João Paulo Carvalho Lustosa da Costa

Multi-dimensional model order selection

Multi-dimensional model order selection (MOS) techniques achieve an improved accuracy, reliability, and robustness, since they consider all dimensions jointly during the estimation of parameters. Additionally, from fundamental identifiability results of multi-dimensional decompositions, it is known that the number of main components can be larger when compared to matrix-based decompositions. In this article, we show how to use tensor calculus to extend matrix-based MOS schemes and we also present our proposed multi-dimensional model order selection scheme based on the closed-form PARAFAC algorithm, which is only applicable to multi-dimensional data. In general, as shown by means of simulations, the Probability of correct Detection (PoD) of our proposed multi-dimensional MOS schemes is much better than the PoD of matrix-based schemes.

Robust R-D parameter estimation via closed-form PARAFAC

R-dimensional parameter estimation problems are common in a variety of signal processing applications. In order to solve such problems, we propose a robust multidimensional model order selection scheme and a robust multidimensional parameter estimation scheme using the closed-form PARAFAC algorithm, which is a recently proposed way to compute the PARAFAC decomposition based on several simultaneous diagonalizations. In general, R-dimensional (R-D) model order selection (MOS) techniques, e.g., the R-D Exponential Fitting Test (R-D EFT), are designed for multidimensional data by taking into account its multidimensional structure. However, the R-D MOS techniques assume that the data is contaminated by white Gaussian noise. To deal with colored noise, we propose the closed-form PARAFAC based model order selection (CFP-MOS) technique based on multiple estimates of the factor matrices provided as an intermediate step by the closed-form PARAFAC algorithm. Additionally, we propose the closed-form PARAFAC based parameter estimator (CFP-PE), which can be applied to extract spatial frequencies in case of arbitrary array geometries.

Semi-Blind Receivers for Joint Symbol and Channel Estimation in Space-Time-Frequency MIMO-OFDM Systems

In wireless communications, increased spectral efficiency and low error rates can be achieved by means of space-time-frequency coded MIMO-OFDM systems. In this work, we consider a MIMO-OFDM transmit signal design combining space-frequency modulation with a time-varying linear precoding technique which allows spreading and multiplexing the transmitted symbols, in both space, time and frequency domains. For this system, we propose two closed-form semi-blind receivers that exploit differently the multilinear structure of the received signal, which is formulated as a nested PARAllel FACtor (PARAFAC) model. First, we devise a least squares Khatri-Rao factorization (LS-KRF) based receiver for joint channel and symbol estimation by making an efficient use of a short frame of pilot symbols. The LS-KRF receiver provides the same performance at a lower computational complexity compared to the alternating least squares (ALS) based receiver. For further reducing pilot overhead, we develop a simplified closed-form PARAFAC (S-CFP) receiver coupled with a pairing algorithm that yields an unambiguous estimation of the transmitted symbols without the need of a pilot frame. The uniqueness conditions, spectral efficiency and computational complexity of the LS-KRF and S-CFP with pairing receivers are analyzed and compared with the ALS receiver. It is shown that the S-CFP with pairing receiver has the same order of computational complexity as the ALS receiver. Meanwhile, simulation results show that our S-CFP with pairing receiver achieves the same or very similar performance of the competing receivers with extra pilot overhead at sufficiently high signal-to-noise ratio (SNR) conditions. On the other hand, it is slightly inferior to them in terms of channel estimation accuracy and bit error rate at lower SNRs.

Attitude determination for unmanned aerial vehicles via an antenna array

An accurate and updated estimate of the attitude of Unmanned Aerial Vehicles (UAVs) is crucial for their control and displacement. Errors in the attitude can cause a misuse of the limited energy sources of UAVs or accidents. For the estimation of the attitude, Inertial Measurement Units (IMUs) are widely applied; they are, however, susceptible to inertial guidance error. With antenna arrays currently being incorporated to UAVs to improve their communication with ground stations, we can take advantage of such an antenna array structure in order to estimate the attitude. In this paper, we therefore propose an attitude estimation system based on an antenna array which could be used to improve the estimates of IMUs. We deliver iterative expressions to compute the attitude under usage of the estimated phase delays of the impinging signals over the antenna array. By means of simulations, we show the feasibility of our proposed solution for different SNR levels as well as for multipath scenarios.

A Signal Adaptive Array Interpolation Approach with Reduced Transformation Bias for DOA estimation of Highly Correlated Signals

Sensor arrays with Vandermonde or centro-hermitian responses cannot always be constructed. However, such array response structure can be achieved by means of a mapping which transforms the real array response to an array response with the desired properties by applying array interpolation algorithms. In this work a low-complexity, multi-sector, signal adaptive array interpolation approach that achieves low transformation bias in the presence of highly correlated signals is presented. Estimation of Signal Parameters via Rotational Invariance (ESPRIT) algorithm with Forward Backward Average (FBA) and Spatial Smoothing (SPS) as well as model order estimation is applied after array interpolation in conjunction with the Vandermonde Invariance Transformation (VIT) to obtain precise high resolution estimates in closed form. A set of numerical simulations show that the proposed approach provides precise estimates for arbitrary array responses in highly correlated signal signal environments.

Improved MRI reconstruction and denoising using SVD-based low-rank approximation

The reconstruction of multi-dimensional magnetic resonsance imaging (MRI) data can be a computationally demanding task. Signal-to-noise ratio is also a concern, specially in high-resolution imaging. Data compression may be useful not only for reducing reconstruction complexity and memory requirements, but also for reducing noise, as it is capable of eliminating spurious components. This work proposes the use of SVD-based low-rank approximation for the reconstruction and denoising of MRI data. The Akaike information criterion is used to estimate the appropriate model order. The model order is used to remove noisy components and to reduce the amount of data to be stored and processed. The proposed method is evaluated using in vivo MRI data. We present images reconstructed using less than 20% visual inspection. A quantitative evaluation is also presented.

Unscented Transformation based array interpolation

It is impossible to enforce exact responses for each sensor involved in an antenna array. Important signal processing techniques such as Estimation of Signal Parameters via Rotational Invariance (ESPRIT), Forward Backward Average (FBA) and Spatial Smoothing (SPS) rely on sensor arrays with Vandermonde or centro-hermitian responses. To achieve such responses array interpolation is often necessary. In this work a novel way of performing array interpolation while minimizing the transformation error using the Unscented Transformation (UT) is presented. The UT provides a different method for mapping interpolated regions and also exhibits a new insight into array interpolation and its current limitations. A set of numerical simulations presents promising results for array interpolation employing the UT.

Neural Network Predictor for Fraud Detection: A Study Case for the Federal Patrimony Department

-Fraud detection is necessary for any financial system. However, the way of committing frauds and also for detecting them have evolved considerably in the lasts years, mainly due the development of new technologies. Therefore, fraud detection via statistical schemes has become an important tool to reduce the chances of frauds. In this paper, we present a study case applied to the tax collection per month of the Federal Patrimony Department (SPU). In this study case, we analyze some of the current methods for fraud detection, as Rule-Based Systems and Neural Networks classifiers, and propose the use of Neural Networks predictors for detecting fraud in time series data of the SPU.

Applying MIMO Techniques to Minimize Energy Consumption for Long Distances Communications in Wireless Sensor Networks

This paper explores the usage of cooperative multiple input multiple output (MIMO) technique to minimize energy consumption used to establish communications among distant nodes in a wireless sensor network (WSN). As energy depletion is an outstanding problem in WSN research field, a number of techniques aim to preserve such resource, especially by means of savings during communication among sensor nodes. One such wide used technique is multi-hop communication to diminish the energy required by a single node to transmit a given message, providing a homogeneous consumption of the energy resources among the nodes in the network. However, it is not the case that multi-hop is always more efficient than single-hop, even that it may represent a great depletion of a single node’s energy. In this paper a cooperative MIMO transmission technique for WSN is presented, which is compared to single-hop and multi-hop transmission ones, highlighting its advantages in relation to both. Simulation results support the statement about the utility in applying the proposed technique for energy saving purposes.

Detection of number of components in CANDECOMP/PARAFAC models via minimum description length

Detecting the number of components of the CANDECOMP/PARAFAC (CP) model, also known as CP model order selection, is an essential task in signal processing and data mining applications. Existing multilinear detection algorithms for handling N-dimensional data, where N ? 3 , e.g., the CORe CONsistency DIAgnostic, rely on the CP decomposition which is computationally very expensive. An alternative solution is to rearrange the tensor as a matrix using the unfolding operation and then utilize the eigenvalues of the resultant matrices for CP model order selection. We propose to employ the eigenvalues associated with the unfolding along merged dimensions, namely, the multi-mode eigenvalues, as well as the n-mode eigenvalues for accurate rank detection. These multiple sets of eigenvalues are combined via the information theoretic criterion. By designing a sequential detection scheme starting from the most squared unfolded matrix, the identifiable rank is increased to the square root of the product of all dimension lengths, which renders the detection algorithm to estimate the rank that can exceed any individual dimension length. The conditions under which the proposed multilinear detection algorithm correctly detects the tensor rank are theoretically investigated and its computational efficiency and detection performance are verified. The problem of CANDECOMP/PARAFAC (CP) model order selection is addressed.Computational efficiency is achieved via matricization of a tensor.Eigenvalues associated with the block or multi-mode matricization are exploited.Able to detect rank up to the square root of the product of all dimension lengths.Accuracy comparable to CP-decomposition based tensor rank detectors.