The bistatic Integrated Sensing and Communication (ISAC) is poised to become a key application for next generation communication networks (e.g., B5G/6G), providing simultaneous sensing and communication services with minimal changes to existing network infrastructure and hardware. However, a significant challenge in bistatic cooperative sensing is clock asynchronism, arising from the use of different clocks at far separated transmitters and receivers. This asynchrony leads to Timing Offsets (TOs) and Carrier Frequency Offsets (CFOs), potentially causing sensing ambiguity. Traditional synchronization methods typically rely on static reference links or GNSS-based timing sources, both of which are often unreliable or unavailable in UAVbased bistatic ISAC scenarios. To overcome these limitations, we propose a Time-Varying Offset Estimation (TVOE) framework tailored for clock-asynchronous bistatic ISAC systems, which leverages the geometrically predictable characteristics of the Line-of-Sight (LoS) path to enable robust, infrastructure-free synchronization. The framework treats the LoS delay and the Doppler shift as dynamic observations and models their evolution as a hidden stochastic process. A state-space formulation is developed to jointly estimate TO and CFO via an Extended Kalman Filter (EKF), enabling real-time tracking of clock offsets across successive frames. Furthermore, the estimated offsets are subsequently applied to correct the timing misalignment of all Non-Line-of-Sight (NLoS) components, thereby enhancing the high-resolution target sensing performance. Extensive simulation results demonstrate that the proposed TVOE method improves the estimation accuracy by 60%.

Hybrid beamforming architectures provide a trade-off between beamforming performance, power consumption, and hardware cost, rendering them suitable for 5G millimeter-wave (mmWave) communications. However, the limited number of radio frequency (RF) chains compared to the large number of antenna elements presents challenges for high-resolution direction of arrival (DoA) and direction of departure (DoD) estimation. While methods like compressive sensing (CS) and beamspace processing have been explored, they suffer from random phase errors and a high computational complexity. In this paper, we propose an ESPRIT-based 2-dimensional (2-D) phase noise parameter compensation (PNPC) algorithm for joint DoD and DoA estimation of the dominant multipath components. The algorithm extends the 2-D beamspace shift invariance equations and introduces a new structure, where the phase error vector resides in the nullspace of a combined matrix. This enables the joint estimation of DoDs, DoAs, and phase errors through an iterative procedure. Our simulation results confirm that the proposed 2-D PNPC-DFT-ESPRIT algorithm achieves a performance close to the ideal 2-D DFT-ESPRIT algorithm without phase errors, even in the challenging case of single RF chains on the transmit and the receive sides.

This paper presents a self-supervised learning approach for online beam synthesis using the reference signal received power (RSRP) measurements in mmWave band communications. We propose a sparse structure which can effectively approximate the true antenna space covariance matrix (ASCM) of the mmWave channel with only a few effective paths. The sparse structure is then forced within the latent space of a model-aided autoencoder (MAE), whose encoding part is a neural network (NN) which estimates the parameters of the effective ASCM by the measured RSRPs, while the decoding part is a closed-form model which reconstructs the RSRPs from the estimated effective ASCM. The MAE is trained based on the similarity loss between the measured RSRPs and the reconstructed RSRPs, such that the ground truth channel state information (CSI) is not needed during the training. The predicted effective spatial covariance matrix is then used to compute the optimal communication beam. Simulations show that the proposed scheme can significantly improve the beamforming performance especially in non-line-of-slight (NLOS) channel conditions.

In this paper, we consider a double-RIS (D-RIS)-aided flat-fading MIMO system and propose an interference-free channel training and estimation protocol, where the two single-reflection links and the one double-reflection link are estimated separately. Specifically, by using the proposed training protocol, the signal measurements of a particular reflection link can be extracted interference-free from the measurements of the superposition of the three links. We show that some channels are associated with two different components of the received signal.Exploiting the common channels involved in the single and double reflection links while recasting the received signals as tensors, we formulate the coupled tensor-based least square Khatri–Rao factorization (C-KRAFT) algorithm which is a closed-form solution and an enhanced iterative solution with less restrictions on the identifiability constraints, the coupled-alternating least square (C-ALS) algorithm. The C-KRAFT and C-ALS based channel estimation schemes are used to obtain the channel matrices in both single and double reflection links.We show that the proposed coupled tensor decomposition-based channel estimation schemes offer more accurate channel estimates under less restrictive identifiability constraints compared to competing channel estimation methods. Simulation results are provided showing the effectiveness of the proposedalgorithms.

Estimation of signal parameters via rotational invariant techniques (ESPRIT) based high-resolution parameter estimation algorithms in discrete Fourier transform (DFT) beamspace are efficient gridless schemes for hybrid beamforming architectures. Since the number of coherent DFT measurements is equal to the number of radio frequency (RF) chains that is much smaller than the number of antennas, only a small spatial region can be scanned coherently. The number of coherent measurements can be increased by generating virtual RF chains through time-domain-multiplexed (TDM) measurements. However, due to hardware imperfections, random phase jump errors between the TDM measurements degrade the direction of arrival (DoA) estimation accuracy. This paper proposes a new 2-dimensional (2-D) beamspace phase noise parameter compensation (PNPC) algorithm, called 2-D PNPC-DFT-ESPRIT, which jointly estimates the random phase jump errors and the DoAs for uniform rectangular arrays (URAs). The 2-D PNPC-DFT-ESPRIT algorithm modifies the beamspace shift invariance equations for URAs, which consider the contributions of the random phase jump errors and the DoAs. An iterative procedure is developed to estimate both jointly. The simulations show that, even in the presence of random phase jump errors, the 2-D PNPC-DFT-ESPRIT algorithm can achieve a similar performance as 2-D DFT ESPRIT without these phase jump errors.

With the deployment of large-scale antenna arrays, the already limited time-frequency resources are becoming increasingly scarce. In this study, we propose a novel Laplacian Pyramid Channel Completion Network (LPCCNet) designed for channel completion, thereby reducing the demand for time-frequency resources in massive MIMO systems. Compared with existing network models, the proposed LPCCNet, by employing a progressive upsampling architecture, effectively mitigates aliasing effects, suppresses error propagation, and achieves a substantial reduction in computational complexity. The simulation results show that LPCCNet achieves a superior channel completion quality compared to existing methods, particularly in rapidly time-varying scenarios.

We consider the problem of max-min beamforming (MMB) for cell-free massive multi-input multi-output (MIMO) systems, where the objective is to maximize the minimum achievable rate among all users. Existing MMB methods are mainly based on deterministic optimization methods, which are computationally inefficient when the problem size grows large. To address this issue, we, in this paper, propose a randomized alternating direction method of multiplier (ADMM) algorithm for large-scale MMB problems. We first propose a novel formulation that transforms the highly challenging feasibility-checking problem into a linearly constrained optimization problem. An efficient randomized ADMM is then developed for solving the linearly constrained problem. Unlike standard ADMM, randomized ADMM only needs to solve a small number of subproblems at each iteration to ensure convergence, thus achieving a substantial complexity reduction. Our theoretical analysis reveals that the proposed algorithm exhibits an$O(1/\bar {t})$convergence rate ($\bar {t}$represents the number of iterations), which is on the same order as its deterministic counterpart. Numerical results show that the proposed algorithm offers a significant complexity advantage over existing methods in solving the MMB problem.

Tensor completion has attracted increasing attention in signal processing, computer vision, and biomedical engineering. By using nuclear norm minimization, a tensor completion problem can be converted into a convex program and enjoys properties gained from matrix completion. The low rank property has been widely used for tensor/matrix completion. However, the prior subspace information can also be utilized, which has been ignored and does not exhibit its full power in the existing formulation. In this paper, we propose a new framework leveraging tensor subspace prior for the sum of nuclear norm (SNN) minimization, which supports a range of tensor decompositions. By using the knowledge of the self-prior (SP)/nonself-prior (NSP) and further designing an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM), the performance of tensor completion can be enhanced. The superiority of the proposed method is verified by extensive numerical experiments.

This paper presents a high-resolution coupled rank-(Lr,Lr,1) block-term decomposition-based near-field localization scheme for multi-static MIMO radar systems. The proposed COBRAS (COupled Block-term decomposition for multi-static RAdar Systems) algorithm uses the exact wavefront model to estimate the target location parameters in 3D space and can be applied to arbitrary array geometries. Compared to the far-field models, the exact near-field wavefront model allows exploiting the distance information for high-accuracy positioning. Moreover, we consider a system with massive antenna arrays, which increases the Fresnel region and expands the range of the near-field assumption. The COBRAS algorithm includes the initial tensor decomposition of the data and further post-processing steps that allow extracting the location parameters. Additionally, we compare the performance of different rank-(Lr,Lr,1) block-term decomposition algorithms and demonstrate how the employment of coupling improves the localization performance compared to the non-coupled solutions.

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. The widely used subspace-based methods provide super-resolution parameter estimation at a low computational cost. However, they require an accurate array calibration, which is difficult for large antenna arrays. Sparsity-based methods have been shown to be more robust than subspace-based methods in difficult scenarios, e.g., in the case with a small number of snapshots and/or correlated sources. In this paper, we consider the direction-of-arrival (DOA) estimation in partly calibrated rectangular arrays comprising several calibrated and identical subarrays. We derive a gridless sparse formulation for DOA estimation based on the shift-invariance properties of the array and develop an efficient algorithm in the alternating direction method of multipliers (ADMM) framework. Numerical simulations show the superior error performance of our proposed method compared to subspace-based methods.

In this paper, we develop a near-field beamforming algorithm that is robust against aperture deformations. We derive analytical expressions on the bounds of the elements of the steering vector as a function of the known bounds of the coordinate displacement. We apply these bounds during the optimization procedure to design beamformers that are robust to aperture perturbations. Simulation results show that the proposed robust near-field beamforming algorithm outperforms the available benchmark in the literature.

This paper proposes novel linear precoding algorithms for Multiple-Input Multiple-Output Bit-Interleaved Coded Modulation (MIMO-BICM) systems that maximize the achievable rate subject to power constraints. To overcome the nonlinear and nonconvex nature of the optimization problem, we rewrite the achievable rate in terms of the log-likelihood ratio (LLR) and introduce manifold-based gradient ascent (MGA) precoding and low-complexity non-iterative algorithms. Simulation results show significant gains in achievable rate and block error rate compared to existing techniques. Additionally, we extend our investigation to linear precoding with the constraint that the precoding matrix is selected from the codebook type-I adopted in Fifth-Generation New Radio (5G NR) networks. We propose heuristic algorithms that exploit the Kronecker and Discrete Fourier Transform (DFT) structure of the codebook and consider the singular vector decomposition (SVD) precoder as the optimal reference precoder. The traditional exhaustive search methods require a high complexity, especially for large codebook sizes. However, our proposed algorithms apply a combination of direct estimation and a low-dimensional search for deriving the indices, resulting in a reduced number of codebook precoder candidates. Simulation results show that our proposed low-complexity algorithms perform comparably to exhaustive search baselines.

Reconfigurable intelligent surfaces (RISs) are deemed as a potential technique for the future of the Internet of Things (IoT) due to their capability of smartly reconfiguring the wireless propagation environment using a large number of low-cost passive elements. To benefit from RIS technology, the problem of RIS-assisted channel state information (CSI) acquisition needs to be carefully considered. Existing channel estimation methods usually ignored the different channel characteristics of direct channel and reflected channels. In fact, the reflected channel can be smartly configured by adjusting the phase shifts of the RIS, which is different from the direct channel due to the different path loss exponents between the transmitter and receiver. Therefore, it is necessary to further develop a RIS-assisted channel estimation to determine the direct and reflected channels, respectively. In this paper, we study a RIS-assisted channel estimation that jointly exploits the properties of the direct and the reflected channel to provide more accurate CSI. The direct channel is estimated using weighted$\ell_1$norm minimization, while the reflected channel is modeled based upon the robust$\ell_{1,\tau}$norm minimization to sequentially estimate the channel parameters. Moreover, by combining the gradient descent and the alternating minimization method, a flexible and fast algorithm is developed to provide a feasible solution. Simulation results demonstrate that an RIS-aided MIMO system significantly reduces the active antennas/RF chains compared to other benchmark schemes.

Probability mass function (PMF) estimation using a low-rank model for the PMF tensor has gained increased popularity in recent years. However, its performance evaluation relied mostly on empirical testing. In this work, we derive theoretical bounds on the attainable performance under this model assumption. We begin by deriving the constrained Cramér-Rao Bound (CCRB) on the low-rank decomposition parameters, and then extend the CCRB to bounds on the mean square error in the resulting estimates of the PMF tensor’s elements, as well as on the mean Kullback-Leibler divergence (KLD) between the estimated and true PMFs. The asymptotic tightness of these bounds is demonstrated by comparing them to the performance of the Maximum Likelihood estimate in a small-scale simulation example.

In this paper, we present a precoder design for multi-user multiple-input multiple-output (MU-MIMO) broadcast systems with rate splitting at the transmitter. The proposed scheme applies to both underloaded and overloaded communication systems and supports the transmission of multiple common and private streams. We show how the generalized singular value (GSVD) and multilinear generalized singular value (ML-GSVD) decompositions can be used to define the number of common and private streams and adjust the message split. Additionally, we present transmit precoding and receive combining designs that allow the simultaneous transmission of common and private streams but do not require successive interference cancellation (SIC) at the receivers and can be used in cases where the total number of streams does not exceed the number of transmit antennas.

In this paper, we present an analytical proof of equivalence of the signal processing in the reduced aperture element space and in beamspace produced by the combination of multiple adjacent DFT beams with a subsequent constraining of the resulting magnitudes. This link finds applications in millimeter wave (mmWave) communications and radars that are typically equipped with a small number of RF chains and employ hybrid beamforming with analog phase shifters. This result unifies the transceiver designs, reduces complexity, and proves the applicability of state-of-the-art beamspace-based methods. It has a special implication for channel estimation at the initial stage when terminals acquire coarse estimates of the Sectors-of-Interest (SoIs). We show that the constrained groups of beams are equivalent to DFT beamformers of a smaller size aperture and present a closed-form expression of the corresponding effective aperture length as a function of the number of beams. We also derive an approximation of this expression to find the indices of the active array elements in a closed form. Finally, we verify this theory and analyze the accuracy of the proposed approximation using numerical simulations.

The application of artificial intelligence and machine learning (AI/ML) into the wireless physical layer is under discussion at 3GPP. Channel state information (CSI) prediction is among the sub use cases being studied. In this work, we propose an AI/ML CSI predictor that aims to compensate the scheduling delays at the base station. The AI/ML CSI predictor operates at the user equipment side and generates the channel reporting based on its prediction. Our AI/ML CSI predictor is designed for the intended prediction time, e.g., 5 ms, by collecting a few past measurements at the input. Our architecture is flexible regarding the number of physical resource blocks and can be used by all user equipments within the cell. Our results show that the proposed AI/ML CSI predictor has the 90 % normalized squared error performance around −13 dB and less than 1.4 % of the predicted eigenvectors have a squared generalized cosine similarity below 0.9, which is much better than zero order hold.

The efficient estimation of an approximate model order is essential for applications with multidimensional data if the observed low-rank data is corrupted by additive noise. Certain signal processing applications such as biomedical studies, where the data are collected simultaneously through heterogeneous sensors, share some common features, i.e., coupled factors among multiple tensors. The exploitation of this coupling can lead to a better model order estimation, especially in case of low SNRs. In this paper, we extend the rank estimation techniques, designed for a single tensor, to noise-corrupted coupled low-rank tensors that share one of their factor matrices. To this end, we consider the joint effect of the global eigenvalues (calculated from the coupled HOSVD) and exploit the exponential behavior of the resulting coupled global eigenvalues. We show that the proposed method outperforms the classical criteria and can be successfully applied to EEG, MEG Magnetometer, and Gradiometer measurements. Our real data simulation results show that the estimated rank is highly reliable in terms of dominant components extraction.

Reconfigurable intelligent surfaces (RISs) have been proposed recently as new technology to tune the wireless propagation channels in real-time. However, most of the current works assume single-RIS (S-RIS)-aided systems, which can be limited in some application scenarios where a transmitter might need a multi-RIS-aided channel to communicate with a receiver. In this paper, we consider a double-RIS (D-RIS)-aided MIMO system and propose an alternating least-squares-based channel estimation method by exploiting the Tucker2 tensor structure of the received signals. Using the proposed method, the cascaded MIMO channel parts can be estimated separately, up to trivial scaling factors. Compared with the S-RIS systems, we show that if the RIS elements of an S-RIS system are distributed carefully between the two RISs in a D-RIS system, the training overhead can be reduced and the estimation accuracy can also be increased. Therefore, D-RIS systems can be seen as an appealing approach to further increase the coverage, capacity, and efficiency of future wireless networks compared to S-RIS systems.

Machine learning (ML) applications for wireless communications have gained momentum on the standardization discussions for 5G advanced and beyond. One of the biggest challenges for real world ML deployment is the need for labeled signals and big measurement campaigns. To overcome those problems, we propose the use of untrained neural networks (UNNs) for MIMO channel recreation/estimation and low over-head reporting. The UNNs learn the propagation environment by fitting a few channel measurements and we exploit their learned prior to provide higher channel estimation gains. Moreover, we present a UNN for simultaneous channel recreation for multiple users, or multiple user equipment (UE) positions, in which we have a trade-off between the estimated channel gain and the number of parameters. Our results show that transfer learning techniques are effective in accessing the learned prior on the environment structure as they provide higher channel gain for neighbouring users. Moreover, the proposed UNN channel state information (CSI) estimators are under-parameterized and can further enable low-overhead CSI reporting.

Channel charting (CC) is an emerging machine learning method for learning a lower-dimensional representation of channel state information (CSI) in multi-antenna systems while simultaneously preserving spatial relations between CSI samples. The driving objective of CC is to learn these representations or channel charts in a fully unsupervised manner, i.e., without the need for having access to explicit geographical information. Based on recent findings in deep manifold learning, this paper addresses the problem of CC via the "not-too-deep" (N2D) approach for deep manifold learning. According to the proposed approach, an embedding of the global channel chart is first learned using a deep neural network (DNN)-based autoencoder (AE), and this embedding is subsequently searched for the underlying manifold using shallow clustering methods. In this way we are able to counter the problem of collapsing extremities - a well known deficiency of channel charting methods, which in previous research efforts could only be mitigated by introducing side-information in form of distance constraints. To further exploit the ever-increasing spatio-temporal CSI resolution in modern multi-antenna systems, we propose to augment the employed AE with convolutional neural network (CNN) input layers. The resulting convolutional autoencoder (CAE) architecture is able to automatically extract sparsely distributed spatio-temporal features from beamspace domain CSI, yielding a reduced computational complexity of the resulting model.

In this work, we propose a two-stage tensor-based receiver for joint channel, phase-noise (PN), and data estimation in MIMO-OFDM systems. First, we cast the received signal at the pilot subcarriers as a third-order PARAFAC model. Based on this model, we propose a closed-form algorithm based on the LS-KRF (Least Squares - Khatri-Rao Factorization) that estimates the channel gains and the phase-noise terms through multiple rank-one factorizations. From the estimated channel, the second stage of the receiver consists of data estimation based on a ZF (Zero-Forcing) receiver that capitalizes on the tensor structure of the received signal at the data subcarriers via a Selective Kronecker Product (SKP) approach. Our numerical simulations show that the proposed receiver achieves an improved performance compared to the state-of-art receivers.

We consider the channel estimation problem in point-to-point reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) MIMO systems. By exploiting the low-rank nature of mmWave channels in the angular domains, we propose a non-iterative Two-stage RIS-aided Channel Estimation (TRICE) framework, where every stage is formulated as a multidimensional direction-of-arrival (DOA) estimation problem. As a result, our TRICE framework is very general in the sense that any efficient multidimensional DOA estimation solution can be readily used in every stage to estimate the associated channel parameters. Numerical results show that the TRICE framework has a lower training overhead and a lower computational complexity, as compared to benchmark solutions.

Conventional canonical polyadic decomposition (CPD) approach for tensor-based sparse array direction-of-arrival (DOA) estimation typically partitions the coarray statistics to generate a full-rank coarray tensor for decomposition. However, such an operation ignores the spatial relevance among the partitioned coarray statistics. In this letter, we propose a coupled coarray tensor CPD-based two-dimensional DOA estimation method for a specially designed coprime L-shaped array. In particular, a shifting coarray concatenation approach is developed to factorize the partitioned fourth-order coarray statistics into multiple coupled coarray tensors. To make full use of the inherent spatial relevance among these coarray tensors, a coupled coarray tensor CPD approach is proposed to jointly decompose them for high-accuracy DOA estimation in a closed-form manner. According to the uniqueness condition analysis on the coupled coarray tensor CPD, an increased number of degrees-of-freedom for the proposed method is guaranteed.

Channel estimation in hybrid analog-digital massive MIMO systems is a challenging problem due to the high channel dimension, low signal-to-noise ratio before beamforming, and reduced number of radio-frequency chains. Compressed sensing based algorithms have been adopted to address these challenges by leveraging the sparse nature of millimeter-wave MIMO channels. In compressed sensing-based methods, the training vectors should be designed carefully to guarantee recoverability. Although using random vectors has an overwhelming recoverability guarantee, it has been recently shown that an optimized update, which could be obtained so that the mutual coherence of the resulting sensing matrix is minimized, can improve the recoverability guarantee. In this paper, we propose an openloop hybrid analog-digital beam-training framework, where a given sensing matrix is decomposed into analog and digital beamformers. The given sensing matrix can be designed efficiently offline to reduce computational complexity. Simulation results show that the proposed training method achieves a lower mutual coherence and an improved channel estimation performance than the other benchmark methods.

In this paper, we propose a new Multilinear Generalized Singular Value Decomposition (ML-GSVD) which allows to jointly factorize a set of matrices with one common dimension. The ML-GSVD is an extension of the Generalized Singular Value Decomposition (GSVD) for more than two matrices. In comparison with other approaches that extend the GSVD, the proposed tensor decomposition preserves the essential properties of the original GSVD, such as orthogonality of the second mode factor matrices. In this work, we introduce two algorithms to compute the ML-GSVD. In addition, we present an application of the ML-GSVD to compute the beamforming matrices for the multi-user MIMO downlink channel with more than two users in wireless communications.

To achieve a reliable communication with short data blocks, we propose a novel decoding strategy for Kronecker-structured constant modulus signals that provides low bit error ratios (BERs) especially in the low energy per bit to noise power spectral density ratio (Eb/No). The encoder exploits the fact that any M-PSK constellation can be factorized as Kronecker products of lower or equal order PSK constellation sets. A construction of two types of schemes is first derived. For such Kronecker-structured schemes, a conceptually simple decoding algorithm is proposed, referred to as Kronecker-RoD (rank-one detector). The decoder is based on a rank-one approximation of the “tensorized” received data block, has a built-in noise rejection capability and a smaller implementation complexity than state-of-the-art detectors. Compared with convolutional codes with hard and soft Viterbi decoding, Kronecker-RoD outperforms the latter in BER performance at same spectral efficiency.

Channel state information (CSI) estimation in hybrid analog-digital (HAD) millimeter-wave (mmWave) massive MIMO systems is a challenging problem due to the high channel dimension and reduced number of radio-frequency chains. However, exploiting the channel sparsity, several methods have been proposed leveraging the compressed sensing (CS) tools. Most of the prior works consider an approximate CS formulation by assuming that the channel parameters lie perfectly on a finite grid neglecting the grid mismatch effect. To resolve this issue, we propose a gridless CS approach that exploits the antenna array geometry. The proposed algorithm is based on an alternating optimization technique and is guaranteed to converge to a local minimum. Simulation results are provided to evaluate the effectiveness of the proposed algorithm.

In this paper, we develop simultaneous detection techniques of signals from multiple users for uplink multi-user MIMO (UL MU-MIMO) systems. Conventional detectors do not take the detection delay into account. Two parallelizing access methods are proposed for UL MU-MIMO systems. The multiple uplink users can be detected in parallel after the parallelizing process. Moreover, the multiple uplink users can be scheduled on the same radio frequency resource as if all the other users did not exist. Therefore, the proposed detection methods can scale up with the system dimensions by keeping the bit error rate (BER) and the detection delay at an acceptable level. Simulation results show that the proposed detection methods via parallel access achieve considerable BER gains with much less detection delay as compared to their conventional counterparts.

The PARAFAC2 decomposition has attracted growing research interest. To compute it, the direct fitting (DF) algorithm is usually employed. In this contribution, we propose to incorporate semi-algebraic approaches for the computation of PARAFAC in the DF algorithm and explore how it should be adapted to largely exploit the resulting diversity in the estimates of factor matrices to enhance the robustness and efficiency. Three versions have been tailored and recommended for different parameter settings according to, e.g., the number of components or tensor dimensions. Extensive numerical simulations have been conducted with both synthetic and measured biomedical as well as wine data to validate the improved performance of the proposed DF algorithms. In addition, it has been shown that applying the geometric search on top of the proposed DF algorithms further boosts their performance.

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

Tensor decompositions are regarded as a powerful tool for multidimensional signal processing. In this contribution, we focus on the well-known Canonical Polyadic (CP) decomposition and present a first-order perturbation analysis of the SEmi-algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalization with Generalized Unfoldings (SECSI-GU), which is advantageous for tensors of an order higher than three. Numerical results indicate that the analytical relative Mean Square Factor Error (rMSFE) of the estimated factor matrices resulting from each generalized unfolding considered in SECSI -GU matches the empirical rMSFE very well. As SECSI -GU considers all possible partitionings of the tensor modes resulting in a large number of candidate factor matrix estimates, an exhaustive search-based criterion to select the final factor matrix estimates leads to a prohibitive computational complexity. The accurate performance prediction achieved by the first-order perturbation analysis conducted in this paper will significantly facilitate the selection of the final factor matrix estimates in an efficient manner and will therefore contribute to a low-complexity enhancement of SECSI-GU.

Tensor contraction is a multilinear algebra operator that defines an inner product between two tensors with compatible dimensions. In this work, we show that the MIMO-OFDM (Multiple-Input Multiple-Output - Orthogonal Frequency Division Multiplexing) received signal can be modeled by means of the tensor contraction operator. This tensor model is obtained without requiring additional spreading and provides a new, compact, and flexible formulation of a MIMO-OFDM system. Moreover, exploiting it at the receiver side facilitates the design of several types of receivers based on iterative LS (Least Squares) or recursive LS. We compare the proposed iterative and recursive LS based receivers with and without enumeration and show their advantages over the traditional ZF -FFT (Zero Forcing - Fast Fourier Transform) receiver for MIMO OFDM. This structured tensor model also opens new research directions. Moreover, our generalized tensor contraction formulation can be extended to different multi-carrier MIMO systems.

In its basic, fully blind form, Independent Component Analysis (ICA) does not rely on a particular statistical model of the sources, but only on their mutual statistical independence, and therefore does not admit a Maximum Likelihood (ML) estimation framework. In semi-blind scenarios statistical models of the sources are available, enabling ML separation. Quasi-ML (QML) methods operate in the (more realistic) fully-blind scenarios, simply by presuming some hypothesized statistical models, thereby obtaining QML separation. When these models are (or are assumed to be) Gaussian with distinct temporal covariance matrices, the (quasi-)likelihood equations take the form of a “Sequentially Drilled Joint Congruence” (SeDJoCo) transformation problem. In this work we state some mild conditions on the sources' true and presumed covariance matrices, which guarantee consistency of the QML separation when the SeDJoCo solution is asymptotically unique. In addition, we derive a necessary “Mutual Diversity” condition on these matrices for the asymptotic uniqueness of the SeDJoCo solution. Finally, we demonstrate the consistency of QML in various simulation scenarios.

Joint EigenValue Decomposition (JEVD) algorithms are widely used in many application scenarios. These algorithms can be divided into different categories based on the cost function that needs to be minimized. Most of the frequently used algorithms in the literature use indirect least square (LS) criteria as a cost function. In this work, we perform a first order perturbation analysis for the JEVD algorithms based on the indirect LS criterion. We also present closed-form expressions for the eigenvector and eigenvalue matrices. The obtained expressions are asymptotic in the signal-to-noise ratio (SNR). Additionally, we use these results to obtain a statistical analysis, where we only assume that the noise has finite second order moments. The simulation results show that the proposed analytical expressions match well to the empirical results of JEVD algorithms which are based on the LS cost function.

In this paper we develop space-time block codes for unique word - orthogonal frequency division multiplexing (UW-OFDM) systems to fully exploit the diversity gain when the channel state information is not available at the transmitter. To this end, we propose two novel space-time block codes (STBCs) for UW-OFDM systems, namely a frequency domain space-time block code and a time-reversal space-time code (TR-STC). The former one is an extension of the traditional space-frequency block codes (SFBCs) for CP-OFDM systems to UW-OFDM systems while the latter one makes use of the frame structure of the UW-OFDM symbols and has a low complexity decoder. Simulation results show that both of the proposed space-time block codes achieve a significant gain compared to the SFBC based CP-OFDM. Moreover, the frequency domain STBC yields a slightly better performance as compared to the TR-STC but has a higher computational complexity.

Multi-beam mobile satellite systems aim at providing broadband and high speed mobile services over a large area to achieve a high system throughput, where hybrid space-ground beamforming is one of the most promising candidates for ground-based beamforming techniques. It not only reduces the feeder link bandwidth to save spectral resources, but also takes advantages of both the on-ground and on-board processing, exhibiting a good trade-off of the performance and the space/ground complexity. In this paper, we propose an efficient hybrid space-ground precoding technique for multi-beam mobile satellite systems. It consists of coarse on-board beamforming and reduced-rank on-ground beamforming based on the feed selection of the phased array antenna. The advantages of the proposed hybrid precoding are shown as compared to the fully on-ground beamforming as well as the existing solutions.

This paper provides a second-order (SO) analytical performance analysis of the 1-D Standard ESPRIT algorithm. Existing performance analysis frameworks are based on first-order (FO) approximations of the parameter estimation error, which are asymptotic in the effective signal-to-noise ratio (SNR), i.e., they become exact for either high SNRs or a large sample size. However, these FO expressions do not capture the algorithmic behavior in the threshold region at low SNRs or for a small sample size. Yet, such conditions are often encountered in practice. Therefore, we present a closed-form expression for the parameter estimation error of 1-D Standard ESPRIT up to the SO that is valid in a wider effective SNR range. Moreover, we derive an analytical mean square error (MSE) expression, where we assume a zero-mean circularly symmetric complex Gaussian noise distribution. Finally, we use the existing FO MSE expression and the derived SO MSE expression to analytically compute the SNR breakdown threshold of the MSE threshold region. Empirical simulations verify the analytical expressions.

The “Sequentially Drilled” Joint Congruence (SeDJoCo) transformation is a set of matrix transformation equations, which coincide with the Likelihood Equations for semi-blind source separation, when each source is modeled as a zero-mean Gaussian process with a known (and distinct) temporal covariance matrix. Therefore, with such a model a solution of SeDJoCo can lead to the Maximum Likelihood (ML) estimate of the separating matrix, which is asymptotically optimal. However, as we have shown in previous work, multiple solutions of SeDJoCo may exist, and the selection of the optimal solution among these (corresponding to the global maximum of the likelihood function) is therefore of considerable interest. In this paper we further extend our results by proposing a new ML approach for the identification and correction of a sub-optimal solution, assuming sources of unrestricted, general temporal covariance structures. We demonstrate the resulting improvement in simulation with non-stationary sources.

In this paper we study the parameter estimation problem of an OFDM based joint wideband SIMO radar and communication system. The parameters to be estimated are time delays, relative velocities, and angle of arrival (DoA) pairs of radar targets. Due to the wideband assumption the received signal on different subcarriers are incoherent and therefore cannot fully exploit the frequency diversity of the OFDM waveform. In order to estimate the parameters jointly and coherently on different subcarriers, we propose an interpolation based coherent multidimensional parameter estimation framework, where firstly the wideband system model is transformed into an equivalent narrowband system model, and then multidimensional parameter estimation algorithms can be applied. More precisely, a wideband R-D periodogram is introduced as a benchmark algorithm and a high-resolution R-D Wideband Unitary Tensor-ESPRIT algorithm is proposed. Simulation results show that the proposed coherent parameter estimation method significantly outperforms the direct application of multidimensional parameter estimation algorithms to the wideband model.

Future mobile radio systems, like 5G, are setting extremely demanding targets with respect to the number of served users, data rates, and latency etc. Advanced techniques such as massive MIMO and joint cooperation over several distributed radio stations are being developed to achieve these targets. Channel prediction has been deemed to be a potential main enabler for these techniques. Here, we exploit the correlation present in the multi-dimensional massive MIMO channel and apply HOSVD-based techniques to improve the prediction of weak channels by devising a denoising step before the state-of-the-art channel predictor. We show that at low signal-to-noise ratios and prediction horizons of 1 ms, there is a gain of more than 7 dB in prediction performance.

The key task in ESPRIT-based parameter estimation is finding the solution to the shift invariance equation (SIE), which is often an overdetermined, linear system of equations. Additional structure is imposed if the two selection matrices, applied to an estimate of the signal subspace, overlap such that the subspace estimation errors on both sides of the SIE are highly correlated. In this letter, we propose a novel SIE solution for Standard ESPRIT and Unitary ESPRIT based on generalized least squares (GLS), assuming a uniform linear array (ULA) and maximum subarray overlap. GLS directly incorporates the statistics of the subspace estimation error via its covariance matrix, which is found analytically by a first-order perturbation expansion. As the subspace error covariance matrix is not invertible, we introduce a regularization with a clever choice of the regularization parameter. The resulting GLS-based Standard ESPRIT and Unitary ESPRIT algorithms achieve a superior performance over existing ESPRIT-type methods and almost attain the Cramér-Rao bound (CRB).

This paper presents a new perspective of beamforming designs in Coordinated Multi-Point (CoMP) downlink systems that are combined with multicast schemes. The beamformer computation is expressed as a joint matrix transformation that can be regarded as an extension of the "Sequentially Drilled" Joint Congruence (SeDJoCo) decomposition. A solution of the proposed joint matrix transformation is devised that takes into account the elimination of the multiuser interference as well as the maximization of the desired signal components. Therefore, it leads to a very effective semi-algebraic solution of beamforming designs for the multicast CoMP downlink, which is evident in the numerical simulations.

With the increased importance of the CP decomposition (CANDECOMP/PARAFAC decomposition), efficient methods for its calculation are necessary. In this paper we present an extension of the SECSI (SEmi-algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization) that is based on new non-symmetric SMDs (Simultaneous Matrix Diagonalizations). Moreover, two different algorithms to calculate non-symmetric SMDs are presented as examples, the TEDIA (TEnsor DIAgonal-ization) algorithm and the IDIEM-NS (Improved DIagonalization using Equivalent Matrices-Non Symmetric) algorithm. The SECSI-TEDIA framework has an increased computational complexity but often achieves a better performance than the original SECSI framework. On the other hand, the SECSI-IDIEM framework offers a lower computational complexity while sacrificing some performance accuracy.

We propose a subspace-based Widely Linear (WL) blind channel estimation scheme based on the iterative power method for the WL constrained minimum variance Code Division Multiple Access (CDMA) receiver. The novel technique approximates the noise subspace by using a matrix power and the WL processing fully exploits the second-order non-circularity of the signal. Two adaptive recursive least squares algorithms are developed using power iterations, which completely avoid the computationally intensive singular value decomposition. Simulation results show an improved performance of the proposed algorithms in terms of convergence and complexity as compared to their linear counterparts.

Estimating the directions of arrival (DOA) of coexisting circular and strictly second-order (SO) non-circular (NC) signals has recently emerged as an active field of research. In previous work, we have proposed two ESPRIT-type algorithms, i.e., C-NC Standard ESPRIT and C-NC Unitary ESPRIT, for this scenario that improve the estimation accuracy of the conventional schemes and increase the number of resolvable signals. In this paper, we present a first-order performance assessment of these two ESPRIT-type algorithms. Specifically, we derive closed-form mean square error (MSE) expressions that are asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximations become exact for either high SNRs or a large sample size. Apart from a zero mean and finite SO moments, no further assumptions on the noise statistics are required. We show that both algorithms perform identical in the high effective SNR regime. Moreover, the analytical results verify the previously observed property that the presence of strictly non-circular sources improves the estimation accuracy of the circular signals.

Direction of arrival (DOA) estimation via sparse signal recovery (SSR) has recently attracted a considerable research interest due to its various advantages over the conventional DOA estimation methods. Yet, the performance of the SSR-based algorithms can be further enhanced by exploiting the structure of strictly non-circular (NC) signals. In this paper, we present a novel strategy to take the NC signal structure into account for the SSR, which results in a two-dimensional SSR problem. Thereby, the known benefits associated with NC sources can be achieved. Moreover, we address the 2-D off-grid problem by proposing a low-complexity procedure that estimates the sources' grid offset from the closest neighboring grid points. For a single off-grid source, we show analytically that the 2-D offset estimation problem is separable, allowing to perform the offset estimation in both dimensions independently. We also propose a numerical procedure for the joint estimation of the grid offsets of two closely-spaced sources. The effectiveness of the proposed methods is demonstrated via simulations.

In the context of Maximum Likelihood (ML) source separation in a semi-blind scenario, where the spectra of the sources are known and distinct, the likelihood equations amount to a set of matrix decompositions (known as the "Sequentially Drilled" Joint Congruence Transformation (SeDJoCo)). However, quite often multiple solutions of SeDJoCo exist, only one of which is the optimal solution, corresponding to the global maximum. In this paper we characterize the different solutions and propose a procedure for detecting whether a given solution is sub-optimal. Moreover, for such sub-optimal solutions we propose a procedure for re-initializing an iterative solver so as to converge to the optimal solution. Using simulation, we present the empirical probability to encounter a sub-optimal solution (by a given iterative algorithm), as well as the resulting separation improvement when applying our proposed re-initialization approach in such cases.

In this paper we study the hybrid precoding design problem for a frequency selective massive MIMO channel, e.g., the millimeter wave (mmWave) massive MIMO channel. In contrast to a traditional MIMO system, a hybrid analog-digital MIMO scheme is preferred for massive MIMO systems due to the high cost and power consumption of the radio frequency (RF) chains. The RF analog precoding is implemented using only phase shift networks, which impose constant modulus constraints on the RF precoding and decoding matrices. Moreover, there is just one common equivalent RF beamforming matrix for all subcarriers. The resulting sum rate maximization problem is non-convex and, therefore we resort to suboptimal solutions. Two methods are introduced, namely, the higher order SVD (HOSVD) based design and the sequential low rank unimodular approximation based design. The former approach exploits the truncated HOSVD of the equivalent channel while the latter approach approximates optimal unconstrained solutions by low rank unimodular approximations. Simulation results show that when the mmWave channel model is used, both approaches outperform the extension of the state of the art compressed sensing based algorithm to the multi-carrier case.

For future 5G systems significant performance benefits are expected from massive MIMO, especially in combination with tight inter-cell cooperation including joint-transmission using cooperative multi-point transmission. Most massive MIMO evaluations concentrate on the base station side with the goal to achieve high spectral efficiency by MU-MIMO or large coverage by strong beamforming gains. Especially for the, here interesting, below 6 GHz RF-bands user equipment (UE) sided analysis is typically limited to four or mostly eight antenna elements per UE, which can be justified by the limited space to place more antenna elements as well as the related UE complexity. At the same time, there would be many benefits from UE-sided beamforming, ranging from improved channel estimation and prediction accuracy, effective interference suppression up to coverage and spectral efficiency gains on the system level. In our previous work, we have already proposed virtual beamforming for channel estimation and prediction, while here we extend the concept to user data transmission over virtually generated beams. Virtual beamforming directly applied to user data can be very inefficient, a challenge we overcome by parallel transmission over a set of coded virtual beams.

A next generation optical wireless communications standard is currently established, denoted as IEEE 802.15.7r1, targeting data rates between 1 Mbit/s and 10 Gbit/s. Selecting an appropriate transmission scheme is one of the critical tasks. Following this issue, this paper gives a review on PAM-FDE in VLC. Based on PAM-FDE laboratory measurements, we demonstrate the need to include highpass filtering into the propagation model. In this paper, numerical analyses investigate the impact of the resulting baseline wander on the performance. We include a multi-level 5S6S coding technique in order to prepare PAM-FDE for practice. Finally, research topics are summarized.

In this contribution we propose two new designs of transmit and receive processing for multi-user multiple-input-multiple-output (MIMO) downlink systems that employ filter bank based multicarrier with offset quadrature amplitude modulation (FBMC/OQAM). Our goal is to overcome the limits on the channel frequency selectivity and/or the allowed number of receive antennas per user terminal that are imposed on the state-of-the-art solutions. In the first method the design of precoders and equalizers is iterative and minimum mean square error (MMSE) based. The second is a closed-form design based on the signal-to-leakage ratio (SLR). Via numerical simulations we evaluate the performance of both methods and demonstrate their superiority over two other approaches in the literature.

This paper addresses the distributed beamforming problem, where widely-linear (WL) processing is employed at both the relays and the receiver to take advantage of strictly second-order (SO) noncircular source signals. We consider a single-antenna communication pair in a relay network, which suffers from strong interference. Assuming perfect channel state information (CSI), we design two algorithms based on the maximization of the signal-to-interference-plus-noise ratio (SINR) under a total relay power constraint. While the first algorithm jointly optimizes the weights at the relays and the receiver using semidefinite relaxation (SDR), the second algorithm performs a separate optimization in closed-form, requiring a substantially lower cost, but yielding almost the same performance. We show through simulations that the respective performance improvements associated with the WL processing at the relays and the receiver accumulate such that significant gains can be achieved compared to linear processing. Also, the complexity of the two algorithms is analyzed.

Recently, ESPRIT-based parameter estimation algorithms have been developed to exploit the structure of signals from strictly second-order (SO) non-circular (NC) sources. They achieve a higher estimation accuracy and can resolve up to twice as many sources. However, these NC methods assume that all the received signals are strictly non-circular. In this paper, we present the C-NC Standard ESPRIT and the C-NC Unitary ESPRIT algorithms designed for the more practical scenario of a received mixture of circular and strictly non-circular signals. Assuming that the number of circular and strictly non-circular signals is known, the two proposed methods yield closed-form estimates and C-NC Unitary ESPRIT also enables an entirely real-valued implementation. As a main result, it is shown that the estimation accuracy of the presented algorithms improves with an increasing number of strictly non-circular signals among a fixed number of sources. Thereby, not only the estimation accuracy of the strictly non-circular signals themselves is improved, but also the estimation accuracy of the circular signals. These results are validated by simulations.

In this paper we study the achievable rate region of an FBMC based two-way decode-and-forward relaying system. Unlike a CPOFDM system, the FBMC based systems experience inter-carrier interference and inter-symbol interference especially in a highly frequency selective channel. To calculate the resulting rate region, we have to solve a joint optimization of the per-subcarrier multitap filters at the relay as well as at the users, which is nonconvex. Therefore, we resort to a two-step approach. First, we design closed-form solutions for the per-subcarrier pre-equalizers and equalizers at all nodes. Then we derive an optimal power allocation scheme to maximize the achievable rate. Simulation results show that the achievable sum rate increases as the number of taps used for pre-equalization and equalization at the subcarriers increases.

This paper investigates the application of filter bank multicarrier modulation based on the OQAM (FBMC/OQAM) to multiple-input-multiple-output (MIMO) systems. Existing solutions guarantee satisfactory performance when the streams multiplexed on each subcarrier (S) and the number of transmit (NT) and receive (NR) antennas are related as S = min (NT, NR). When ST, NR), the techniques presented in previous works either exhibit an error floor or perform much worse than orthogonal frequency division multiplexing (OFDM). To make progress towards the combination of FBMC/OQAM with MIMO we propose a two-step approach and a coordinated beamforming algorithm to design the transmit and the receive processing. Numerical results show that the two-step method provides similar bit error rate (BER) as OFDM when S + 1 = NT= NR. Resorting to the coordinated beamforming solution, which is based on an iterative method, the application of FBMC/OQAM is extended to the general case ST, NR). Hence, the techniques presented in this paper demonstrate that FBMC/OQAM can achieve practically the same BER as OFDM with an increased spectral efficiency and a significantly decreased out-of-band radiation, which is an important advantage for non-contiguous spectrum allocations.

We propose a novel joint channel estimator for a relaying MIMO communication system. Considering a three-hop relaying protocol, our combined alternating least squares (Comb-ALS) algorithm obtains cooperative diversity by fully exploiting the tensor algebraic structures of the available cooperative MIMO links. This is achieved by coupling the tensor data for the different relay-assisted links to iteratively estimate the channel matrices. Simulation results corroborate the effectiveness of the proposed tensor-based joint channel estimator in comparison with a sequential tensor-based method and a sequential LS estimator.

Energy efficient beamforming is studied for a MIMO two-way non-regenerative relaying system with multi-antenna users and a multi-antenna relay. The resulting optimization problem is non-convex. A Dinkelbach based alternating maximization (DAM) method is proposed to achieve an iterative design of the relay amplification matrix and the beamforming vectors at the users.

Recently, the 2q-MUSIC (q ≥ 2) direction finding algorithm has been developed for non-Gaussian sources and square arrangements of the 2qth-order data statistics, to overcome the main limitations of MUSIC and to improve the performance of 4-MUSIC for multiple sources. To further improve the performance of the 2q-MUSIC algorithm, the purpose of this paper is to extend the latter to rectangular arrangements of the data statistics, giving rise to rectangular 2q-MUSIC algorithms. It is shown in particular that rectangular arrangements of the higher order (HO) data statistics allow to optimize the compromise between performance and maximal number of sources to be processed. Besides, it also allows a complexity reduction for a given level of performance. These results, completely new, should open new perspectives for HO array processing.

In this contribution, we propose a coordinated transmit beamforming technique for point-to-point multiple-input-multiple-output (MIMO) filter bank based multi-carrier with offset quadrature amplitude modulation (FBMC/OQAM) systems. To enable reliable transmissions when the number of transmit antennas does not exceed the number of receive antennas and the channel is not flat fading, we design a joint and iterative procedure to calculate the precoding matrix and the decoding matrix for each subcarrier. Simulation results show that the proposed algorithm outperforms the existing transmission strategies for MIMO FBMC/OQAM systems. It is also observed that by employing the proposed coordinated beamforming scheme, the MIMO FBMC/OQAM system achieves a similar bit error rate (BER) performance as its orthogonal frequency division multiplexing with the cyclic prefix insertion (CP-OFDM) based counterpart while exhibiting superiority in terms of a higher spectral efficiency, a greater robustness against synchronization errors, and a lower out-of-band radiation.

Compressive Sensing (CS) allows to acquire signals at sampling rates significantly lower than the Nyquist rate, provided that the signals possess a sparse representation in an appropriate basis. However, in some applications of CS, the dictionary providing the sparse description is partially or entirely unknown. It has been shown that dictionary learning algorithms are able to estimate the basis vectors from a set of training samples. In some applications the dictionary is multidimensional, e.g., when estimating jointly azimuth and elevation in a 2-D direction of arrival (DOA) estimation context. In this paper we show that existing dictionary learning algorithms can be extended to exploit this structure, thereby providing a more accurate estimate of the dictionary. As examples we choose two prominent dictionary learning algorithms, the method of optimal directions (MOD) and the K-SVD algorithm. We propose tensor-based multidimensional extensions for both algorithms and show their improved performances numerically.

Spatial smoothing is a widely used preprocessing scheme to improve the performance of high-resolution parameter estimation algorithms in case of coherent signals or a small number of available snapshots. In this paper, we present a first-order performance analysis of Standard and Unitary ESPRIT as well as NC Standard and NC Unitary ESPRIT for strictly second-order (SO) non-circular (NC) sources when spatial smoothing is applied. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximations become exact for either high SNRs or a large sample size. Moreover, they are explicit in the noise realizations, i.e., only a zero-mean and finite SO moments of the noise are required. We show that both NC ESPRIT-type algorithms with spatial smoothing perform asymptotically identical in the high effective SNR. Also, for the special case of a single source, we analytically derive the optimal number of subarrays for spatial smoothing and show that no gain from strictly non-circular sources is achieved in this case.

In this paper, we consider the problem of optimizing the transmit co-variance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimate receiver, and multiple non-cooperating eavesdroppers that are all equipped with multiple antennas. Specifically, we design the transmit covariance matrix by maximizing the secrecy rate under a total power constraint, which is a non-convex difference of convex functions (DC) programming problem. We develop an algorithm, termed alternating matrix POTDC algorithm, based on alternating optimization of the eigenvalues and the eigenvectors of the transmit covariance matrix. The proposed alternating matrix POTDC method provides insights into the non-convex nature of the problem and is very general, i.e., additional constraints on the co-variance matrix can easily be incorporated. The secrecy rate performance of the proposed algorithm is demonstrated by simulations.

In this paper we consider a multi-pair two-way relaying network with two types of relays, namely, smart multi-antenna amplify and forward relays and dumb repeaters. The smart relays are able to perform adaptive linear precoding while the dumb repeaters are only able to forward the received signals. Utilizing an interference neutralization scheme, a closed-form transmit strategy can be computed for our scenario. We derive necessary and sufficient conditions for the feasibility of interference neutralization. This provides interesting insights how to choose system parameters like the number of antennas and the number of relays. When the SINR balancing problem is considered, simulation results show that the interference neutralization solution provides a balance between the computational complexity and the performance when compared to optimal transmit strategies.

The authors present a robust adaptive beamforming algorithm based on the worst‐case (WC) criterion and the constrained constant modulus (CCM) approach, which exploits the constant modulus property of the desired signal. Similar to the existing worst‐case beamformer with the minimum variance design, the problem can be reformulated as a second‐order cone programme and solved with interior point methods. An analysis of the optimisation problem is carried out and conditions are obtained for enforcing its convexity and for adjusting its parameters. Furthermore, low‐complexity robust adaptive beamforming algorithms based on the modified conjugate gradient and an alternating optimisation strategy are proposed. The proposed low‐complexity algorithms can compute the existing WC constrained minimum variance and the proposed WC‐CCM designs with a quadratic cost in the number of parameters. Simulations show that the proposed WC‐CCM algorithm performs better than existing robust beamforming algorithms. Moreover, the numerical results also show that the performances of the proposed low‐complexity algorithms are equivalent or better than that of existing robust algorithms, whereas the complexity is more than an order of magnitude lower.

We propose a reduced-rank beamformer based on the rank-$D$Joint Iterative Optimization (JIO) of the modified Widely Linear Constrained Minimum Variance (WLCMV) problem for non-circular signals. The novel WLCMV-JIO scheme takes advantage of both the Widely Linear (WL) processing and the reduced-rank concept, outperforming its linear counterpart as well as the full-rank WL beamformer. We develop an augmented recursive least squares algorithm and present an improved structured version with a much more efficient implementation. It is shown that the improved adaptive scheme achieves the best convergence performance among all the considered methods with a low computational complexity.

Tomlinson-Harashima precoding (THP) is a nonlinear processing technique employed at the transmit side which is a dual to the successive interference cancelation (SIC) detection at the receive side. Like SIC detection, the performance of THP strongly depends on the ordering of the precoded symbols. The optimal ordering algorithm, however, is impractical for multiuser MIMO (MU-MIMO) systems with multiple receive antennas due to the fact that the users are geographically distributed. In this paper, we propose a multi-branch THP (MB-THP) scheme and algorithms that employ multiple transmit processing and ordering strategies along with a selection scheme to mitigate interference in MU-MIMO systems. Two types of multi-branch THP (MB-THP) structures are proposed. The first one employs a decentralized strategy with diagonal weighted filters at the receivers of the users and the second uses a diagonal weighted filter at the transmitter. The MB-MMSE-THP algorithms are also derived based on an extended system model with the aid of an LQ decomposition, which is much simpler compared to the conventional MMSE-THP algorithms. Simulation results show that a better bit error rate (BER) performance can be achieved by the proposed MB-MMSE-THP precoder with a small computational complexity increase.

This paper presents a widely-linear (WL) distributed beamforming algorithm that takes advantage of strictly second-order (SO) non-circular source signals. We consider a single-antenna source-destination pair, which is assisted by multiple relays but suffers from strong interference. Assuming that perfect channel state information (CSI) is available, we design our algorithm based on the maximization of the signal-to-interference-plus-noise ratio (SINR) under a total relay power constraint after applying WL processing. We prove that in the case of no interference, the proposed WL distributed beamforming algorithm provides an SINR gain of 3 dB over its linear counterpart due to a virtual doubling of the number of relays. Also, the complexity is analyzed and simulations for the interference scenario show the performance gains in terms of the SINR and the bit error rate (BER).

High-resolution parameter estimation algorithms designed to benefit from the presence of non-circular (NC) source signals allow for an increased identifiability and a lower estimation error. In this paper, we present a 1-D first-order performance analysis of the NC standard ESPRIT and NC Unitary ESPRIT estimation schemes for strictly second-order (SO) non-circular sources, where NC Unitary ESPRIT has a lower complexity and a better performance in the low signal-to-noise ratio (SNR) regime. Our derived expressions are asymptotic in the effective SNR and explicit in the noise realizations, i.e., no assumptions about the noise statistics are necessary. As a main result, we show that the asymptotic performance of both NC ESPRIT-type algorithms is identical in the effective SNR and that NC Unitary ESPRIT is even applicable to array geometries without a centro-symmetric structure as required for Unitary ESPRIT.

Block diagonalization (BD) is a low-complexity linear precoding technique for multi-user MIMO (MU-MIMO) downlink systems, which can provide a performance that is close to theMU-MIMO capacity. However, imperfect channel state information (CSI) will result in a degraded performance of the BD scheme. Thus, studying the performance of BD under imperfect CSI is crucial for a practical system design since the robustness of BD to real-world imperfections should be verified. In this paper we apply a first-order perturbation analysis of the SVD to derive analytic expressions of the signal to interference plus noise ratio (SINR) for each subchannel of each UT using BD in presence of imperfect CSI. To demonstrate the usefulness of these expressions, a robust BD technique via worst SINR maximization is developed. Numerical simulations show the accuracy and the usefulness of the derived analytical results.

Distributed hash tables (DHTs) provide reliable distributed data management in a decentralized fashion that is well suited to self-organizing cluster-based ad-hoc networks. However, existing DHT approaches strive to optimize some combination of the total overlay message load, lookup delays, or load balance between the overlay nodes while ignoring the underlying physical characteristics of ad-hoc networks without infrastructure. In such networks, this inevitably leads to a high overhead in terms of the number of physical underlay transmissions. While location aware DHT approaches do reduce the number of underlay transmissions, they are not designed to exploit physical and link layer communication techniques such as cluster-based ad- hoc network structure or cooperative relaying. In this paper, we introduce novel location and resource aware DHT protocols that incorporate underlay cluster information into their proximity link selection. These and existing DHT protocols are evaluated in simulations that use realistic wireless transmission protocols and parameters along with mobile nodes with limited lifetimes. Comparisons of the number of required overlay and underlay hops as well as the amount of consumed power suggest a tradeoff between the underlay and overlay overhead in existing schemes, while the proposed novel protocols demonstrate both overlay and underlay benefits.

Our main emphasis is on the use of enhanced OFDM and filter bank based multicarrier (FB-MC) waveforms for utilizing effectively the available fragmented spectrum in heterogeneous radio environments. Special attention is on the broadband-narrowband coexistence scenario of the Professional Mobile Radio (PMR) evolution. The target here is to provide broadband data services in coexistence with narrowband legacy services of the TETRA family. The core idea is a multi-mode radio platform, based on variable filter bank processing, which is able to perform modulation/detection functions simultaneously for different signal formats with adjustable center frequencies, bandwidths and subchannel spacings.

Future cellular mobile radio systems - sometimes called beyond 4G (B4G) - will have to provide by factors higher network performance. Promising concepts like interference mitigation based on joint cooperative multipoint transmission (JT CoMP), multiple input multiple output (MIMO) or - more recently - massive MIMO depend on accurate and reliable channel state information. With so called model based channel prediction (MBCP) we proposed a powerful but challenging means, in theory promising to outperform state of the art Wiener or Kalman filtering. Here we analyze some important aspects of MBCP and suggest suitable enhancements for channel and parameter estimation of multi path components. Based on ray tracing tools and measurements the high potential of enlarged measurement bandwidth or virtual beamforming are being assessed. More work will be needed to understand the full potential and limitations of MBCP, being currently conducted in the EU funded project METIS.

Block diagonalization (BD) based precoding techniques are well-known linear transmit strategies for multiuser MIMO (MU-MIMO) systems. By employing BD-type precoding algorithms at the transmit side, the MU-MIMO broadcast channel is decomposed into multiple independent parallel single user MIMO (SU-MIMO) channels and achieves the maximum diversity order at high data rates. The main computational complexity of BD-type precoding algorithms comes from two singular value decomposition (SVD) operations, which depend on the number of users and the dimensions of each user's channel matrix. In this work, low-complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of BD-type precoding algorithms. We devise a strategy based on a common channel inversion technique, QR decompositions, and lattice reductions to decouple the MU-MIMO channel into equivalent SU-MIMO channels. Analytical and simulation results show that the proposed precoding algorithms can achieve a comparable sum-rate performance as BD-type precoding algorithms, substantial bit error rate (BER) performance gains, and a simplified receiver structure, while requiring a much lower complexity.

The problem of sum-rate maximization with minimum power consumption is studied for a decode-and-forward (DF) multiple-input multiple-output (MIMO) two-way relaying system consisting of two sources and one relay. Two scenarios are investigated. In the first scenario, the relay optimizes its own power allocation/beamforming strategy given that the strategies of the sources maximize the sum-rate of the multiple-access channel (MAC) phase. In the second scenario, the relay and the sources jointly optimize their power allocation/beamforming strategies over both the MAC and broadcasting (BC) phases. The considered problem of sum-rate maximization with minimum power consumption is shown to be nonconvex in both scenarios. For the first scenario, an algorithm is proposed to find the optimal strategy of the relay. For the second scenario, the sources and the relay find their strategies either through transferring the original nonconvex problem into corresponding convex problems or using a proposed low-complexity algorithm. Simulation results demonstrate the performance of proposed algorithms.

The problem of sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying is considered. Mathematically, this problem is equivalent to the constrained maximization of the product of quadratic ratios that is a non-convex problem. Such problems appear also in many other applications. This problem can be further relaxed into a difference-of-convex functions (DC) programming problem, which is typically solved using the branch-and-bound method without polynomial-time complexity guarantees. We, however, develop a polynomial-time convex optimization-based algorithm for solving the corresponding DC programming problem named polynomial-time DC (POTDC). POTDC is based on a specific parameterization of the problem, semi-definite programming (SDP) relaxation, linearization, and iterations over a single parameter. The complexity of the problem solved at each iteration of the algorithm is equivalent to that of the SDP problem. The effectiveness of the proposed POTDC method for the sum-rate maximization in two-way AF MIMO relay systems is shown.

There has been much activity on model selection for multi-dimensional data in recent years under the assumption of a Gaussian noise distribution. However, methods which are optimal for Gaussian noise are very sensitive against brief sensor failures. We suggest two robust model order selection schemes for multi-dimensional data based on the MM-estimator of the covariance of the r-mode unfoldings of the complex valued data tensor. Simulation results are given for 2-D and 3-D uniform rectangular arrays based source enumeration, both for Gaussian noise and a brief sensor failure.

We consider a multi-pair two-way relay network with multiple single antenna amplify-and-forward relays. The sum rate maximization problem subject to a total transmit power constraint is studied for such network. The optimization problem is non-convex. First, we show that the problem is a monotonic optimization problem and propose a polyblock approximation algorithm for obtaining the global optimum. However, this algorithm is only suitable for benchmarking because of its high computational complexity. After observing that the necessary optimality condition for our problem is similar to that of the generalized eigenvalue problem, we propose to use the generalized power iterative algorithm which can approach the global optimum recursively. Finally, we propose the total signal-to-interference-plus-noise ratio (SINR) eigen-beamformer which is a closed-form suboptimal solution that reduces the computational complexity significantly. Simulation results show that the proposed algorithms outperform the existing scheme. Moreover, the total SINR eigen-beamformer almost achieves the performance of the optimal solution.

Clustering is an essential tool to facilitate the function of self-organizing peer-to-peer and sensor networks. The LEACH (Low-Energy Adaptive Clustering Hierarchy) algorithm for forming clusters in ad-hoc networks represents a probabilistic way of choosing cluster-heads which shows a large variation over the average link distances of clusters and leads to uneven energy consumption during the transmission phase. However LEACH has the advantage that the energy load of being cluster-head is distributed among all the nodes resulting in a longer network life-time. On the other hand, the RSSI (Received Signal Strength Indicator)-based algorithms try to reduce the variation over the average link distances of clusters by means of choosing cluster-heads in the areas of higher node density in order to have an even energy consumption during transmission phase. But it distributes the energy load of being the cluster-head between some specific nodes which leads to a shorter network life-time. Here, we propose a new clustering scheme E-RSSI (Enhanced RSSI), which has the main advantages of the RSSI based schemes as well as LEACH. The average link distance of E-RSSI is almost the same as the average link distance of RSSI. And E-RSSI, like RSSI, has a significantly smaller variation over the average link distances in comparison with LEACH and at the same time shows significant improvement in network life-time. E-RSSI produces a low energy cost per node like RSSI and a more evenly distributed energy cost per node like LEACH therefore a prolonged network life-time.

By employing the regularized block diagonalization (RBD) preprocessing technique, the multi-user multi-input multi-output (MU-MIMO) broadcast channel is decomposed into multiple parallel independent single user multi-input multi-output (SU-MIMO) channels and achieves the maximum diversity order at high data rates. The computational complexity of RBD, however, is relatively high due to two singular value decomposition (SVD) operations. In this paper, a low-complexity lattice reduction aided RBD is proposed. The first SVD is replaced by a QR decomposition, and the orthogonalization procedure provided by the second SVD is substituted by a lattice reduction whose complexity is mainly contributed by a QR decomposition. Simulation results show that the proposed algorithm can achieve almost the same sum-rate as RBD while offering a lower complexity and substantial BER gains with perfect as well as imperfect channel state information at the transmit side.

In this work, we propose adaptive frequency-domain biased estimation algorithms with mechanisms to automatically adjust the shrink age factors. The proposed estimation algorithms improve the performance of the conventional least squares (LS) estimator in terms of mean-squared error (MSE), while requiring a very modest in crease in complexity. An extension of the Cramer-Rao Lower Bound (CRLB) is computed in order to serve as a performance benchmark for the MSE performance of the biased estimators. We consider an application of the proposed algorithms to single-carrier frequency domain equalization (SC-FDE) of direct-sequence ultra-wideband (DS-UWB) systems, in which the channel estimation is performed by the proposed algorithms. The simulation results show that the proposed algorithms significantly outperform existing methods.

In this paper, we derive the analytical performance of 1-D standard ESPRIT and 1-D Unitary ESPRIT using one iteration of Structured Least Squares to solve the shift invariance equations. First, we provide the estimation error of the fc-th spatial frequency as an explicit expression of the noise realization, which requires no assumptions about the statistics of the noise. Then, we compute the statistical expectation over zero mean circularly symmetric white noise and provide explicit formulas for the resulting mean square errors. All expressions are asymptotic in the effective SNR, i.e., they become exact as either the number of snapshots or the SNR tends to infinity.

We propose a non-data-aided adaptive beamforming algorithm based on Widely Linear (WL) processing techniques and the Auxiliary Vector Filtering (AVF) algorithm for non-circular signals, where only the steering vector of the desired user is known. The proposed Widely Linear Auxiliary Vector Filtering (WL-AVF) algorithm recursively updates the filter weights by a sequence of auxiliary vectors that are designed according to the Widely Linearly Constrained Minimum Variance (WLCMV) criterion. It takes full advantage of the second-order statistics of the non-circular data, achieving a higher maximum signal-to-interference-plus-noise ratio (SINR) than the linear AVF. Key properties of the proposed WL-AVF are analyzed. Simulation results show that the WL-AVF beamforming algorithm performs the best among the existing adaptive algorithms.

Relays represent a promising approach to extend the cell coverage, combat the strong shadowing effects as well as guarantee the QoS in dense networks. Among the numerous existing relaying techniques, two-way relaying uses the radio resource in a particular efficient manner. Moreover, amplify and forward (AF) relays cause less delays and require lower hardware complexity. Therefore, we consider multi-user two-way relaying with MIMO AF relays where a base station (BS) and multiple users (UT) exchange messages via the relay in this paper. We propose three sub-optimal algorithms for computing the transmit and receive beamforming matrices at the BS as well as the amplification matrix at the relay. Simulations show that block diagonalization (BD) combined with the algebraic norm-maximizing (ANOMAX) transmit strategy provides the best balance between complexity and performance, the zero-forcing dirty paper coding (ZFDPC) based design can perform well when the system is heavily loaded, and the channel inversion (CI) based design yields the lowest complexity. All three algorithms outperform a recently proposed technique from the literature.

Ad-hoc networks that support multi-hopping can provide a range of solutions for range-limited sensor and machine-to-machine networks. However such networks have their own set of implementation and performance issues. Clustering helps in organizing the networks and providing a backbone for routing data packets over multi-hop links. However multi-hopping itself can cause a loss in performance compared to single-hop systems. This is because, as shown in the paper, the ergodic capacity of links in such networks is a decreasing function of the number of hops. Also error-propagation over multiple hops can result in a much reduced performance. Hence it is beneficial to reduce the number of hops in multi-hop networks. One way to do this is to employ cooperative MIMO (Multiple Input Multiple Output) techniques to increase the range of these devices. This will result in reducing the number of hops. However incorporating cooperative MIMO in an ad-hoc network without central control and with self-organised routing can be challenging. In this paper, we present a novel joint clustering and routing mechanism to simplify and define the procedure for nodes to employ cooperative MIMO to gain an increase in performance. We introduce the concept of 'cooperative-MIMO-linked neighboring clusters' and describe how that can be used in conjunction with our specialized routing mechanism AOCMR (Ad-hoc On-Demand Cooperative MIMO Routing), to enable nodes to efficiently communicate in large scale networks in a decentralized manner.

Subspace-based high-resolution parameter algorithms such as ESPRIT, MUSIC, or RARE are known as efficient and versatile tools in various signal processing applications including radar, sonar, medical imaging, or the analysis of MIMO channel sounder measurements. Since these techniques are based on the singular value decomposition (SVD), their performance can be analyzed with the help of SVD-based perturbation theory. Recently we have demonstrated that in the R-dimensional case (R ≥ 2), the estimation accuracy of these schemes can be improved by replacing the measurement matrix by a measurement tensor and the SVD by the Higher-Order SVD (HOSVD). In case of ESPRIT, this gives rise to the family of Tensor-ESPRIT algorithms, e.g., standard Tensor-ESPRIT and Unitary Tensor-ESPRIT. In this paper we derive the analytical performance for Tensor-ESPRIT-type algorithms via a recently introduced perturbation theory for the HOSVD-based signal subspace estimate. All expressions are asymptotic in the SNR, but not in the sample size. We first present the explicit equations as a function of the current noise realization, where no assumption on the statistics of symbols or noise are required. Next, we show the result of performing statistical expectation over white Gaussian noise. To demonstrate the usefulness of the results we also present a compact expression for the asymptotic efficiency in the case of a single source, which is only a function of the array size.

In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. In the literature, the relay amplification matrix which maximizes the sum rate in two-way relaying is not known for the general MIMO case. However, the maximization of the channels' Frobenius norms is easily achieved via the Algebraic Norm-Maximizing (ANOMAX) transmit strategy. While this scheme provides a significant improvement in the received signals' strengths, it does not reach the full multiplexing gain for high SNRs due to its low rank nature. Therefore, we propose a simple strategy to restore the rank while preserving the same subspaces via an optimization over the profile of the singular values. The resulting scheme is called rank-restored ANOMAX (RR-ANOMAX). The main benefit of this approach is that the computational complexity is very low. Moreover, its performance is very close to the one-way upper-bound which is obtained by considering the two transmission directions as independent one-way relaying channels.

In this paper, we propose a new algorithm for jointly processing a set of Hermitian matrices. It is called structured joint congruence (STJOCO) transformation. Instead of simultaneously diagonalizing a set of matrices, the STJOCO transformation finds a non-singular matrix which jointly minimizes the squared magnitude of the off-diagonal elements in the ith row and the ith column of the ith matrix in the set. The STJOCO transformation is proposed for real-valued as well as complex-valued matrices and the corresponding new scaling-invariant cost function is introduced. Numerical simulations demonstrate the efficiency of the algorithm. As an example application for the STJOCO transformation we present coordinated beamforming (CBF), where the system has a smaller number of transmit antennas than the aggregate number of receive antennas. In the literature, the transmit-receive beamforming weights of CBF are obtained via iterative algorithms, where the convergence of these iterative algorithms cannot be guaranteed. We show that the STJOCO transformation represents an elegant closed-form solution for the transmit-receive beamforming weights of CBF and can achieve the same sum rate performance as existing iterative algorithms.

In this paper, we propose a reduced-rank direction of arrival (DOA) estimation algorithm based on joint and iterative subspace optimization (JISO) with grid search . The reduced-rank scheme includes a rank reduction matrix and an auxiliary reduced-rank parameter vector. They are jointly and iteratively optimized with a recursive least squares algorithm (RLS) to calculate the output power spectrum. The proposed JISO-RLS DOA estimation algorithm provides an efficient way to iteratively estimate the rank reduction matrix and the auxiliary reduced-rank vector. It is suitable for DOA estimation with large arrays and can be extended to arbitrary array geometries. It exhibits an advantage over MUSIC and ESPRIT when many sources exist in the system. A spatial smoothing (SS) technique is employed for dealing with highly correlated sources. Simulation results show that the JISO-RLS has a better performance than existing Capon and subspace-based DOA estimation methods.

We propose a b-bit non-coherent receiver based on a Digital Code Matched Filter (DCMF) for a low data rate Time- Hopping Pulse Position Modulation Ultra Wide Band (TH-PPMUWB) system. The DCMF follows after a high-speed but lowresolution (b-bit, 1 ≤ b ≤ 4) Analog-to-Digital Convertor (ADC) and is employed before the non-coherent detection. It is matched to the user-specific sequence and restricts the non-coherent combining only to the multipath arrivals. The performance of the proposed receiver is analyzed in the presence of Multi- User Interference (MUI), considering both perfect and imperfect power control. The influence of Automatic Gain Control (AGC) for the b-bit ADC (b ≠ 1) plays an important role in the system performance. To suppress the strong interference, a b-bit adaptive non-coherent receiver based on a DCMF is proposed, providing a high robustness to the MUI. We also discuss the selection of the TH codes and the corresponding parameters that trade-off the receiver performance.

The concept of Ad-hoc mobile networks that support multi-hopping has been around for some time now. However, making sure that such decentralized networks are completely self-organizing is not a trivial task and raises various issues relating to network management, routing, interference, etc. We have built a software SONIR (Self-Organizing Network with Intelligent Relaying), in MATLAB, which implements an end-to-end multi-hop, virtual MIMO system, capable of dealing with mobility of nodes in a Rayleigh fading environment. Different methods for clustering, mobility managment, routing, virtual MIMO, etc. have been implemented. These methods work on different OSI layers. Our main goal is to be able to visualize such a system as a whole in order to see the end-to-end performance as well as solve the possible issues that arise with it.

Recently, many authors have shown that high-resolution parameter estimation schemes can be significantly improved if the sources are non-circular. For example, enhanced versions of root MUSIC and standard ESPRIT for non-circular sources as well as the entirely real-valued NC unitary ESPRIT algorithm have been proposed. We can achieve further enhancements in the R-dimensional (R-D) case by using tensor algebra to express and manipulate multidimensional signals in their natural R-D structure. This has led to tensor-based parameter estimation algorithms with enhanced estimation accuracy such as R-D unitary tensor- ESPRIT. In this paper we demonstrate how to achieve both benefits at the same time. This is not straightforward since the usual method to exploit non-circular sources destroys the tensor structure and therefore a new approach had to be found. This approach allows us to derive the NC R-D unitary tensor-ESPRIT algorithm which exploits the non-circularity of the sources and the R-D structure of the measured signals jointly. Numerical computer simulations demonstrate the benefit in terms of a significantly improved accuracy compared to state of the art algorithms.

In this paper we study two-way relaying with amplify-and-forward (AF) relays. In two-way relaying, two terminals exchange data with the help of an intermediate relay station. In order to enable mass deployment of these relays, we focus on very simple AF relays that do not have any channel state information. Hence, to separate the data streams in two-way relaying, both user terminals need reliable knowledge of all relevant channel parameters. We therefore propose the novel tensor-based channel estimation algorithm TENCE that provides both terminals with full knowledge of all channel parameters involved in the transmission. The solution is algebraic, i.e., it does not require any iterative procedures. Moreover, TENCE is applicable to arbitrary antenna configurations. We also derive criteria for the design of the pilot symbols and the corresponding relay amplification matrices. Computer simulations demonstrate the achievable channel estimation accuracy.

In this paper, we study the achievable throughput for regularized block diagonalization (RBD) precoding in multi-user MIMO broadcast channels at high SNRs. By applying an analytical framework for a high SNR affine approximation to capacity, we derive the multiplexing gains and the power offsets for RBD in two cases separately. In the first case, we assume that the aggregate number of receive antennas is less than or equal to the number of transmit antennas. It is found that RBD can maintain the same multiplexing gain as dirty paper coding (DPC) and block diagonalization (BD) precoding at high SNRs and has a smaller power offset than BD. The sum rate differences relative to DPC and BD are analyzed and bounded as simple functions of the system parameters. In the second case, we assume that the aggregate number of receive antennas is larger than the number of transmit antennas. Although RBD can still be performed, the achievable throughput is degraded with an increasing number of receive antennas. The benefit of spatial multiplexing is completely lost due to a unit spatial multiplexing gain at high SNRs.

The efficient analysis of electroencephalographic (EEG) data is a long standing problem in neuroscience, which has regained new interest due to the possibilities of multidimensional signal processing. We analyze event related multi-channel EEG recordings on the basis of the time-varying spectrum for each channel. It is a common approach to use wavelet transformations for the time-frequency analysis (TFA) of the data. To identify the signal components we decompose the data into time-frequency-space atoms using parallel factor (PARAFAC) analysis. In this paper we show that a TFA based on the Wigner-Ville distribution together with the recently developed closed-form PARAFAC algorithm enhance the separability of the signal components. This renders it an attractive approach for processing EEG data. Additionally, we introduce the new concept of component amplitudes, which resolve the scaling ambiguity in the PARAFAC model and can be used to judge the relevance of the individual components.

We consider multi-user MIMO broadcast channels with limited feedback. A recently proposed linear preceding technique, regularized block diagonalization (RBD), is used to mitigate multi-user interference. We assume that each receiver has estimated channel state information (CSI) via downlink training and independently quantizes its channel by using an efficient channel quantization scheme that we propose in this paper. The transmitter acquires the quantized CSI from each receiver through a noiseless and delayed feedback channel. The achievable rates are studied under these assumptions. We derive an upper bound for the rate loss compared to the case that the transmitter has perfect CSI and quantify the impact of channel estimation errors, quantization errors, and outdated quantized CSI on the rate loss. Furthermore, we provide an expression of the number of feedback bits needed per user to maitain that bound. It is found that the delay of the feedback is the predominant cause of performance degradation in the case of rapidly changing channel impulse response.

We consider a low data rate non-coherent impulse radio ultra-wideband (IR-UWB) system based on binary pulse position modulation (2-PPM), which applies sparse codes to enable code division multiple access (CDMA). The suitability of sparse codes (i.e., codes with a low code weight) is investigated considering multi-user interference (MUI) and multipath propagation. The decoding of the particular CDMA code takes place after non-coherent combining. Different sparse codes such as time hopping (TH) random codes, TH codes constructed from M-sequences, and optical orthogonal codes are employed. We propose a semi-analytical performance analysis method using Gaussian approximation and the statistics of the code collisions to obtain the bit error rate expressions, which is much more accurate than the code correlation function. The multiple access performance is analyzed in terms of the signal-to-noise ratio (SNR) as well as the number of supported users.

Two-way relaying is a promising scheme to achieve the ubiquitous mobile access to a reliable high data rate service, which is targeted for future mobile communication systems. In this contribution, we investigate two-way relaying with an amplify and forward relay, where the relay as well as the terminals are equipped with multiple antennas. Assuming that the terminals possess channel knowledge, the bidirectional two-way relaying channel is decoupled into two parallel effective single-user MIMO channels by subtracting the self-interference at the terminals. Thereby, any single-user MIMO technique can be applied to transmit the data. We derive an algebraic norm-maximizing (ANOMAX) transmit strategy by finding the relay amplification matrix which maximizes the weighted sum of the Frobenius norms of the effective channels and discuss the implications of this solution on the resulting signal to noise ratios. Finally, we compare ANOMAX to other existing transmission strategies via numerical computer simulations.

Spatial smoothing is a widely used preprocessing scheme for direction-of-arrival (DOA) estimation of more than one source from a single snapshot, although the effective array aperture gets reduced by this process. In this paper we propose a preprocessing scheme applicable for DOA estimation algorithms that exploit the shift invariance property of the array steering matrix and call it spatial smoothing with improved aperture (SSIA). SSIA, when applied to a noise corrupted data vector, improves the effective array aperture significantly as opposed to conventional spatial smoothing. Simulations confirm the significant performance gain provided by SSIA in conjunction with Unitary ESPRIT.

This paper presents an adaptive codebook design method, which introduces a transition probability based codeword sorting scheme in an effort to reduce the feedback overhead by exploiting the temporal correlation of the channel. The adaptive codebook sorts the codewords in the increasing order of the chordal distance with respect to the initial codeword, which is the codeword chosen at the previous time step. The adaptive codebook method in conjunction with the lossless data compression scheme requires much less feedback overhead compared with currently available techniques, e.g., the recursive codebook scheme, at the cost of slightly increased memory requirements.

The particular topology found in metropolitan areas can be exploited by employing relay nodes, which turn one-hop non-line-of-sight connections into multi-hop line-of-sight ones, thereby reducing the shadowing. However, this topology should also be considered to avoid multi-user interference and thus exploit the spatial resources optimally. Nevertheless, in most approaches which deal with this scenario, the interference is either completely neglected or estimated with strong simplifications. In this paper, we analyze the interference among users in a 4-way junction on the downlink and show that it should not be ignored. Based on this observation, we propose the channel representative interference cancelation (CRIC) scheme. The interference between users in the same street is suppressed by CDMA, whereas the one between users of different streets by the Successive Minimum Mean Square Error (SMMSE) precoder. Due to the dimensionality restrictions given by SMMSE, we introduce a channel representative, which, serving as a virtual user, reflects the spatial features of all users in one street.

This work proposes a low-complexity blind adaptive reduced-rank method (BARC) for symbol estimation using an adaptive decimation and interpolation scheme based on diversity-combining and the constant modulus criterion for interference suppression. The proposed approach employs an iterative procedure to jointly optimize the interpolation, decimation and estimation tasks for blind reduced-rank parameter estimation. We describe joint iterative estimators based on the constrained constant modulus (CCM) criterion, introduce alternative decimation structures, including the optimal decimation scheme, and develop low-complexity stochastic gradient adaptive algorithms for the proposed structure. Simulations for a CDMA interference suppression application show an excellent performance and substantial gains over prior art.

Parallel factor analysis (PARAFAC) is a branch of multi-way signal processing that has received increased attention recently. This is due to the large class of applications as well as the milestone identifiability results demonstrating the superiority to matrix (two-way) analysis approaches. A significant amount of research was dedicated to iterative methods to estimate the factors from noisy data. In many situations these require many iterations and are not guaranteed to converge to the global optimum. Therefore, suboptimal closed-form solutions were proposed as initializations. In this contribution we derive a closed-form solution to completely replace the iterative approach by transforming PARAFAC into several joint diagonalization problems. Thereby, we obtain several estimates for each of the factors and present a new "best matching" scheme to select the best estimate for each factor. In contrast to the techniques known from the literature, our closed-form solution can efficiently exploit symmetric as well as Hermitian symmetric models and solve the underdetermined case, if there are at least two modes that are non-degenerate and full rank. This closed-form solution achieves approximately the same performance as previously proposed iterative solutions and even outperforms them in critical scenarios.

Regularized block diagonalization (RBD) is a new linear precoding technique for the multi-antenna broadcast channel and has a significantly improved sum rate and diversity order compared to all previously proposed linear precoding techniques. We consider a limited feedback system with RBD precoding, in which each receiver has perfect channel state information (CSI) and quantizes its channel. The transmitter receives the quantized CSI with a finite number of feedback bits from each receiver. In contrast to zero-forcing (ZF) or block diagonalization (BD) precoding, where the transmitter only requires the channel direction information which refers to the knowledge of subspaces spanned by the users' channel matrices, for RBD precoding the transmitter additionally requires the channel magnitude information which defines the strength of the eigenmodes of the users' channel matrices. The key contribution of our work is that we propose a new scheme for the channel quantization to supply the transmitter with both channel direction and magnitude information. Based on this new scheme, firstly, we investigate a random vector quantization (RVQ). We derive a bound for the throughput loss due to imperfect CSI and find a way to achieve the bound by linearly increasing the number of feedback bits with the system SNR. Secondly, we modify the LBG vector quantization algorithm to obtain a dominant eigenvector based LBG (DE- LBG) vector quantization which can significantly reduce the number of feedback bits compared to RVQ. Finally, we demonstrate that the DE-LBG vector quantization can be applied to an OFDM-based multi-user MIMO system.

In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference.

In this paper we present a blind interference suppression technique for DS-CDMA systems based on a reduced-rank decomposition of a code-constrained constant modulus design criterion. We describe a least-squares (LS) type design criterion for blind linear detectors using the constrained optimization of the constant modulus cost function subject to code constraints. Based on this design approach and using the Lanczos algorithm, a multistage decomposition in the Krylov subspace is devised for blind reduced-rank parameter estimation. A computationally efficient blind reduced-rank LS type algorithm is also developed and compared with existing methods. Numerical results show that the proposed full-rank and reduced-rank techniques outperform existing methods for the linear suppression of multi-access and intersymbol interference in DS-CDMA systems.

Multidimensional ESPRIT-type parameter estimation algorithms obtain their frequency estimates from the solution of sets of highly structured equations (the shift invariance equations). The structured least squares (SLS) algorithm is known as an efficient method to obtain these solutions since the inherent structure is explicitly taken into account. In this contribution we show that if the underlying R-dimensional signals are represented by tensors, this structure can be exploited even further. In addition to an improved signal subspace estimate, the SLS algorithm is modified to directly exploit the tensor structure of the signal subspace obtained through the higher order SVD. The resulting algorithm which we term tensor-structure SLS offers a superior performance compared to existing approaches in critical cases, e.g., if there are highly correlated sources or a small number of available snapshots.

For UWB impulse radio transmission based on orthogonal pulse-position modulation, signal detection with non-coherent path diversity combing is analyzed. The performance of single- window and weighted sub-window combing is compared with the performance bound of non-coherent detection. This performance bound is derived using the maximum-likelihood decision rule. For numerical evaluations, measured UWB channels (non-LOS, office) are used. Intersymbol interferences are not taken into account, since non-coherent detection is primarily an alternative for low data-rate, low power applications.

This contribution is focused on direction of arrival (DoA) estimation with a regular-hexagonal shaped ESPAR (electronically steerable parasitic antenna radiator) array that has received increased attention recently. It is shown how the estimation accuracy is improved by employing non-circular (NC) signal constellations that facilitate the application of the NC Unitary ESPRIT algorithm. It is demonstrated how this method allows the joint estimation of the azimuth and the elevation angles of up to eight uncorrelated sources with a 7-element ESPAR array. Moreover, the achievable benefits of using non-circular sources are assessed by studying deterministic Cramer-Rao bounds. It is shown that for special phase constellations between the impinging wavefronts the estimation accuracy is independent of the angular separation of the corresponding DoAs

In this paper, the multi-user MIMO downlink channel is considered, where a single transmitter (base station) sends data to several users within the same resource unit. Assuming perfect channel state information (CSI) at the transmitter, different linear precoding schemes are studied, aiming at mean square error minimizing transmission to all users. The exact MMSE solution can be obtained by exploiting uplink/downlink duality. A suboptimal solution based on necessary conditions for MMSE optimality may also be computed directly in the downlink domain. Our results indicate that the performance difference between the direct and duality-based method that is visible in uncoded BER curves vanishes when channel coding is introduced to the system. We also compare the MMSE-optimal approaches to other existing linear precoding schemes (BD, S-MMSE)

Spatial multiplexing in the downlink of wireless multiple antenna communications promises high gains in system throughput. However, spatially correlated users and a limited number of antennas at the base station motivates the need for a scheduling algorithm which efficiently arranges users into groups to be served in different time or frequency slots. In this paper we propose a novel tree-based scheduling algorithm which successfully solves this problem achieving a close to optimum grouping strategy. The algorithm has been tested with zero forcing beamforming techniques and is based on a new metric for the user performance considering the effect of other users present in the same group analyzing their spatial features.

Multi-user multiple-input multiple-output (MU MIMO) systems have the advantage of combining the high capacity achievable with MIMO processing and the benefits of space division multiple access. Previously proposed techniques that use the channel state information at the transmitter to improve the performance of the downlink suffer from a capacity loss due to a zero multi-user interference (MUI) constraint or they have to allow some MUI to improve the system performance. In this paper we propose a combination of one linear precoding technique named successive optimization (SO) and a nonlinear precoding technique, Tomlinson-Harashima precoding (THP). It uses all of the subspaces available in a MU MIMO system and can completely eliminate multi-user interference. We show that SO THP provides a very high capacity and a better BER performance than similar minimum mean-square-error (MMSE) THP precoding techniques at low SNR especially for the users equipped with multiple antennas. SO THP is also less sensitive to channel estimation errors than MMSE THP precoding. Thereby, we minimize the capacity loss due to the MUI cancellation and we reduce the complexity of the receiver since there is no MUI in the system.

In this contribution we investigate the cross-layer issues occurring in a multi-user MIMO scenario. The scenario is based on a geometric model, thus containing realistic correlations in space, time, and frequency. As typical service we assume an audio transmission, where we evaluate the transmission quality by using the PEAQ (perceptual evaluation of audio quality) parameter. To build the bridge from the audio quality to the physical layer we derive a mapping from the PEAQ parameter to operation points consisting of required data rates and maximum allowable frame error rates. The optimization goal is to assure that each user attains a certain quality while minimizing the costs, i.e., bandwidth or transmission power. The parameters to be optimized are the multiple access scheme (SDMA, TDMA), the MIMO transmission mode (beamforming on one or two eigen-beams with diversity combining or multiple data streams, i.e., spatial multiplexing) and the choice of the modulation and coding scheme

In this contribution we propose a new way to state and solve the channel equalization problem for an OFDM (orthogonal frequency division multiplexing) system, without the use of a guard interval. Therefore, the spectral efficiency is increased. The approach is based on the channel representation as a polynomial matrix. We develop a new decomposition of this matrix, which diagonalizes the channel matrix independently of the channel realization. It leads to a simple inversion of the channel matrix. The decomposition consists of forward and inverse DFTs and polynomial diagonal matrices. Further on, there is no restriction on the length of the channel impulse response.

Wireless infrared is an attractive alternative for short-range indoor communications. However, mainly as a result of the physical properties of the detector, one serious problem is the power efficiency of the transmission. Under the assumptions of a fixed average optical power and additive white Gaussian noise, we derive the maximum coding gains attainable with optimized on-off keying, where "optimized" refers to the probability of the logical "1" pulses in the transmitted data stream. Uncoded on-off keying acts as the reference scheme. We also consider orthogonal pulse-position modulation, having favorable spectral characteristics, with and without additional coding and compare the corresponding coding gains with the limits for binary transmission

Estimating the directions of arrival of several wavefronts impinging on an array of sensors is a requirement in a variety of applications including radar, mobile communications, sonar, and seismology. Subspace based high-resolution parameter estimation schemes like ESPRIT and MUSIC have become very popular. Such parameter estimation algorithms often use forward-backward averaging to enhance their resolution, especially in the case of correlated sources. Further enhancements can be achieved if the source signals are non-circular. We derive an efficient subspace estimation scheme that exploits the non-circularity of the sources and already includes forward-backward averaging. Moreover, appropriate spatial smoothing techniques are introduced. Completely real-valued implementations of 1D and 2D unitary ESPRIT for non-circular sources are presented as examples. In these cases, NC unitary ESPRIT improves the resolution capability and the noise robustness of standard ESPRIT as well as unitary ESPRIT and can handle more sources than sensors.

In this contribution we propose a subspace-based channel model suitable to represent frequency selective time variant MIMO channels. This approach captures the true nature of the MIMO channel maintaining the spatial correlation present between the antenna arrays. Correlation in time and frequency is conserved as well. The decomposition into eigenmodes, which form the channel subspace, gives an interesting interpretation of the channel's eigenstructure. These investigations lead to a very efficient method to synthesize new channels with the same correlation in time, frequency and space of a reference channel. The model allows the interpolation of a channel in order to retrieve more samples in frequency and time to perform statistical analysis such as bit error rate and capacity curves. In addition the model allows the generation of new random channels with the same spatial, time, and frequency correlations of a reference channel, which, for instance, could be obtained from measurements.

In the downlink of a multi-user MIMO (multiple input multiple output) communication system where each user has an arbitrary QoS requirement, intelligent algorithms are needed to choose transmit vectors. Here we present a new method of choosing transmit vectors that minimizes total transmitted power. The approach is based on previous iterative interference balancing algorithms, but it is initialized by applying a "block-diagonalization" algorithm that helps improve convergence speed. When the channel supports multiple data streams per user, power is distributed among the data streams by bit-loading using the channel gains derived from the block-diagonalization step. The result is a solution which is not guaranteed to converge to the global optimum, but will reach a solution that is either optimal or near-optimal with high probability and at minimal computational cost.

To enable efficient detection strategies in wireless communications a guard period is frequently inserted into the transmitted data symbols. This is the case in OFDM systems and in single-carrier systems with frequency domain equalization. Especially for transmissions over wireless channels with long delay spreads the required guard period is quite long. Here we present efficient data detection algorithms that are applicable if a guard period is not inserted after every symbol or if it is omitted completely. The increase of the computational requirements in the base station is moderate and can be implemented via parallel processing. Finally, an OFDM system without guard periods is presented as an example.

Large area synchronized (LAS)-CDMA has been proposed to enhance third generation and fourth generation wireless systems. LAS-CDMA is based on multiple access codes that result from a combination of LA codes and pulse compressing LS codes. To reduce multiple access interference and intersymbol interference in time dispersive channels, LS codes have perfect auto-correlation and cross-correlation functions in a certain vicinity of the zero shift. In this paper, we provide systematic methods and the underlying theory for the construction of such codes that go far beyond the examples revealed by LinkAir (2000).

Third-generation mobile radio systems use time division-code division multiple access (TD-CDMA) in their time division duplex (TDD) mode. Due to the time division multiple access (TDMA) component of TD-CDMA, joint (or multi-user) detection techniques can be implemented with a reasonable complexity. Therefore, joint-detection will already be implemented in the first phase of the system deployment to eliminate the intracell interference. In a TD-CDMA mobile radio system, joint-detection is performed by solving a least squares problem, where the system matrix has a block-Sylvester structure. We present and compare several techniques that reduce the computational complexity of the joint-detection task even further by exploiting this block-Sylvester structure and by incorporating different approximations. These techniques are based on the Cholesky factorization, the Levinson algorithm, the Schur algorithm, and on Fourier techniques, respectively. The focus of this paper is on Fourier techniques since they have the smallest computational complexity and achieve the same performance as the joint-detection algorithm that does not use any approximations. Similar to the well-known implementation of fast convolutions, the resulting Fourier-based joint-detection scheme also uses a sequence of fast Fourier transforms (FFTs) and overlapping. It is well suited for the implementation on parallel hardware architectures.

This paper presents a vision for wireless communication systems beyond the third generation, which comprises a combination of several optimized access systems on a common IP-based medium-access and core network platform. These different access systems will interwork via horizontal and vertical handover, service negotiation, and global roaming. The different access systems are allocated to different cell layers in the sense of hierarchical cells with respect to cell size, coverage, and mobility to provide globally optimized seamless services to all users. This vision requires extensive international research and standardization activities to solve many technical challenges. Key issues are the global interworking of different access systems on a common platform, the implementation of multimode and multiband terminals and base stations by software-defined radio concepts as well as advanced antenna concepts.

A real-valued (unitary) formulation of the popular root-MUSIC direction-of-arrival (DOA) estimation technique is considered. This unitary root-MUSIC algorithm is shown to reduce the computational complexity in the eigenanalysis stage of root-MUSIC, because it exploits the eigendecomposition of a real-valued covariance matrix. Theoretical, numerical, and experimental results are presented showing that, additionally, unitary root-MUSIC has improved threshold and asymptotic performances relative to conventional root-MUSIC. It can be then recommended that the former technique should always be preferred to the conventional root-MUSIC algorithm.

The third-generation mobile radio system UTRA that has been specified in the Third Generation Partnership Project (3GPP) consists of an FDD and a TDD mode. This paper presents the UTRA TDD mode, which is based on TD-CDMA. Important system features are explained in detail. Moreover, an overview of the system architecture and the radio interface protocols is given. Furthermore, the physical layer of UTRA TDD is explained, and the protocol operation is described.

Adaptive space-frequency RAKE receivers use maximum ratio combining and multi-user interference suppression to obtain a considerable increase in performance in DS-CDMA systems such as WCDMA. To this end, the signal-plus-interference-and-noise and the interference-plus-noise space-time covariance matrices are estimated. The computational complexity is reduced significantly by transforming the covariance matrices into the space-frequency domain and by omitting noisy space-frequency bins. The optimum weight vector for symbol decisions is the "largest" generalized eigenvector of the resulting matrix pencil. By iteratively updating the optimum weight vector slot by slot, real-time applicability becomes feasible while the fast fading is still tracked. The performance and the computational complexity depend on the number of space-frequency bins, antenna elements, and iterations. Therefore, the performance can easily be scaled with respect to the available computational power.

A new pseudo-noise resampling technique is proposed to mitigate the effect of outliers in Unitary ESPRIT. This scheme improves the performance of Unitary ESPRIT in unreliable situations, where the so-called reliability test has a failure. For this purpose, we exploit a pseudo-noise resampling of a failed Unitary ESPRIT estimator with a censored selection of "successful" resamplings recovering the non-failed outputs of the reliability test.

It is essential for an efficient frequency and time slot allocation procedure in future mobile communication systems using space division multiple access (SDMA) to determine the mobiles that are spatially well separated from one another. Thus, once a mobile desires to initiate a call, precise knowledge of the 2-D arrival angles of its dominant wavefronts is required. In this application, 3-D Unitary ESPRIT for joint 2-D angle and carrier estimation offers an efficient way to handle such mobile access requests since it provides efficient high-resolution measurements of the spatial characteristics of the wireless channel, even if only a small number of antennas is available at the base station. Automatic pairing of the 3-D estimates is achieved via a new simultaneous Schur decomposition (SSD) of three real-valued, non-symmetric matrices. In general, the SSD enables an R-dimensional extension of Unitary ESPRIT (R/spl ges/3) to estimate several undamped R-dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems. We present a Jacobi-type method to calculate the SSD. For each of the R dimensions, the corresponding frequency estimates are obtained from the real eigenvalues of a real valued matrix. The SSD jointly estimates the eigenvalues of all R-matrices and, thereby, achieves automatic pairing of the estimated R-dimensional modes via a closed-form procedure that neither requires any search nor any other heuristic pairing strategy.

ESPRIT type high-resolution (spatial) frequency estimation techniques, like standard ESPRIT, state space methods, matrix pencil methods, or Unitary ESPRIT, obtain their (spatial) frequency estimates from the solution of a highly-structured, overdetermined system of equations. Here, the structure is defined in terms of two selection matrices applied to a matrix spanning the estimated signal subspace. Structured least squares (SLS) is a new algorithm to solve this overdetermined system, the so called invariance equation, by preserving its structure. Simulations confirm that SLS outperforms the least squares (LS) and total least squares (TLS) solutions of this invariance equation, since the accuracy of the resulting (spatial) frequency estimates and the accuracy of the underlying signal subspace are improved significantly. Furthermore, SLS can be used to improve the accuracy of adaptive frequency estimating schemes that are based on fast adaptive subspace tracking techniques. Moreover, SLS has been extended to the two-dimensional (2-D) case to be used in conjunction with 2-D Unitary ESPRIT, an efficient ESPRIT-type algorithm that provides automatically paired 2-D (spatial) frequency estimates.

The 2D DFT beamspace ESPRIT is an algorithm for use in conjunction with uniform rectangular arrays (URAs) that provides automatically paired azimuth and elevation angle estimates of incident signals via a closed-form procedure. We investigate the statistical performance of 2D DFT beamspace ESPRIT. Expressions for the 2D DFT beamspace ESPRIT estimator variances are obtained. Samples variances of the azimuth and elevation angle estimates obtained through Monte Carlo simulations are shown to be in close agreement with theoretically predicted variances.

This paper presents efficient Schur-type algorithms for estimating the column space (signal subspace) of a low rank data matrix corrupted by additive noise. Its computational structure and complexity are similar to that of an LQ-decomposition, except for the fact that plane and hyperbolic rotations are used. Therefore, they are well suited for a parallel (systolic) implementation. The required rank decision, i.e., an estimate of the number of signals, is automatic, and updating as well as downdating are straightforward. The new scheme computes a matrix of minimal rank which is /spl gamma/-close to the data matrix in the matrix 2-norm, where /spl gamma/ is a threshold that can be determined from the noise level. Since the resulting approximation error is not minimized, critical scenarios lead to a certain loss of accuracy compared to SVD-based methods. This loss of accuracy is compensated by using unitary ESPRIT in conjunction with the Schur-type subspace estimation scheme. Unitary ESPRIT represents a simple way to constrain the estimated phase factors to the unit circle and provides a new reliability test. Due to the special algebraic structure of the problem, all required factorizations can be transformed into decompositions of real-valued matrices of the same size. The advantages of unitary ESPRIT dramatically improve the resulting subspace estimates, such that the performance of unitary Schur ESPRIT is comparable to that of SVD-based methods, at a fraction of the computational cost. Compared to the original Schur method, unitary Schur ESPRIT yields improved subspace estimates with a reduced computational load, since it is formulated in terms of real-valued computations throughout.

Considers multiple narrowband signals that are incident upon a planar sensor array. 2D unitary ESPRIT is a new closed-form high resolution algorithm to provide automatically paired source azimuth and elevation angle estimates along with an efficient way to reconstruct the impinging signals. In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two array axes. 2D unitary ESPRIT offers several advantages over other ESPRIT based closed-form 2D angle estimation techniques. First, except for the final eigenvalue decomposition of dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to an efficient DFT beamspace implementation. Third, it is also applicable to array configurations that do not exhibit three identical subarrays, as long as the array is centro-symmetric and possesses invariances in two distinct directions. Finally, 2D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common.

ESPRIT is a high-resolution signal parameter estimation technique based on the translational invariance structure of a sensor array. Previous ESPRIT algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary. Unitary ESPRIT, however, exploits this knowledge to estimate the directions of arrival in a straightforward way yielding more accurate results. This is particularly useful in situations where the standard ESPRIT algorithm faces severe problems, such as closely spaced sources or short window lengths. The improved subspace estimates form the basis for several algorithms to separate and reconstruct superimposed signals arriving from different directions. Moreover, Unitary ESPRIT improves the performance of recently developed subspace estimation schemes, that only approximate the optimal signal subspace, but can be updated with significant computational savings.>