The JDTDOA algorithm applied to signal recovery : a performance analysis

This article suggests a novel method to retrieve a narrowband signal sent in a multipath environment with a delay spread considering ISI between symbols. The proposed method does not require any preamble nor known signal. Using the joint direction and time delay of arrivals estimation algorithm developed in prior work, the directions and time delays of arrival in the multipath channel are jointly estimated and associated while keeping a low computational cost. In this process, a MVDR beamformed copy of each arriving signal is created. The quality of these “pseudo copies” is evaluated and compared to the original direct and reflected signals in this work. Another beamforming method, the Moore–Penrose pseudoinverse, with better retrieval of the direct and reflected signals is also proposed. Using a simple delay-and-sum operation on the previously beamformed copies, it is possible to substantially improve the the system’s performance in terms of bit error rate. An approach using oversampling on the array antenna is introduced to improve performance. Numerical simulations are discussed to support theory

Grid-free compressive beamforming

The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve high-resolution imaging. On a discrete angular grid, the CS reconstruction degrades due to basis mismatch when the DOAs do not coincide with the angular directions on the grid. To overcome this limitation, a continuous formulation of the DOA problem is employed and an optimization procedure is introduced, which promotes sparsity on a continuous optimization variable. The DOA estimation problem with infinitely many unknowns, i.e., source locations and amplitudes, is solved over a few optimization variables with semidefinite programming. The grid-free CS reconstruction provides high-resolution imaging even with non-uniform arrays, single-snapshot data and under noisy conditions as demonstrated on experimental towed array data.Comment: 14 pages, 8 figures, journal pape

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

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

Estimating the time and angle of arrivals in mobile communications

Dans ce projet, nous présentons une méthode nouvelle et précise d’estimation de la direction et des délais d’arrivée dans un environnement à trajets multiples, à des fins d’estimation de canal. Récemment, les méthodes de super-résolution ont été largement utilisées pour l’estimation à haute-résolution de la direction d’arrivée (DOA) ou de la différence de temps d’arrivée (TDOA). L’algorithme proposé dans ce travail est applicable à l’estimation d’un canal espace-temps pour des systèmes de traitement spatio-temporel qui emploient la technologie hybride DOA / TDOA. L’estimateur est basé sur l’algorithme MUSIC classique pour trouver la DOA et en profitant d’un simple corrélateur, il est possible de trouver le retard de chaque arrivée. Il est pertinent d’associer chaque angle à son propre retard pour être capable d’estimer les caractéristiques du canal quand nous ne connaissons pas la séquence transmise par l’émetteur. Pour ce faire, nous proposons une formation de faisceaux (voix) très simple et optimale par l’application du MVDR (Maximum Variance Distortion-less Response). Cette formation de faisceaux maximise le signal desiré par rapport aux autres signaux. Après détermination de l’angle d’arrivée par l’algorithme MUSIC, nous appliquons l’algorithme de formation de faisceaux MVDR pour obtenir le signal qui est reçu par le réseau d’antennes pour une direction. Ce signal est corrélé avec les autres signaux correspondants aux autres directions d’arrivée. Les pics dans les figures ainsi obtenues montrent le décalage temporel de chaque source par rapport à celle obtenue par la formation de faisceaux MVDR. La soustraction du plus petit décalage, correspondant au premier signal reçu à chaque décalage temporel, nous donne le temps d’arrivée de chaque source. Pour être plus précis, nous pouvons choisir la moyenne des vecteurs des délais estimés, chacun étant obtenu à partir d’une angle pour l’algorithme MVDR.In this project, we present a novel and precise way of estimating the direction and delay of arrivals in multipath environment for channel estimation purposes. Recently, super-resolution methods have been widely used for high resolution Direction Of Arrival (DOA) or Time Difference Of Arrival (TDOA) estimation. The proposed algorithm in this work is applicable to space-time channel estimation for space-time processing systems that employ hybrid DOA/TDOA technology. The estimator is based on the conventional MUSIC algorithm to find the DOA and by using a simple correlator it is possible to find the delay of each arrival. It is of interest to associate each angle to its proper delay to be able to estimate the characteristics of the channel when we have no knowledge about the transmitted sequence. To do this, we suggest a very simple and optimal beamforming method by performing Maximum Variance Distortion-less Response (MVDR). This beamforming maximizes the desired signal in the desired direction compare to the other signals that come from other directions. After finding the DOAs by MUSIC algorithm and selecting our desired direction, we obtain the signal from this direction by applying MVDR beamforming. Then, we perform a correlation between this signal and the others incoming signals from other directions. The peaks in the simulation figures illustrate the delay between each source with the obtained signal from MVDR. If we subtract the delay of the first arrival (the smallest delay in time), from the delays indicated in the figures, we can obtain the delay of each arrival. To be more precise, the mean of these estimated TOAs vector follows the exact TOA of each source