily be designed in practice than a time-domain equalizer. This is illustrated in the second part, where we adapt an existing semi-blind equalization algorithm for a generalized space-time block coded (GSTBC) MIMO SC system to a semi-blind per-tone equalization algorithm for a GSTBC MIMO OFDM system.

We design constellations for non-coherent space-time systems. Given in algebraic form, the constructed constellations are easy to design, enjoy full diversity, allow for a simplified maximum likelihood detector, and achieve performance comparable to existing designs that rely on computer search.

The combination of space-time block coding (STBC) and direct-sequence code-division multiple access (DS-CDMA) has the potential to increase the performance of multiple users in a cellular network. However, if not carefully designed, the resulting transmission scheme suffers from increased multiuser interference (MUI), which dramatically deteriorates the performance. To tackle this MUI problem in the downlink, we combine two specific DS-CDMA and STBC techniques, namely single-carrier block transmission (SCBT) DS-CDMA and time-reversal STBC. The resulting transmission scheme allows for deterministic maximum-likelihood (ML) user separation through low-complexity code-matched filtering, as well as deterministic ML transmit stream separation through linear processing. Moreover, it can achieve maximum diversity gains of N/sub T/N/sub R/(L+1) for every user in the system, irrespective of the system load, where N/sub T/ is the number of transmit antennas, N/sub R/ the number of receive antennas, and L the order of the underlying multipath channels. In addition, it turns out that a low-complexity linear receiver based on frequency-domain equalization comes close to extracting the full diversity in reduced, as well as full load settings. In this perspective, we also develop two (recursive) least squares methods for direct equalizer design. Simulation results demonstrate the outstanding performance of the proposed transceiver compared to competing alternatives.

Per-tone equalization has recently been proposed as an alternative receiver structure for discrete multitone-based systems improving upon the well-known structure based on time-domain equalization. Fast initialization of all the equalizer coefficients has been identified as an open problem. In this letter, a recursive initialization scheme based on recursive least squares with inverse updating is presented for the per-tone equalizers. Simulation results show convergence with an acceptably small number of training symbols. Complexity calculations are made for per-tone equalization and for the case where tones are grouped. It is demonstrated with an example that in the latter case, initialization complexity becomes sufficiently low and comparable to complexity during data transmission.

Suppression of multiuser interference (MUI) and mitigation of time- and frequency-selective (doubly selective) channel effects constitute major challenges in the design of third-generation wireless mobile systems. Relying on a basis expansion model (BEM) for doubly selective channels, we develop a channel-independent block spreading scheme that preserves mutual orthogonality among single-cell users at the receiver. This alleviates the need for complex multiuser detection, and enables separation of the desired user by a simple code-matched channel-independent block despreading scheme that is maximum-likelihood (ML) optimal under the BEM plus white Gaussian noise assumption on the channel. In addition, each user achieves the maximum delay-Doppler diversity for Gaussian distributed BEM coefficients. Issues like links with existing multiuser transceivers, existence, user efficiency, special cases, backward compatibility with direct-sequence code-division multiple access (DS-CDMA), and error control coding, are briefly discussed.

Single-carrier block transmission (SCBT) DS-CDMA, also known as chip-interleaved block-spread (CIBS) CDMA, is an interesting transmission technique for future broadband cellular systems because it inherits the benign properties of both SCBT and CDMA. By zero padding (ZP) each chip block, the orthogonality of the spreading codes is retained regardless of the underlying multipath channel which allows for deterministic maximum likelihood (ML) user separation employing low-complexity code-matched filtering. In this paper, we focus on downlink single-carrier block transmissions with known symbol padding (KSP) (as opposed to ZP) which pad each chip block with a postfix of known symbols that can be used for training purposes at the receiver. Specifically, we propose three methods for direct equalizer estimation that all exploit the presence of the known symbol postfix but differ in the amount of additional a-priori information they assume to determine the equalizer coefficients. Simulation results demonstrate the outstanding performance of the semi-blind joint CDMP/KSP-trained method, that additionally assumes knowledge of a code division multiplexed pilot (CDMP) and the multiuser code correlation matrix.

We rely on a Basis Expansion Model (BEM) for the channel, to design three Space-Time-Doppler (SID) codecs that enable maximum diversity gains, when block transmissions undergo time-selective fading effects. Within the constraints of each maximum-diversity design, it is also possible to achieve maximum coding gain, at least when the BEM parameters are i.i.d. The theoretical results are corroborated by simulation results and the BEM is validated.

Recently, a so-termed Chip-Interleaved Block-Spread (CIBS) CDMA system has been introduced, which enables Multi-User Interference (MUI) free reception. This transceiver can be used in the uplink as well as in the downlink. In this paper, we focus on the downlink and compare the downlink CIBS-CDMA system employing an MUI-free receiver with the conventional downlink Direct-Sequence (DS) CDMA system employing a chip equalizer receiver. The analysis, which is validated by simulation results, reveals that CIBS-CDMA with an MUI-free receiver has a number of advantages over DS-CDMA with a chip equalizer receiver.

In this paper, we extend space-time block coding techniques, originally proposed for point-to-point communication links, to point-to-multipoint communication links, thereby taking into account the multiple access technique in the design of the transmission scheme. In specific, we propose two per-tone linear space-time chip equalizers for a space-time coded MC-DS-CDMA downlink with linear precoding. Both the training-based and the semi-blind chip equalizer exploit the presence of a continuous code-multiplexed pilot in the transmitted signal but differ in the amount of a-priori information they assume to estimate their coefficients. With Mttransmit antennas at the base-station, Mrreceive antennas at the mobile station and L the order of the multipath channel, they come close to extracting the full diversity of order Mt· Mr· (L + 1) in reduced as well as full load settings.

In downlink CDMA, frequency-selectivity destroys the orthogonality of the user signals and introduces multi-user interference (MUI). A space-time chip equalizer is an attractive tool to restore the orthogonality of the user signals and suppress MUI. Recently, efficient pilot-based methods have been developed to design such a space-time chip equalizer. In this paper, we show how these pilot-based methods can be generalized to space-time coded downlink CDMA. As space-time coded downlink CDMA transmission scheme, we consider the conventional single-antenna downlink CDMA transmission scheme followed by a space-time block code for single-carrier block transmissions that exploits the maximum achievable diversity in a frequency-selective fading channel. Simulation results show improved performance over a pilot-based space-time RAKE-type receiver applied to the space-time coded downlink CDMA transmission schemes that were proposed for the UMTS and IS-2000 W-CDMA standards.

In the downlink of WCDMA systems, multi-path propagation destroys the orthogonality of the user signals and causes multi-user interference (MUI). Chip-level equalization can restore the orthogonality and suppress the MUI. However, adaptive implementations of the chip-level equalizer receiver that can track time-varying multi-path channels are hard to realize in practice for two reasons: loss of spectral efficiency when using a training sequence and loss of performance when using pure blind techniques. We propose new training-based and semi-blind space-time chip-level equalizer receivers for the downlink of WCDMA systems employing long spreading codes and a continuous code-multiplexed pilot. The proposed receivers exploit the presence of common pilot symbols in the so-called Common PIlot CHannel (CPICH) of the Universal Terrestrial Radio Access (UTRA) for 3G systems. Moreover, they can simultaneously track multiple base-station signals, whenever the mobile station enters soft handover mode. For both receivers, we derive a recursive least squares (RLS) algorithm for adaptive processing. The proposed receivers are compared with the conventional space-time RAKE receiver and the ideal space-time chip-level equalizer receiver both in terms of performance and complexity.

Suppression of multiuser interference (MUI) and mitigation of time- and frequency-selective effects constitute major challenges in the design of third-generation wireless mobile systems. Relying on block spreading and judiciously chosen time-frequency guard intervals, we propose a multiuser transceiver that eliminates MUI deterministically and guarantees symbol detectability in the presence of unknown time- and frequency-selective fading. Blind channel estimation is also investigated. Simulation results demonstrate the validity of the theoretical results and show improved performance of the proposed transceiver over a multi-user time-frequency RAKE receiver.

In the downlink of WCDMA systems, multipath propagation destroys the orthogonality of the user signals and causes multi-user interference (MUI). Chip-level equalization can restore the orthogonality and suppress the MUI. However, adaptive implementations of the chip equalizer receiver that can track time-varying multipath channels are hard to realize in practice. In this paper, we propose new training-based and semi-blind space-time chip equalizer receivers for the downlink of WCDMA systems employing long spreading codes and a code-multiplexed pilot. The proposed receivers exploit the presence of common pilot symbols in the so-called Common Pilot Channel (CPICH) of the Universal Terrestrial Radio Access (UTRA) for 3G systems. Moreover, they can simultaneously track multiple base-station signals, whenever the mobile station enters soft handover mode. For both receivers, we derive a Least Squares algorithm for block processing and a Recursive Least Squares algorithm for adaptive processing. The proposed receivers are compared in terms of performance with the conventional space-time RAKE receiver and the ideal fully-trained space-time chip equalizer receiver.

Recently, an alternative receiver structure was presented for discrete multitone (DMT)-based systems. The traditional structure consisting of a (real) time domain equalizer (TEQ) with a (complex) 1-tap frequency domain equalizer (FEQ) per tone is modified into a structure with a (complex) multitap FEQ per tone. The signal-to-noise ratio (SNR) for each individual tone is maximized, hence the term "per tone equalization". Here, we derive an equalization scheme for DMT-based systems in an alternative way. We start from the assumption that the transmission channel to equalize has an infinite impulse response (IIR) or pole-zero model. We conclude that, under certain numerator and denominator conditions, the per tone equalizer is a close approximation of the optimal minimum mean square error (MMSE) equalizer. In case the numerator order condition is not fulfilled, we propose a low-complexity generalization of the per tone equalizer. This generalization is based on a suboptimal MMSE criterion and exploits transmit redundancy introduced by means of pilot and/or unused tones. We evaluate the performance of the new, generalized per tone equalizer in an ADSL context. The principles are applicable to OFDM as well.

In the forward link of WCDMA systems, the multipath propagation channel destroys the orthogonality of the spreading codes and therefore causes multi-user interference (MUI). We propose new training-based and semi-blind space-time chip equalizer receivers for the forward link of WCDMA systems with a continuous code-multiplexed pilot. Both least-squares (LS) algorithms for block processing and recursive least-squares (RLS) algorithms for adaptive processing are derived. The proposed receivers can track fast fading multipath channels and outperform the RAKE receiver with perfect channel knowledge.

In the forward link of WCDMA systems, multipath propagation destroys the orthogonality of the user signals and causes multi-user interference (MUI). Channel equalization can restore the orthogonality and suppress the MUI. However, adaptive implementations of the chip equalizer receiver that can track time-varying multipath channels are hard to realize in practice. In this paper, we propose new training-based and semi-blind space-time chip equalizer receivers for the forward link of WCDMA systems employing long spreading codes and a time-multiplexed pilot. The proposed receivers exploit the presence of user specific pilot symbols in the so-called dedicated physical control channel (DPCCH) of the Universal Terrestrial Radio Access (UTRA). Whereas the DPCCH-trained receiver only assumes knowledge of the desired user's pilot symbols and code sequence in a training-based cost function, the enhanced DPCCH-trained receiver assumes knowledge of each active user's pilot symbols and code sequence in a semi-blind cost function. For both receivers, we derive a least squares algorithm for block processing and a recursive least squares algorithm for adaptive processing. Both receivers can track time-varying multipath channels and outperform the conventional RAKE receiver with perfect channel knowledge. The enhanced DPCCH-trained chip equalizer receiver outperforms the regular DPCCH-trained chip equalizer receiver and comes close to the performance of the ideal fully-trained chip equalizer receiver.

An alternative receiver structure is presented for discrete multitone-based systems. The usual structure consisting of a (real) time-domain equalizer in combination with a (complex) 1-tap frequency-domain equalizer (FEQ) per tone, is modified into a structure with a (complex) multitap FEQ per tone. By solving a minimum mean-square-error problem, the signal-to-noise ratio is maximized for each individual tone. The result is a larger bit rate while complexity during data transmission is kept at the same level. Moreover, the per tone equalization is shown to have a reduced sensitivity to the synchronization delay.

This work focuses on the forward link in a CDMA based multiuser communication system experiencing frequency dependent multipath fading. The mobile handset is assumed to have two antennas, either spatially separated or having diverse polarizations. Previous work on linear equalizers to restore orthogonality of the Walsh-Hadamard channel codes in this scenario led to a comparison of zero-forcing (ZF) equalizers and the RAKE receiver. A chip-rate MMSE equalizer is derived that minimizes the MSE between the synchronous "sum signal" of all the users from a given base station and the equalized chip sequence; this equalizer is followed by correlation with the desired user's spreading code times the base-station's long code. In this MMSE derivation, the sum of chip sequences of all the users is modeled as an i.i.d. random sequence. This leads to a "simple" MMSE equalizer that does not depend on the Walsh-Hadamard spreading codes, or the long code, currently employed at the base station. For further improvement, the "best" equalizer delay is chosen to minimize the MSE. Theoretically, the MMSE equalizer approaches the RAKE receiver at low SNR and the ZF equalizer at high SNR. Simulation results show that the ZF equalizer's average performance is dominated by a very small percentage of "bad channels" with close to common zeroes, while the MMSE equalizer is resistant to this pathological noise gain problem. The end result is that the MMSE's average BER performance is dramatically better than that of both ZF and RAKE (even though only moderately better than ZF for most well behaved channels).

We consider a shift-orthogonal (a shift-orthogonal set of code sequences is used) quasi-synchronous DS-CDMA system based on block spreading in the presence of frequency-selective fading. For such a system, we can develop a simple receiver that eliminates the multi-user interference (MUI) deterministically, without using any channel information, and suppresses the remaining (single-user) intersymbol interference (ISI), using a single-user channel estimation method (training-based or blind) or using a single-user direct approach (training-based or blind). The proposed transceiver is less complex than the previously developed VL-AMOUR transceiver (which has the same properties as the proposed transceiver), while their performances are comparable.