This paper presents a novel sequential estimator for the direction-of-arrival and polynomial coefficients of wideband polynomial-phase signals impinging on a sensor array. Addressing the computational challenges of Maximum-likelihood estimation for this problem, we propose a method leveraging random sampling consensus (RANSAC) applied to the time-frequency spatial signatures of sources. Our approach supports multiple sources and higher-order polynomials by employing coherent array processing and sequential approximations of the Maximum-likelihood cost function. We also propose a low-complexity variant that estimates source directions via angular domain random sampling. Numerical evaluations demonstrate that the proposed methods achieve Cramér-Rao bounds in challenging multi-source scenarios, including closely spaced time-frequency spatial signatures, highlighting their suitability for advanced radar signal processing applications.

Arrays of ultrasonic sensors are capable of 3D imaging in air and an affordable supplement to other sensing modalities, such as radar, lidar, and camera, i.e.in heterogeneous sensing systems. However, manufacturing tolerances of air-coupled ultrasonic sensors may lead to amplitude and phase deviations. Together with artifacts from imperfect knowledge of the array geometry, there are numerous factors that can impair the imaging performance of an array. We propose a reference-based calibration method to overcome possible limitations. First, we introduce a novel tensor signal model to capture the characteristics of piezoelectric ultrasonic transducers (PUTs) and the underlying multidimensional nature of a multiple-input multiple-output (MIMO) sensor array. Second, we formulate and solve an optimization problem based on this model to obtain the calibrated parameters of the array. Third, we assess both our model and the commonly used analytic model using real data from a 3D imaging experiment. The experiment reveals that our array response model we learned with calibration data yields an imaging performance similar to that of the analytic array model, which requires perfect array geometry information. • A tensor model characterizes the array response in air-coupled ultrasound imaging. • Model parameters are learned from real calibration data recorded at TU Darmstadt. • A modified BCD algorithm with proven convergence offers parallelizable calibration. • The calibration method is tested with synthetic data and real image measurements.

Localization in terrestrial and non-terrestrial networks plays an important role in various applications, such as autonomous driving, robotics, and unmanned aerial vehicles. Although the relative distances between neighboring devices can be directly detected by embedded sensors, the relative distances between non-neighboring devices are usually not available, which results in a sparse version of the Euclidean Distance Matrix (EDM). Since the complete EDM is low-rank and the information of the relative distances is distributed over the network, we consider a distributed localization approach based on the low-rank matrix completion using the singular value thresholding algorithm. The proposed approach is carried out in a distributed manner as the singular values and singular vectors are estimated by the distributed eigenvalue decomposition. It avoids gathering all information in a central server and only requires direct communication and distance estimation between neighboring sensors. Hence, the distance information acquired in each sensor and the coordinates of the sensors are kept private to the sensor. The proposed distributed low-rank matrix completion approach is also applicable, e.g., in the distributed recommendation system.

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.

5G mechanisms typically rely on resource over-provisioning or static reservations to satisfy the stringent demands of critical connections. Consequently, 5G networks are inefficient in fulfilling application's low delay and high reliability requirements. Emerging 6G use cases will be even more demanding in terms of delay and reliability. Therefore, the usage of existing mechanisms would result in immense operational costs for the mobile network operators due to their in-efficiency. This highlights the need for investigating sophisticated mechanisms with the evolution towards 6G networks, providing reliability in a cost-efficient manner. This paper examines how to prioritize critical connections over non-critical ones, while constructively exploiting the available resources. To achieve this goal, we propose an intelligent admission control (AC) scheme for a radio access node (AN). More specifically, using AI/ML techniques, the AN forecasts the number of incoming critical connections and supports their reliability requirements by dynamically reserving resources for them, consequently affecting the admission of non-critical connections. Our simulation-based evaluations show that the proposed approach improves a baseline approach – not using intelligence –as it is capable of providing reliability to a larger number of connections, while efficiently utilizing system's resources. Thus, our work provides evidence of the potential of using intelligence for next-generation admission control design.

Coordinated weighted sum-rate maximization in multicell MIMO networks with intra- and intercell interference and local channel state at the base stations is recognized as an important yet difficult problem. A classical, locally optimal solution is obtained by the weighted minimum mean squared error (WMMSE) algorithm which facilitates a distributed implementation in multicell networks. However, it often suffers from slow convergence and therefore large communication overhead. To obtain more practical solutions, the unrolling/unfolding of traditional iterative algorithms gained significant attention. In this work, we demonstrate a complete unfolding of the WMMSE algorithm for transceiver design in multicell MU-MIMO interference channels with local channel state information. The resulting architecture termed GCN-WMMSE applies ideas from graph signal processing and is agnostic to different wireless network topologies, while exhibiting a low number of trainable parameters and high efficiency w.r.t. training data. It significantly reduces the number of required iterations while achieving performance similar to the WMMSE algorithm, alleviating the overhead in a distributed deployment. Additionally, we review previous architectures based on unrolling the WMMSE algorithm and compare them to GCN-WMMSE in their specific applicable domains.

Recent studies on designing 6G networks, especially when it comes to satisfying the stringent latency and reliability requirements, identify native integration of Artificial Intelligence (AI) as a key enabler. Although 5G systems support features to provide high-reliability communication, they mostly rely on resource over-provisioning and are hence inefficient. We identify the need for addressing the problem of resource-efficiency from the perspective of 6G systems. The dynamic behaviors of radio access networks, due to varying radio channel conditions, pose an additional challenge in achieving high resource-efficiency. In this respect, we present and evaluate a Machine Learning (ML)-based mechanism for efficient support of safety-critical communication with stringent latency and reliability requirements. This mechanism is embedded in the admission control (AC) of an access node (AN) and uses Least Absolute Shrinkage and Selection Operator (LASSO)-based resource budget prediction while admitting new connection requests to the network. The goal is to maximize the number of clients admitted into the system while maintaining the reliability of the previously admitted critical connections. Our simulation-based evaluations highlight that the proposed approach outperforms the baseline approach - not featuring ML - by about 17% in terms of the average per-session reliability of safety-critical connections at different network load conditions, and hence, provide further evidence on the potentials of ML for next-generation networks design.

The Partial Relaxation framework has recently been introduced to address the Direction-of-Arrival (DOA) estimation problem [1]–[3]. DOA estimators under the Partial Relaxation (PR) framework are computationally efficient while preserving excellent DOA estimation accuracy. This is achieved by keeping the structure of the signal from the desired direction unchanged while relaxing the structure of the signals from the remaining undesired directions. This type of relaxation allows to compute closed-form estimates for the undesired signal part and improves the accuracy of the DOA estimates compared to conventional spectral-search methods like, e.g. MUSIC. Following a similar approach as in [4] the PR framework is combined with the Orthogonal Least Squares (OLS) technique of [5]. A novel DOA estimator is proposed that is based on Partially-Relaxed Weighted Subspace Fitting (PR-WSF) in which the DOAs are iteratively estimated. Thereby, one DOA is estimated per iteration, while accounting for both the signal contributions under the previously-determined DOAs, with full signal structure, as well as the remaining DOAs with relaxed structure. Moreover, an efficient implementation of the Partially-Relaxed Orthogonal Least Squares Weighted Subspace Fitting (PR-OLS-WSF) method is proposed that provides similar computational cost as the MUSIC algorithm. Simulation results show that the proposed PR-OLS-WSF estimator provides excellent performance especially in difficult scenarios with low Signal-to-Noise-Ratio (SNR) and closely spaced sources.

We propose a new formulation for the joint phase retrieval and dictionary learning problem with a reduced number of regularization parameters to be tuned. A parallel algorithm based on the block successive convex approximation framework is developed for the proposed formulation. The performance of the algorithm is evaluated when applied to sparse channel estimation in a multi-antenna random access network. Simulation results on synthetic data show the efficiency of the proposed technique compared to the state-of-the-art method.

In this paper, the outlier production mechanism of the G-MUSIC Direction-of-Arrival estimation technique is investigated using tools from Random Matrix Theory. The G-MUSIC Direction-of-Arrival estimation technique is an improved version of the conventional MUSIC method that provides superior performance in low sample size scenarios. The stochastic behavior of the G-MUSIC cost function is analyzed in the asymptotic regime where both the number of snapshots and the number of antennas increase without bound at the same rate. The finite dimensional distribution of the G-MUSIC cost function is shown to be asymptotically jointly Gaussian. Furthermore, the probability of resolution of the G-MUSIC Direction-of-Arrival estimator is characterized by means of the derived asymptotic probability density function of the G-MUSIC cost function.

In practical applications, non-Gaussianity of the signal at the sensor array is detrimental to the performance of conventional Direction-of-Arrival (DOA) estimators developed under the Gaussian model. In this paper, we propose a novel robust DOA estimator from the data collected at the sensor array under the corruption of non-Gaussian interference and noise. Additionally, the Cramér-Rao bound for DOA parameters under the considered signal model is derived. Simulation results show that the proposed estimator exhibits near-optimal estimation performance under the assumed model while being robust to model mismatch and/or the presence of outliers.

Reliable connectivity between vehicle and mobile edge computing (MEC) server is paramount to exchange the information in time and without loss. Reliable vehicle-MEC communication is supported by different mechanisms of 3GPP 5G mobile networks, however, they are often inefficient in keeping the balance between reliability of the connection and the associated operational service costs of mobile operators, such as resource usage and signaling load, to provide the desired reliability. In this respect, we identify the challenges that need to be overcome to maintain cost-efficient reliable connection between vehicle and MEC server. We propose the usage of distributed intelligence to address the challenges and analyze the categories of distributed machine learning from the perspective of solving the challenges.

The Partial Relaxation approach has recently been proposed to solve the Direction-of-Arrival estimation problem [1], [2]. In this paper, we investigate the outlier production mechanism of the Partially Relaxed Deterministic Maximum Likelihood (PR-DML) Direction-of-Arrival estimator using tools from Random Matrix Theory. An accurate description of the probability of resolution for the PR-DML estimator is provided by analyzing the asymptotic stochastic behavior of the PR-DML cost function, assuming that both the number of antennas and the number of snapshots increase without bound at the same rate. The finite dimensional distribution of the PR-DML cost function is shown to be Gaussian in this asymptotic regime and this result is used to compute the probability of resolution.

A family of computationally efficient DOA estimators under the partial relaxation framework has recently been proposed. In this framework, the manifold structure of the "interfering" signals is relaxed, and only the manifold structure of one desired signal is retained. This particular type of relaxation results in closed-form estimates for the interference parameters and enhances the estimation performance compared to the conventional spectral-search methods. By adopting the principle of the partial relaxation approach, in this paper, a modification of the Orthogonal Matching Pursuit algorithm is proposed and applied to the Direction-of-Arrival estimation problem. In each iteration of the proposed partial relaxation-based orthogonal matching pursuit (PR-OMP) algorithm, the impact on the receive signal from the previously-estimated directions and the remaining direction with the relaxed steering structure are considered. Simulations show that the proposed PR-OMP algorithm outperforms conventional estimators in the case of low Signal-to-Noise-Ratio or small number of snapshots.

In this paper, we study the sparse phase retrieval problem, that is, to estimate a sparse signal from a small number of noisy magnitude-only measurements. We propose an iterative soft-thresholding with exact line search algorithm (STELA). It is a parallel coordinate descent algorithm, which has several attractive features: i) fast convergence, as the approximate problem solved at each iteration exploits the original problem structure, ii) low complexity, as all variable updates have a closed-form expression, iii) easy implementation, as no hyperparameters are involved, and iv) guaranteed convergence to a stationary point for general measurements. These advantages are also demonstrated by numerical tests.

This paper deals with semi-blind channel estimation in Single-Input Single-Output (SISO) Orthogonal Frequency Division Multiplexing (OFDM) communications system. The proposed algorithm proceeds in two main stages. The first one addresses the pilot-based Time-Of-Arrival (TOA) estimation using subspace methods and then estimates the channel through its specular model. In the second stage, one considers a decision feedback equalizer that is used to refine the channel parameters estimates. Simulation results show that good performance can be reached with only one OFDM pilot symbol with appropriate windowing using only one iteration. A significant performance improvement as compared to the pilot-based TOA method is observed.

In this paper, the Cramér-Rao Bound for the Direction-ofArrival parameter under the partial relaxation framework is derived. We introduce a non-redundant parameterization of the signal model corresponding to the partial relaxation framework, in which the array structure in part of the steering matrix is neglected while the rank of the relaxed steering matrix is maintained. We prove that the stochastic Cramér-Rao Bound for the Direction-of-Arrival parameter under the partial relaxation signal model is lower-bounded by that of the conventional stochastic Cramér-Rao Bound. Furthermore, we prove that the partial relaxation estimator for the Weighted Subspace Fitting criterion asymptotically achieves the conventional Cramér-Rao Bound in the case of uncorrelated source signals.

Hybrid analog-digital precoding significantly reduces the hardware costs in massive multiple-input multiple-output (MIMO) transceivers when compared with fully digital precoding at the expense of increased transmit power. In order to mitigate the above-mentioned shortfall, we use the concept of constructive interference-based precoding, which has been shown to offer significant transmit power savings when compared with the conventional interference suppression-based precoding in fully digital multiuser MIMO systems. Moreover, in order to circumvent the potential quality-of-service degradation at the users due to the hardware impairments in the transmitters, we judiciously incorporate robustness against such vulnerabilities in the precoder design. Since the undertaken constructive interference-based robust hybrid precoding problem is nonconvex with infinite constraints and thus difficult to solve optimally, we decompose the problem into two subtasks, namely, analog precoding and digital precoding. In this paper, we propose an algorithm to compute the optimal constructive interference-based robust digital precoders. Furthermore, we devise a scheme to facilitate the implementation of the proposed algorithm in a low-complexity and distributed manner. We also discuss the block-level analog precoding techniques. The simulation results demonstrate the superiority of the proposed algorithm and its implementation scheme over the state-of-the-art methods.

In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand, its convergence to a stationary point is guaranteed, while ADMM algorithms only converge for convex problems. Furthermore, the exact line search procedure in the proposed algorithm is performed efficiently in closed-form to avoid the meticulous choice of stepsizes, which is however a common bottleneck in subgradient algorithms and successive convex approximation algorithms. Finally, the proposed algorithm is numerically tested.

Future generations of mobile communication networks are envisioned to utilize dense deployments of heterogeneous cell types to fulfill increasing performance requirements. An efficient and optimized utilization of the network resources, including user allocation management and load balancing between cells, is crucial for such networks to maintain high throughput and to handle increasing interferences. Due to the combinatorial nature of user allocation, load balancing is a mixed-integer linear problem that does not scale well will the number of users and cells. Heuristic methods to solve similar problems in this context are available, but they typically require extensive coordination between network entities while achieving highly suboptimal performance. We propose a machine learning based approach that achieves close to optimal performance while requiring very limited local interaction and computational effort during operation.

In the partial relaxation approach, at each desired direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. By adopting this approach, in this paper, a new estimator based on the unconstrained covariance fitting problem is proposed. To obtain the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied. Simulation results show that the performance of the proposed estimator is superior to the classical and other partial relaxation methods, especially in the case of low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a reasonable computational cost.

In this paper, we consider the energy efficiency optimization problem in MIMO multi-cell systems, where all users suffer from intercell interference. To solve this multi-objective optimization problem, we consider both socially optimal solutions and max-min fairness solutions. We propose two novel iterative algorithms that converge to socially optimal solutions and max-min fairness solutions. The proposed algorithms have the following advantages: 1) fast convergence as the structure of the original optimization problem is preserved as much as possible in the approximate problem solved in each iteration, and 2) efficient implementation as each approximate problem is natural for parallel computation and/or its solution has a closed-form expression. The advantages of the proposed algorithms are also illustrated numerically.

For the upcoming fifth generation of wireless mobile communication networks, heterogeneous cellular architectures with a dense deployment of low-power small cells have been proposed to satisfy increasing data demands. Energy harvesting small cells, which operate with renewable energy sources such as solar energy and the potential for power storage, can be utilized to decrease the power consumption of the network if their activities are carefully scheduled based on the forecasted demand. In this work, we propose a novel approach for small cell energy management and activity scheduling, where not only the small cell activity but also the duration of time-slots in which the schedule is applied, are optimized. Cell load balancing is performed by solving separate mixed integer optimization problems, one each for activity optimization and for timescale optimization. Simulation results show that the proposed scheme is successful in finding an optimized small cell activity schedule for given energy levels and demand forecasts, and that there is a significant benefit achievable through the proposed timescale optimization approach.

We consider the problem of designing hybrid analog-digital beamformers in a downlink multi-user large-scale MIMO system. The objective is to minimize the total transmit power, while fulfilling SINR targets of all users. A dual virtual uplink problem is formulated for the original downlink problem based on the uplink-downlink duality theory, in order to decouple the digital beamformers in the constraints. Furthermore, an optimal method and a sub-optimal iterative method are devised to compute solutions of the hybrid beamforming problem. Simulation results demonstrate that the iterative method yields nearly optimal performance, despite its remarkably low complexity.

In this paper, we study a constructive interference based cognitive radio beamforming optimization problem under perfect channel state information at the transmitter and the knowledge of data information. The beamformers are designed to minimize the worst secondary user's symbol error probability under constraints on the instantaneous total transmit power, and the power of the instantaneous interference in the primary link. The problem is formulated as a bivariate probabilistic constrained programming problem and can be solved using the barrier method. Our simulations indicate that the proposed technique offers a significantly improved performance over the conventional technique, while guaranteeing the quality of service (QoS) of primary users on an instantaneous basis, in contrast to the average QoS guarantees of conventional beamformers.

We present an equivalent, compact reformulation of the ℓ2,1mixed-norm minimization problem for joint sparse signal reconstruction from multiple measurement vectors (MMVs). The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the joint sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the ℓ2,1mixed-norm minimization and the atomic-norm minimization.

Parameter estimation has applications in many fields of signal processing, such as spectral analysis or direction-of-arrival estimation. Subspace-based methods like root-MUSIC and ESPRIT provide high parameter resolution at low computational complexity by exploiting specific sampling structure, namely uniform linear sampling and shift-invariant sampling, respectively. On the other hand, compressed sensing has been shown to outperform subspace-based methods in difficult scenarios such as low number of measurement vectors, high noise power or correlated signals. While it is well known that uniform sampling admits gridless compressed sensing methods, e.g., based on atomic norm minimization, no such approaches are known for shift-invariant sampling. In this paper we present a novel approach for gridless compressed sensing under shift-invariant sampling. We show by numerical experiments that the proposed method outperforms ESPRIT in difficult scenarios.

Multi-hop communication is a spectral-efficient approach for connecting multiple pairs when direct links are absent or have insufficient strength. In this paper, we highlight the benefits of improper Gaussian signaling for a multi-pair full-duplex MIMO relay network in terms of power efficiency. By employing improper Gaussian transmission, the power minimization problem under rate constraints is intrinsically a non-convex problem due to non-convex rate expressions in the constraint set. We utilize Fenchel's inequality to linearize the non-convex part of the constraint, which results in feasible solutions of the problem in polynomial time. This approximation results in an upper-bound for the original problem which gets tighter in the number of iterations performed. The solution is compared with analytical beamforming solutions, namely zero-forcing (ZF) and maximum-ratio transmission/combining (MRT/MRC). Due to the feasibility of single rank real-valued transmission in improper Gaussian signaling, the optimal solution switches to single rank transmission depending on the constraints defined by the requests of the users, which can not be captured by proper Gaussian signaling.

In this paper, we propose a novel iterative algorithm based on successive convex approximation for the nonconvex energy efficiency optimization problem in massive MIMO networks. The stationary points of the original problem are found by solving a sequence of successively refined approximate problems, and the proposed algorithm has the following advantages: 1) fast convergence as the structure of the original energy efficiency function is preserved as much as possible in the approximate problem, and 2) easy implementation as each approximate problem is natural for parallel computation and all variable updates have a closed-form expression. The proposed algorithm is guaranteed to converge and its advantages are also illustrated numerically.

In this work we present a novel scheme for load management in microgrids based on stochastic scheduling of loads under risk-limiting constraints. When trying to enforce adequate power supply in a microgrid, the volatility of renewable resources such as wind energy has to be considered. In the risk of inadequate power supply, loads have to be scheduled, which can be achieved by directly controlling individual loads or by setting pricing incentives to encourage beneficial behavior of the customers. A common drawback of conventional methods lies in the need of sophisticated control strategies and a significant amount of real-time signaling exchange between the microgrid and the central control unit. To address these issues, we propose a scheme that does not require a direct control of individual loads. Our method relies on sorting the appliances in the network into groups, and allowing these groups to schedule themselves stochastically according to broadcasted scheduling probabilities. In this paper, we propose an optimization problem to determine these group scheduling probabilities, as well as for choosing the best utilization of conventional generators, in a day-ahead planning scenario of an isolated microgrid. Using an outage-risk limiting constraint, we control the risk of inadequate power supply causing network outages. The proposed scheme can be easily implemented with unidirectional communication from a central control unit via simple broadcast messages.

In this paper, we investigate user association and resource block (RB) allocation in downlink heterogeneous cellular networks. Our goal is to jointly optimize user association and RB allocation to maximize network throughput while taking into account fairness among users. To effectively control interference, RB muting is employed. The problem is addressed in an integer linear programming (ILP) framework. Due to the combinatorial nature of the problem, the computational complexity of solving it becomes prohibitively high even for medium size networks. Therefore, we propose to decouple user association from the original problem, and formulate a low-complexity ILP problem for the optimal RB allocation and muting. Simulation results show that the proposed RB allocation and muting scheme achieves significantly higher throughput and better fairness compared with conventional schemes.

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading ] to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cramer-Rao bound for a low number of iterations.

This paper addresses multiuser downlink beamforming with shaping constraints under the assumption that the transmitter has long-term covariance based channel state information (CSI). Beamformers are designed to maximize the minimum average signal-to-interference-plus-noise ratio (SINR) of users subject to a total transmit power constraint and additional shaping constraints. We combine beam-forming with full-rate quasi-orthogonal space time block coding (QOSTBC) to increase the number of beamforming weight vectors and associated degrees of freedom much beyond the limits achieved by the Alamouti code in the beamformer design. The use of QOSTBC destroys the full-orthogonality structure of the corresponding equivalent channel matrix such that generally maximum-likelihood (ML) pairwise decoding has to be applied for optimal decoding. As an alternative to the pairwise decoding, we propose a simple phase rotation scheme on beamformers at the transmitter side that enables simplified symbol-wise decoding. The original beam-forming problem is transformed to a semidefinite programming (SDP) problem which can be solved optimally for a massive number of shaping constraints. Simulation results demonstrate a significant performance improvement over the existing approaches.

The maximum likelihood (ML) and maximum a posteriori (MAP) estimation techniques are widely used to address the direction-of-arrival (DOA) estimation problems, an important topic in sensor array processing. Conventionally the ML estimators in the DOA estimation context assume the sensor noise to follow a Gaussian distribution. In real-life application, however, this assumption is sometimes not valid, and it is often more accurate to model the noise as a non-Gaussian process. In this paper we derive an iterative ML as well as an iterative MAP estimation algorithm for the DOA estimation problem under the spherically invariant random process noise assumption, one of the most popular non-Gaussian models, especially in the radar context. Numerical simulation results are provided to assess our proposed algorithms and to show their advantage in terms of performance over the conventional ML algorithm.

In this work, we propose a differential beamforming (DBF) scheme for bi-directional communication between two single-antenna terminals via a multi-antenna relay station (RS). The proposed scheme utilizes differential phase-shift keying modulation to enable beamforming at the RS without knowledge of the instantaneous channel state information (CSI) at any entity in the network. In our differential scheme, receive and transmit beamforming at the RS is performed based on the implicit CSI contained in the received signals in the preceding time slots. Thus, the DBF scheme is applicable even if the communication channels are time-variant. For time-invariant channels, we show that our DBF scheme is associated with a performance penalty of 3 dB as compared to the ideal amplify-and-forward relaying scheme, which requires perfect CSI. Our simulation results confirm the analytical results for time-invariant channels. For time-variant channels, the simulation demonstrate a high performance gain of the DBF scheme compared to schemes of the literature.

We consider in this paper multiuser downlink beamforming with interference cancellation (BFIC). In our BFIC problem, the total transmitted power of the base station (BS) is minimized under signal-to-interference-plus-noise ratio (SINR) requirements of the mobile stations (MSs) and single-stage interference cancellation (SSIC) is adopted at the MSs. The challenge of the problem lies in its combinatorial and non-convex nature. We propose a semidefinite programming (SDP) based branch-and-bound (BnB) algorithm to (optimally) solve the BFIC problem. The SDP-based BnB algorithm employs SDP and sequential second-order cone programming. We further develop a fast heuristic algorithm for large-scale applications. Simulations show that employing SSIC achieves significant reductions in total transmitted BS power. The proposed SDP-based BnB algorithm optimally solves all considered instances of the BFIC problem, and the heuristic algorithm yields near-optimal solutions.

The resolvability of two closely-spaced signals is an important performance measure for parametric estimation problems. In this paper we investigate the so-called resolution limit (RL) in a MIMO radar context, i.e., the minimum angular separation required to resolve two closely-spaced targets. Due to the limited number of elementary scatterers, the Gaussian modeling of the clutter is inappropriate. In our analysis, we consider a K-distributed clutter which is a well-established approximation of the real clutter. Finally, our RL's expression reveals a number of insightful properties that are discussed in detail and, numerical examples are provided to corroborate the theoretical analysis.

This paper considers robust codebook-based downlink beamforming (i.e., single-layer precoding), where the beamformer of each user is chosen from a fixed beamformer codebook defined, e.g., in LTE and LTE-A. Admission control and power allocation are embedded in the precoding vector selection procedure. The objective is to maximize the system utility, defined as the revenue gained from admitting users minus the cost for the transmitted power of the base station. We adopt the quality-of-service constrained approach and the robustness against channel covariance estimation errors is realized with worst-case design. The robust codebook-based beamforming problem, which is a bi-level mixed integer program, is converted into a more tractable mixed integer second-order cone program. Techniques are proposed to customize the convex continuous relaxation based branch-and-cut algorithm to compute the optimal solutions. A low-complexity inflation procedure is also developed to compute the near-optimal solutions for practical applications. Numerical examples show that the gap between the average number of admitted users achieved by the fast inflation procedure and that of the optimal solutions is less than 11.6% for all considered simulation settings. Further, the inflation procedure yields optimal solutions in 88% of the Monte Carlo runs under specific parameter settings.

In this paper we take a new perspective on the worst case robust multiuser downlink beamforming problem with imperfect second order channel state information at the transmitter. Recognizing that all channel covariance matrices form a Riemannian manifold, we propose to use a measure properly defined along this manifold in order to model the set of mismatched channel covariance matrices for which robustness shall be guaranteed. This leads to a new robust beamforming problem formulation for which a convex approximation is derived. Simulation results show a dramatically improved performance of the proposed scheme, both in terms of transmission power and constraint satisfaction, as compared to the previous methods.

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical expression of this resolution limit, w.r.t. the angular parameters of interest between two closely spaced point sources in the far-field region. As by-products, closed-form expressions of the Cramér-Rao bound have been derived. Finally, with the aid of numerical tools, we confirm the validity of our derivation and provide a detailed discussion on several enlightening properties of the ARL revealed by our expression, with an emphasis on the impact of the signal correlation.

This letter considers joint beamformer assignment and power allocation (BAPA) for codebook-based downlink beamforming. The BAPA problem represents a mixed integer combinatorial program since beamformer assignments involve binary decisions and beamformer assignments of multiple users are coupled in the downlink SINR constraints. We develop a mixed integer linear program formulation of the BAPA problem, which can be solved using, e.g., the branch-and-cut method. To derive low-complexity solutions, we introduce a virtual uplink problem, in which beamformer assignments of different users are decoupled. We establish the uplink-downlink duality of the two problems and develop a customized iterative algorithm to solve the BAPA problem. Analytic studies show that the customized algorithm yields either optimal (within the desired numerical accuracy) solutions of the BAPA problem (when it is feasible), or infeasibility certificates (when infeasible). The performance of the algorithm is demonstrated with numerical examples.

We consider the problem of transmit beamforming in multi-group multicasting systems with covariance-based channel state information (CSI) available at the transmitter where the total transmitted power is minimized subject to quality-of-service (QoS) constraints at the receivers. Previous approaches for this problem are based on semidefinite relaxation (SDR) and require randomization and costly power scaling which is avoided in our approach. The proposed technique can be viewed as a non-trivial extension of the iterative second-order cone programming (SOCP) approach, which is restricted to the case of instantaneous (rank-one) CSI, to the beamforming problem with higher-rank channel covariance matrices. Computer simulations reveal that the proposed technique exhibits superior performance in terms of total transmitted power at a reduced computational complexity as compared to the SDR method.

Coordinated Multi-Point Transmission (CoMP) has been proposed for 4G standards, like WiMAX and LTE-Advanced, as an effective mean to control intercell interference and to increase spectral efficiency in single frequency reuse networks. In practical systems, the remarkable benefits of CoMP operation over conventional single basestation transmission need to be traded against a significant overhead in network complexity and associated operational costs. In order to retain the benefits of CoMP at reasonable costs, we consider the problem of joint basestation selection and multicell beamforming (JBSB). We address this problem via a mixed integer second order cone programming (MI-SOCP) approach. We propose a novel MI-SOCP formulation of the JBSB problem and a reformulation with tighter continuous relaxations. Based on this formulation, we propose fast algorithms to find almost optimal feasible solutions. We show via simulations that the proposed algorithms outperform existing solutions in terms of both complexity and total transmitted power at a guaranteed signal-to-interference-plus-noise-ratio (SINR) level at each mobile station (MS).

We consider the problem of worst-case robust beamforming for multi-group multicasting network with erroneous channel state information (CSI). In previous beamforming techniques robustness is ensured for all mismatch matrices of bounded Frobenius norm. In contrast, we present an alternative method of bounding the channel uncertainties, where we only limit the trace of the mismatch matrices. This approach leads to a problem formulation of reduced complexity as compared to the previous methods. Our goal is to minimize the total transmitted power subject to the worst-case user quality-of service (QoS) constraints. Lagrange duality is used to obtain a simple reformulation of the worst-case beamforming problem. The resulting non-convex problem can then be converted into a convex form using semidefinite relaxation (SDR) that can be solved efficiently using interior point methods. The resulting problem is a linear second-order cone programming (SOCP) problem as opposed to the quadratic SOCP problems in the previous robust approaches. Simulation results also show that the proposed method offers a significantly improved performance in terms of transmitted power.

We generalize the concept of multiuser peer-to-peer (MUP2P) relay networks to that of a multi-group multicasting (MGM) relay network where each source may broadcast its message to a group of multiple users. State-of-the-art beamforming methods, which have been proposed for MUP2P relay networks, are shown to be straightforwardly extendable to such MGM networks. These methods aim to minimize the total transmitted relay power subject to receiver quality-of-service (QoS) constraints using convex approximations of the underlying non-convex problem. Due to the increase in number of receivers, these approximations may become inaccurate in the MGM case leading to severe performance degradation and problem infeasibility. To avoid this drawback, we propose an iterative method where the aforementioned convex approximations are successively improved. Our technique overcomes the difficulties emerging in the MGM and MUP2P relay networks for large numbers of users and outperforms the state-of-the-art methods developed for MUP2P relay networks.

In this paper, a new direction-of-arrival (DOA) estimation technique applicable to partly-calibrated arrays (PCAs) composed of arbitrary subarrays with unknown subarray displacements is developed. The new method is not restricted to any specific array geometry and allows joint estimation of the DOAs and calibration of the entire sensor array. Computer simulations show that the proposed approach substantially outperforms the known DOA estimation methods applicable to such PCAs.

We consider an underlay cognitive radio system consisting of a secondary transmitter (ST), K secondary receivers (SRs) and a primary receiver (PR). Data transmission is granted to the ST under the constraint that the generated peak interference to the PR is below a predetermined interference temperature level. Assuming that the ST can adaptively adjust its transmit power according to the fading state of the channel, our objective is to analyze the link reliability in terms of the symbol error rate (SER). In particular, we derive the exact SER expressions under the assumption that opportunistic scheduling is applied at the ST, where the SR with the highest channel gain is exclusively selected for data transmission. Numerical simulations are performed to verify the obtained SER expressions. Our results show that there exists an error floor region due to the interference constraint, i.e., the SER approaches to a certain constant as the allowed peak transmit power threshold increases. Moreover, we show that opportunistic scheduling can improve the SER performance under a fixed interference constraint.

We consider the overlay cognitive radio channel where the cognitive user is admitted to transmit simultaneously with the primary user provided that the instantaneous rate of primary link is not degraded. Assuming causal knowledge of the primary user's message at the cognitive transmitter (CT), we analyze the transmission rates of the cognitive user in the single-input multiple-output (SIMO) and the multiple-input single-output (MISO) configurations. In particular, the CT uses a part of its transmit power to assist the primary user in delivering the primary user's message and the other part of its power is used to deliver its own message. The transmit power and the beamformers are designed to maximize the rate of the cognitive user while fixing the the rate of the primary user. Our simulation results show that the proposed scheme yields improved system performance compared to the interweave scheme where any interference to the primary user is prohibited.

We address the problem of worst-case robust downlink beamforming for a multi-antenna secondary network (SN) in a cognitive radio framework. An important issue is the interference leaked to the primary users (PUs) resulting from the transmission between the SN base station and the secondary users (SUs). Our aim is to provide the SUs with a minimum acceptable quality-of-service (QoS), while keeping the interference to the PUs below a given threshold. Previous solutions for this scenario involve several coarse approximations. Here we avoid these approximations and obtain an exact reformulation of the worst-case problem using Lagrange duality. Finally, we use semidefinite relaxation (SDR) to convert the resulting problem to a convex form. Computer simulations show that the SDR step does not involve any approximation as the resulting solution is always rank-one.

We study the fundamental capacity limits of the underlay cognitive broadcast (BC) channel under average transmit power and average interference power constraints. In a fading environment, the sum capacity is found from a constrained water-filling solution given in. This solution is investigated for different average transmit power budgets and average interference thresholds, and its specific regions are characterized. Further, capacity expressions are derived for the Rayleigh fading case. In a system with K users and Rayleigh fading channels, it is shown that the capacity scales like log(log(K)) for large K. This result indicates that the same multiuser diversity gain can be achieved in a cognitive BC system as in the conventional BC system without spectrum sharing.

In this paper, the downlink opportunistic scheduling approach is studied in a multiuser environment with single-antenna transmitter and users. Exact bit error rate (BER) expressions are derived under the assumptions of full and quantized channel state information (CSI) at the transmitter. These expressions are then used to optimize the channel state feedback parameters. Moreover, asymptotic BERs are investigated in the limiting cases of a high signal-to-noise ratio (SNR) and a large number of users K. It is shown that both under the full and quantized CSI assumptions, the achieved BER is proportional to SNR-Kand K-SNRin these two asymptotic cases, respectively. This means that the diversity order is equal to K, whereas the multiuser diversity gain is equal to SNR. In the case when the CSI feedback is quantized, the impact of feedback errors on the achieved BER is studied. It is shown that the opportunistic scheduling can greatly improve the BER performance even if the feedback is quite low-rate and erroneous.

A novel algorithm for estimating multi-dimensional damped harmonics is proposed. A matrix polynomial is formed from the weighed sum of multiple shift invariances contained in the data model. Necessary and sufficient conditions are derived that reveal that the damped harmonics can be uniquely determined from the roots of the matrix polynomial. The proposed algorithm reveal a seamless link between two important classes of search free subspace methods. The classical rooting based harmonic estimation methods that exploit the complete invariance structure and the single invariance ESPRIT algorithms. We show that both approaches can be expressed under this general framework by an appropriate choice of the weights.

We address the problem of estimating the frequencies and damping factors of a multidimensional signal which consists of several damped complex exponentials. Such a problem is of interest in several applications, such as nuclear magnetic resonance spectroscopy, where the 2-dimensional (2D) frequencies and damping factors are used to determine the structure of proteins. We herein propose a new algorithm which exploits the multiple-invariance structure that exists in the data model. Unlike search-based parameter estimation techniques, such as D-MUSIC of Y. Li et al. (1998), which have been developed for multidimensional harmonic retrieval of damped exponentials, our algorithm uses polynomial rooting to obtain the parameters of interest efficiently in a search-free fashion.

In array interpolation, the optimal design of the virtual array geometry is still an open question. It is usually done heuristically by placing a virtual ULA into the center of the original array and fitting orientation and aperture by rule of thumb. In this paper, we parameterize the array manifold by its arc length and use this representation for the design of a virtual array manifold that optimally matches the directional properties of the original array. We verify the advantages of our new design method by simulation results and give some deeper understanding about the interrelation between the interpolation error, the condition number of the interpolation matrix and the DOA estimation bias.

Multidimensional harmonic retrieval (HR) problems often appear in the context of MIMO wireless channel sounding. In particular, for a double-directional parametric MIMO channel model with uniform linear transmit and receive arrays, and a fixed wireless scenario (static - no Doppler), fitting the channel model parameters amounts to a 3D harmonic retrieval problem. For this latter problem, we develop two new algorithms. One is based on conjugate-folding of the 3D data and reduction to an eigenvalue decomposition problem; the other on a 3D version of the rank reduction estimator (RARE) applied to a subspace extracted from a single data snapshot, using 3D conjugate-folding. Both algorithms remain operative close to the best known model identifiability boundary. The two algorithms are compared via pertinent simulations.

We address the problem of data independent robust array interpolation over large angular sectors. Previous interpolation methods apply the root-MUSIC principle to interpolation data of a predefined virtual ULA manifold. These methods either suffer from severely biased direction-of-arrival estimates due to interpolation errors or rely on data dependent interpolation matrix design. In this paper a new interpolation approach is proposed. Instead of transforming the original array geometry to the rather restrictive ULA structure, here interpolation is performed with the objective to create a virtual array manifold which is a shifted version of the real array manifold. This artificial shift-invariance can be exploited by the well-known ESPRIT algorithm. A joint design of virtual array geometry and interpolation matrix yields additional degrees of freedom which reduce interpolation errors and allow us to increase the interpolation sector. The new algorithm enjoys both simple design procedure and fast implementation and offers reliable DOA estimation for a wide range of different scenarios.

In this paper, a new approach to the multi-dimensional harmonic retrieval problem is proposed. The novel method is based on a multi-dimensional extension of the Rank Reduction Estimator (RARE), originally developed for DOA estimation in partly calibrated arrays. In the K-D RARE algorithm the frequency parameters in the various dimensions are sequentially estimated. The dimensionality of the estimation problem and therefore the computational load of the optimization procedure is successively reduced exploiting the rich multidimensional structure of the estimation problem. This important property yields various benefits like high estimation performance, weak identifiability conditions and automatically associated parameter estimates. The performance of the algorithm is illustrated with the example of MIMO communication channel estimation based on the double-directional channel model. Numerical examples based on simulated and measured data recorded from the RUSK vector channel sounder at 2 GHz are presented.

We study the uniqueness of the signal Direction Of Arrival (DOA) estimates obtained using the RAnk Reduction Estimator (RARE) [I] in partly calibrated subarray-based sensor arrays. A new identifiability condition is derived for such class of arrays which guarantees that the array manifold is unambiguous. The equivalence of the MUSIC solution for the signal DOA's (obtained in the fully calibrated array case) and the RARE solution (obtained in the case of partly calibrated array of the same configuration) is proved and the uniqueness of the RARE DOA estimates is established.

We study Friedlander's (1993) array interpolation technique, whose main shortcoming in multisource scenarios is that it does not provide sufficient robustness against sources arriving outside specified interpolation sectors. In this letter, we develop a new robust interpolation approach by minimizing the interpolation error inside the sectors of interest while setting multiple "stopband" constraints outside these sectors to prevent performance degradation effects caused by out-of-sector sources. Computationally efficient convex formulations of the robust interpolation matrix design problem using second-order cone programming are derived.

The stochastic Cramer-Rao bound (CRB) plays an important role in array processing because several high-resolution direction-of-arrival (DOA) estimation methods are known to achieve! this bound asymptotically In this paper, we study the stochastic CRB on DOA estimation accuracy in the general case of arbitrary unknown noise field parametrized by a vector of unknowns. We derive explicit closed-form expressions for the CRB and examine its properties theoretically and by representative numerical examples.

We consider the direction finding problem in time-varying arrays composed of identically oriented subarrays displaced by unknown vector translations. A new eigenstructure-based estimator is proposed for such a class of partly calibrated sensor arrays.

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.