Model Order Selection for Collision Multiplicity Estimation

The collision multiplicity (CM) is the number of users involved in a collision. The CM estimation is an essential step in multi-packet reception (MPR) techniques and in collision resolution (CR) methods. We propose two techniques to estimate collision multiplicities in the context of IEEE 802.11 networks. These two techniques have been initially designed in the context of source separation. The first estimation technique is based on eigenvalue statistics. The second technique is based on the exponentially embedded family (EEF). These two techniques outperform current estimation techniques in terms of underestimation rate (UNDER). The reason for this is twofold. First, current techniques are based on a uniform distribution of signal samples whereas the proposed methods rely on a Gaussian distribution. Second, current techniques use a small number of observations whereas the proposed methods use a number of observations much greater than the number of signals to be separated. This is in accordance with typical source separation techniques

Subspace averaging for source enumeration in large arrays

Subspace averaging is proposed and examined as a method of enumerating sources in large linear arrays, under conditions of low sample support. The key idea is to exploit shift invariance as a way of extracting many subspaces, which may then be approximated by a single extrinsic average. An automatic order determination rule for this extrinsic average is then the rule for determining the number of sources. Experimental results are presented for cases where the number of array snapshots is roughly half the number of array elements, and sources are well separated with respect to the Rayleigh limit.The work of I. Santamaría has been partially supported by the Ministerio de Economía y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grant TEC2016-75067-C4-4-R (CARMEN). The work of D. Ramírez has been partly supported by Ministerio de Economía of Spain under projects: OTOSIS (TEC2013-41718-R) and the COMONSENS Network (TEC2015-69648-REDC), by the Ministerio de Economía of Spain jointly with the European Commission (ERDF) under projects ADVENTURE (TEC2015-69868-C2-1-R) and CAIMAN (TEC2017-86921- C2-2-R), and by the Comunidad de Madrid under project CASI-CAM-CM (S2013/ICE-2845). The work of L. L. Scharf was supported by the National Science Foundation (NSF) under grant CCF-1018472

Neural Networks for improved signal source enumeration and localization with unsteered antenna arrays

Direction of Arrival estimation using unsteered antenna arrays, unlike mechanically scanned or phased arrays, requires complex algorithms which perform poorly with small aperture arrays or without a large number of observations, or snapshots. In general, these algorithms compute a sample covriance matrix to obtain the direction of arrival and some require a prior estimate of the number of signal sources. Herein, artificial neural network architectures are proposed which demonstrate improved estimation of the number of signal sources, the true signal covariance matrix, and the direction of arrival. The proposed number of source estimation network demonstrates robust performance in the case of coherent signals where conventional methods fail. For covariance matrix estimation, four different network architectures are assessed and the best performing architecture achieves a 20 times improvement in performance over the sample covariance matrix. Additionally, this network can achieve comparable performance to the sample covariance matrix with 1/8-th the amount of snapshots. For direction of arrival estimation, preliminary results are provided comparing six architectures which all demonstrate high levels of accuracy and demonstrate the benefits of progressively training artificial neural networks by training on a sequence of sub- problems and extending to the network to encapsulate the entire process

Estimation of Collision Multiplicities in IEEE 802.11-based WLANs

Abstract—Estimating the collision multiplicity (CM), i.e. the number of users involved in a collision, is a key task in multipacket reception (MPR) approaches and in collision resolution (CR) techniques. A new technique is proposed for IEEE 802.11 networks. The technique is based on recent advances in random matrix theory and rely on eigenvalue statistics. Provided that the eigenvalues of the covariance matrix of the observations are above a given threshold, signal eigenvalues can be separated from noise eigenvalues since their respective probability density functions are converging toward two different laws: a Gaussian law for the signal eigenvalues and a Tracy-Widom law for the noise eigenvalues. The proposed technique outperforms current estimation techniques in terms of underestimation rate. Moreover, this paper reveals that, contrary to what is generally assumed in current MPR techniques, a single observation of the colliding signals is far from being sufficient to perform a reliable CM estimation

Subspace averaging and order determination for source enumeration

In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yuejie Chi. The work of V. Garg and I. Santamaria was supported in part by the Ministerio de Economía y Competitividad (MINECO) of Spain, and in part by the AEI/FEDER funds of the E.U., under Grants TEC2016-75067-C4-4-R (CARMEN), TEC2015-69648-REDC, and BES-2017-080542. The work of D. Ramírez was supported in part by the Ministerio de Ciencia, Innovación y Universidades under Grant TEC2017-92552-EXP (aMBITION), in part by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under Grants TEC2015-69868-C2-1-R (ADVENTURE) and TEC2017-86921-C2-2-R (CAIMAN), and in part by The Comunidad de Madrid under Grant Y2018/TCS-4705 (PRACTICOCM). The work of L. L. Scharf was supported in part by the U.S. NSF under Contract CISE-1712788

Subspace-based order estimation techniques in massive MIMO

Order estimation, also known as source enumeration, is a classical problem in array signal processing which consists in estimating the number of signals received by an array of sensors. In the last decades, numerous approaches to this problem have been proposed. However, the need of working with large-scale arrays (like in massive MIMO systems), low signal-to-noise- ratios, and poor sample regime scenarios, introduce new challenges to order estimation problems. For instance, most of the classical approaches are based on information theoretic criteria, which usually require a large sample size, typically several times larger than the number of sensors. Obtaining a number of samples several times larger than the number of sensors is not always possible with large-scale arrays. In addition, most of the methods found in literature assume that the noise is spatially white, which is very restrictive for many practical scenarios. This dissertation deals with the problem of source enumeration for large-scale arrays, and proposes solutions that work robustly in the small sample regime under various noise models. The first part of the dissertation solves the problem by applying the idea of subspace averaging. The input data are modelled as subspaces, and an average or central subspace is computed. The source enumeration problem can be seen as an estimation of the dimension of the central subspace. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. The proposed SA criterion is especially effective in high-dimensional scenarios with low sample support for uniform linear arrays in the presence of white noise. Further, the proposed SA method is extended for: i) non-white noises, and ii) non-uniform linear arrays. The SA criterion is sensitive with the chosen dimension of extracted subspaces. To solve this problem, we combine the SA technique with a majority vote approach. The number of sources is detected for increasing dimensions of the SA technique and then a majority vote is applied to determine the final estimate. Further, to extend SA for arrays with arbitrary geometries, the SA is combined with a sparse reconstruction (SR) step. In the first step, each received snapshot is approximated by a sparse linear combination of the rest of snapshots. The SR problem is regularized by the logarithm-based surrogate of the l-0 norm and solved using a majorization-minimization approach. Based on the SR solution, a sampling mechanism is proposed in the second step to generate a collection of subspaces, all of which approximately span the same signal subspace. Finally, the dimension of the average of this collection of subspaces provides a robust estimate for the number of sources. The second half of the dissertation introduces a completely different approach to the order estimation for uniform linear arrays, which is based on matrix completion algorithms. This part first discusses the problem of order estimation in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. The proposed method performs robustly for both small and large-scale arrays with few snapshots. Finally, an approach to work with a reduced number of radio–frequency (RF) chains is proposed. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low- rank structure of the signal subspace, but also the shift-invariance property of uniform linear arrays, which results in a better estimation of the signal subspace. In addition, the effect of MC on DOA estimation is discussed under the perturbation theory framework. Further, this approach is extended to devise a novel order estimation criterion for missing data scenario. The proposed source enumeration criterion is based on the chordal subspace distance between two sub-matrices extracted from the reconstructed matrix after using MC for increasing rank values. We show that the proposed order estimation criterion performs consistently with a very few available entries in the data matrix.This work was supported by the Ministerio de Ciencia e Innovación (MICINN) of Spain, under grants TEC2016-75067-C4-4-R (CARMEN) and BES-2017-080542

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications