arXiv subjects

Geert Leus

Publications and source records attributed to Geert Leus.

At least 109 records · Page 6Linked to original sources

arXiv2015

Achievable Rates of Multi-User Millimeter Wave Systems with Hybrid Precoding

Millimeter wave (mmWave) systems will likely employ large antenna arrays at both the transmitters and receivers. A natural application of antenna arrays is simultaneous transmission to multiple users, which requires multi-user precoding at the transmitter. Hardware constraints, however, make it difficult to apply conventional lower frequency MIMO precoding techniques at mmWave. This paper proposes and analyzes a low complexity hybrid analog/digital beamforming algorithm for downlink multi-user mmWave systems. Hybrid precoding involves a combination of analog and digital processing that is motivated by the requirement to reduce the power consumption of the complete radio frequency and mixed signal hardware. The proposed algorithm configures hybrid precoders at the transmitter and analog combiners at multiple receivers with a small training and feedback overhead. For this algorithm, we derive a lower bound on the achievable rate for the case of single-path channels, show its asymptotic optimality at large numbers of antennas, and make useful insights for more general cases. Simulation results show that the proposed algorithm offers higher sum rates compared with analog-only beamforming, and approaches the performance of the unconstrained digital precoding solutions.

cs.IT↗

arXiv2015

Sampling of graph signals with successive local aggregations

A new scheme to sample signals defined in the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so-called graph-shift operator. Most of the works that have looked at this problem have focused on using the value of the signal observed at a subset of nodes to recover the signal in the entire graph. Differently, the sampling scheme proposed here uses as input observations taken at a single node. The observations correspond to sequential applications of the graph-shift operator, which are linear combinations of the information gathered by the neighbors of the node. When the graph corresponds to a directed cycle (which is the support of time-varying signals), our method is equivalent to the classical sampling in the time domain. When the graph is more general, we show that the Vandermonde structure of the sampling matrix, which is critical to guarantee recovery when sampling time-varying signals, is preserved. Sampling and interpolation are analyzed first in the absence of noise and then noise is considered. We then study the recovery of the sampled signal when the specific set of frequencies that is active is not known. Moreover, we present a more general sampling scheme, under which, either our aggregation approach or the alternative approach of sampling a graph signal by observing the value of the signal at a subset of nodes can be both viewed as particular cases. The last part of the paper presents numerical experiments that illustrate the results developed through both synthetic graph signals and a real-world graph of the economy of the United States.

cs.SI↗

arXiv2015

Distributed Autoregressive Moving Average Graph Filters

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

cs.SI↗

arXiv2015

Limited Feedback Hybrid Precoding for Multi-User Millimeter Wave Systems

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

cs.IT↗

arXiv2015

Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics

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

math.ST↗

arXiv2014

Compressive Periodogram Reconstruction Using Uniform Binning

In this paper, two problems that show great similarities are examined. The first problem is the reconstruction of the angular-domain periodogram from spatial-domain signals received at different time indices. The second one is the reconstruction of the frequency-domain periodogram from time-domain signals received at different wireless sensors. We split the entire angular or frequency band into uniform bins. The bin size is set such that the received spectra at two frequencies or angles, whose distance is equal to or larger than the size of a bin, are uncorrelated. These problems in the two different domains lead to a similar circulant structure in the so-called coset correlation matrix. This circulant structure allows for a strong compression and a simple least-squares reconstruction method. The latter is possible under the full column rank condition of the system matrix, which can be achieved by designing the spatial or temporal sampling patterns based on a circular sparse ruler. We analyze the statistical performance of the compressively reconstructed periodogram including bias and variance. We further consider the case when the bins are so small that the received spectra at two frequencies or angles, with a spacing between them larger than the size of the bin, can still be correlated. In this case, the resulting coset correlation matrix is generally not circulant and thus a special approach is required.

cs.OH↗

arXiv2014

Distributed Time-Varying Stochastic Optimization and Utility-Based Communication

We devise a distributed asynchronous stochastic epsilon-gradient-based algorithm to enable a network of computing and communicating nodes to solve a constrained discrete-time time-varying stochastic convex optimization problem. Each node updates its own decision variable only once every discrete time step. Under some assumptions (among which, strong convexity, Lipschitz continuity of the gradient, persistent excitation), we prove the algorithm's asymptotic convergence in expectation to an error bound whose size is related to the constant stepsize choice alpha, the variability in time of the optimization problem, and to the accuracy epsilon. Moreover, the convergence rate is linear. Then, we show how to compute locally stochastic epsilon-gradients that depend also on the time-varying noise probability density function (PDF) of the neighboring nodes, without requiring the neighbors to send such PDFs at each time step. We devise utility-based policies to allow each node to decide whether to send or not the most up-to-date PDF, which guarantee a given user-specified error level epsilon in the computation of the stochastic epsilon-gradient. Numerical simulations display the added value of the proposed approach and its relevance for estimation and control of time-varying processes and networked systems.

math.OC↗

arXiv2014

Cooperative Compressive Power Spectrum Estimation

We examine power spectrum estimation from wide-sense stationary signals received at different wireless sensors. We organize multiple sensors into several groups, where each group estimates the temporal correlation only at particular lags, which are different from group to group. A fusion centre collects all the correlation estimates from different groups of sensors, and uses them to estimate the power spectrum. This reduces the required sampling rate per sensor. We further investigate the conditions required for the system matrix to have full column rank, which allows for a least-squares reconstruction method.

math.SP↗

arXiv2014

Sparsity-Promoting Sensor Selection for Non-linear Measurement Models

Sensor selection is an important design problem in large-scale sensor networks. Sensor selection can be interpreted as the problem of selecting the best subset of sensors that guarantees a certain estimation performance. We focus on observations that are related to a general non-linear model. The proposed framework is valid as long as the observations are independent, and its likelihood satisfies the regularity conditions. We use several functions of the Cramér-Rao bound (CRB) as a performance measure. We formulate the sensor selection problem as the design of a selection vector, which in its original form is a nonconvex l0-(quasi) norm optimization problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. We also propose a projected subgradient algorithm that is attractive for large-scale problems and also show how the algorithm can be easily distributed. The proposed framework is illustrated with a number of examples related to sensor placement design for localization.

cs.IT↗

arXiv2014

Cramer Rao Lower Bound for Underwater Range Estimation with Noisy Sound Speed Profile

In this paper, the Cramer Rao bound (CRB) for range estimation between two underwater nodes is calculated under a Gaussian noise assumption on the measurements. The nodes can measure their depths, their mutual time of flight, and they have access to noisy sound speed samples at different depths. The effect of each measurement on the CRB will be analyzed, and it will be shown that for long distances, the effect of the sound speed measurement noise is dominant, and its impact depends on the positions of the nodes, actual sound speed profile, the number of sound speed samples, and the depths at which the sound speed samples are gathered.

cs.IT↗

arXiv2014

Compressive Joint Angular-Frequency Power Spectrum Estimation

We introduce a new compressive power spectrum estimation approach in both frequency and direction of arrival (DOA). Wide-sense stationary signals produced by multiple uncorrelated sources are compressed in both the time and spatial domain where the latter compression is implemented by activating only some of the antennas in the underlying uniform linear array (ULA).We sample the received signal at every active antenna at sub-Nyquist rate, compute both the temporal and spatial correlation functions between the sub-Nyquist rate samples, and apply least squares to reconstruct the full-blown two-dimensional power spectrum matrix where the rows and columns correspond to the frequencies and the angles, respectively. This is possible under the full column rank condition of the system matrices and without applying any sparsity constraint on the signal statistics. Further, we can estimate the DOAs of the sources by locating the peaks of the angular power spectrum. We can theoretically estimate the frequency bands and the DOAs of more uncorrelated sources than active sensors using sub-Nyquist sampling.

math.SP↗

arXiv2014

Collision Tolerant Packet Scheduling for Underwater Acoustic Localization

This article considers the joint problem of packet scheduling and self-localization in an underwater acoustic sensor network where sensor nodes are distributed randomly in an operating area. In terms of packet scheduling, our goal is to minimize the localization time, and to do so we consider two packet transmission schemes, namely a collision-free scheme (CFS), and a collision-tolerant scheme (CTS). The required localization time is formulated for these schemes, and through analytical results and numerical examples their performances are shown to be generally comparable. However, when the packet duration is short (as is the case for a localization packet), and the operating area is large (above 3km in at least one dimension), the collision-tolerant scheme requires a smaller localization time than the collision-free scheme. After gathering enough measurements, an iterative Gauss-Newton algorithm is employed by each sensor node for self-localization, and the Cramer Rao lower bound is evaluated as a benchmark. Although CTS consumes more energy for packet transmission, it provides a better localization accuracy. Additionally, in this scheme the anchor nodes work independently of each other, and can operate asynchronously which leads to a simplified implementation.

cs.IT↗

arXiv2014

Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems

Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates thanks to the large bandwidth available at mmWave frequencies. To realize sufficient link margin, mmWave systems will employ directional beamforming with large antenna arrays at both the transmitter and receiver. Due to the high cost and power consumption of gigasample mixed-signal devices, mmWave precoding will likely be divided among the analog and digital domains. The large number of antennas and the presence of analog beamforming requires the development of mmWave-specific channel estimation and precoding algorithms. This paper develops an adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel. To enable the efficient operation of this algorithm, a novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths. For single-path channels, an upper bound on the estimation error probability using the proposed algorithm is derived, and some insights into the efficient allocation of the training power among the adaptive stages of the algorithm are obtained. The adaptive channel estimation algorithm is then extended to the multi-path case relying on the sparse nature of the channel. Using the estimated channel, this paper proposes a new hybrid analog/digital precoding algorithm that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains compared to exhaustive channel training algorithms. The results also illustrate that the proposed algorithms can approach the coverage probability achieved by perfect channel knowledge even in the presence of interference.

cs.IT↗

arXiv2014

Joint relative position and velocity estimation for an anchorless network of mobile nodes

Localization is a fundamental challenge for any wireless network of nodes, in particular when the nodes are mobile. We present an extension of the classical Multidimensional scaling (MDS) for an anchorless network of mobile nodes, wherein the solutions to the time-varying relative node positions are shown to lie in the derivatives of the time-varying inter-nodal pairwise distances. Moreover, we show that the relative position of a mobile node at each time instance is only dependent on the initial relative position, relative velocity and a common rotation matrix of the respective node, which are estimated using MDS-like and least squares estimators. Simulations are conducted to evaluate the performance of the proposed solutions and the results are presented.

stat.AP↗

arXiv2013

Distributed Maximum Likelihood Sensor Network Localization

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks.

cs.IT↗

arXiv2013

Compressed Sensing for Block-Sparse Smooth Signals

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

stat.ML↗

arXiv2013

Rigid Body Localization Using Sensor Networks: Position and Orientation Estimation

In this paper, we propose a novel framework called rigid body localization for joint position and orientation estimation of a rigid body. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the sensors on the rigid body, or the absolute position of the rigid body itself is not known. However, we know how the sensors are mounted on the rigid body, i.e., the sensor topology is known. Using range-only measurements between the sensors and a few anchors (nodes with known absolute positions), and without using any inertial measurements (e.g., accelerometers), we estimate the position and orientation of the rigid body. For this purpose, the absolute position of the sensors is expressed as an affine function of the Stiefel manifold. In other words, we represent the orientation as a rotation matrix, and absolute position as a translation vector. We propose a least-squares (LS), simplified unitarily constrained LS (SUC-LS), and optimal unitarily constrained least-squares (OUC-LS) estimator, where the latter is based on Newton's method. As a benchmark, we derive a unitarily constrained Cramér-Rao bound (UC-CRB). The known topology of the sensors can sometimes be perturbed during fabrication. To take these perturbations into account, a simplified unitarily constrained total-least-squares (SUC-TLS), and an optimal unitarily constrained total-least-squares (OUC-TLS) estimator are also proposed.

cs.IT↗

arXiv2013

Position and Orientation Estimation of a Rigid Body: Rigid Body Localization

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

cs.IT↗