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Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances ; Alves Martins, Wallace ; in IEEE Transactions on Signal and Information Processing over Networks (2020) This paper proposes the augmentation of the adjacency model of networks for graph signal processing. It is assumed that no information about the network is available, apart from the initial adjacency ... [more ▼] This paper proposes the augmentation of the adjacency model of networks for graph signal processing. It is assumed that no information about the network is available, apart from the initial adjacency matrix. In the proposed model, additional edges are created according to a Markov relation imposed between nodes. This information is incorporated into the extended-adjacency matrix as a function of the diffusion distance between nodes. The diffusion distance measures similarities between nodes at a certain diffusion scale or time, and is a metric adopted from diffusion maps. Similarly, the proposed extended-adjacency matrix depends on the diffusion scale, which enables the definition of a scale-dependent graph Fourier transform. We conduct theoretical analyses of both the extended adjacency and the corresponding graph Fourier transform and show that different diffusion scales lead to different graph-frequency perspectives. At different scales, the transform discriminates shifted ranges of signal variations across the graph, revealing more information on the graph signal when compared to traditional approaches. The scale-dependent graph Fourier transform is applied for anomaly detection and is shown to outperform the conventional graph Fourier transform. [less ▲] Detailed reference viewed: 184 (7 UL)On the Convergence of Max-Min Fairness Power Allocation in Massive MIMO Systems ; ; et al in IEEE Communications Letters (2020) Power allocation techniques, among which the max-min fairness power allocation (MMFPA) is one of the most widely used, are essential to guarantee good data throughput for all users in a cell. Recently, an ... [more ▼] Power allocation techniques, among which the max-min fairness power allocation (MMFPA) is one of the most widely used, are essential to guarantee good data throughput for all users in a cell. Recently, an efficient MMFPA algorithm for massive multiple-input multiple-output (MIMO) systems has been proposed. However, this algorithm is susceptible to the initial search interval employed by the underlying bisection search. Even if the optimal point belongs to the initial search interval, this algorithm may fail to converge to such a point. In this paper, we use the Perron-Frobenius theory to explain this issue and provide search intervals that guarantee convergence to the optimal point. Furthermore, we propose the bound test procedure as an efficient way of initializing the search interval. Simulation results corroborate our findings. [less ▲] Detailed reference viewed: 118 (5 UL)Adaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance Analysis ; ; Alves Martins, Wallace et al in IEEE Transactions on Signal and Information Processing over Networks (2020) This paper develops adaptive graph filters that operate in reproducing kernel Hilbert spaces. We consider both centralized and fully distributed implementations. We first define nonlinear graph filters ... [more ▼] This paper develops adaptive graph filters that operate in reproducing kernel Hilbert spaces. We consider both centralized and fully distributed implementations. We first define nonlinear graph filters that operate on graph-shifted versions of the input signal. We then propose a centralized graph kernel least mean squares (GKLMS) algorithm to identify nonlinear graph filters' model parameters. To reduce the dictionary size of the centralized GKLMS, we apply the principles of coherence check and random Fourier features (RFF). The resulting algorithms have performance close to that of the GKLMS algorithm. Additionally, we leverage the graph structure to derive the distributed graph diffusion KLMS (GDKLMS) algorithms. We show that, unlike the coherence check-based approach, the GDKLMS based on RFF avoids the use of a pre-trained dictionary through its data independent fixed structure. We conduct a detailed performance study of the proposed RFF-based GDKLMS, and the conditions for its convergence both in mean and mean-squared senses are derived. Extensive numerical simulations show that GKLMS and GDKLMS can successfully identify nonlinear graph filters and adapt to model changes. Furthermore, RFF-based strategies show faster convergence for model identification and exhibit better tracking performance in model-changing scenarios. [less ▲] Detailed reference viewed: 62 (3 UL)Joint Forecasting and Interpolation of Time-Varying Graph Signals Using Deep Learning ; Alves Martins, Wallace ; Chatzinotas, Symeon et al in IEEE Transactions on Signal and Information Processing over Networks (2020) We tackle the problem of forecasting network-signal snapshots using past signal measurements acquired by a subset of network nodes. This task can be seen as a combination of multivariate time-series ... [more ▼] We tackle the problem of forecasting network-signal snapshots using past signal measurements acquired by a subset of network nodes. This task can be seen as a combination of multivariate time-series forecasting (temporal prediction) and graph signal interpolation (spatial prediction). This is a fundamental problem for many applications wherein deploying a high granularity network is impractical. Our solution combines recurrent neural networks with frequency-analysis tools from graph signal processing, and assumes that data is sufficiently smooth with respect to the underlying graph. The proposed learning model outperforms state-of-the-art deep learning techniques, especially when predictions are made using a small subset of network nodes, considering two distinct real world datasets: temperatures in the US and speed flow in Seattle. The results also indicate that our method can handle noisy signals and missing data, making it suitable to many practical applications. [less ▲] Detailed reference viewed: 78 (4 UL)Intersymbol and Intercarrier Interference in OFDM Transmissions Through Highly Dispersive Channels Alves Martins, Wallace ; ; et al in Proc. of the 27th European Signal Processing Conference (EUSIPCO-2019) (2019, September) Detailed reference viewed: 113 (11 UL)Time-Deconvolutive CNMF for Multichannel Blind Source Separation ; ; Alves Martins, Wallace in Anais do XXXVII Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT 2019) (2019, September) Detailed reference viewed: 94 (6 UL)On the Use of Vertex-Frequency Analysis for Anomaly Detection in Graph Signals ; Alves Martins, Wallace ; Chatzinotas, Symeon et al in Anais do XXXVII Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT 2019) (2019, September) Detailed reference viewed: 170 (27 UL)Semi-blind Data-Selective and Multiple Threshold Volterra Adaptive Filtering ; Alves Martins, Wallace in Circuits, Systems, and Signal Processing (2019) This work proposes the use of data-selective semi-blind schemes in order to decrease the amount of data used to train the adaptive filters that employ Volterra series, while reducing its computational ... [more ▼] This work proposes the use of data-selective semi-blind schemes in order to decrease the amount of data used to train the adaptive filters that employ Volterra series, while reducing its computational complexity. It is also proposed a data-selective technique that exploits the structure of Volterra series, employing a different filter for each of its kernels. The parameter vector of these filters grows as the order of the kernel increases. Therefore, by assigning larger error thresholds to higher-order filters, it is possible to decrease their update rates, thus reducing the overall computational complexity. Results in an equalization setup indicate that both proposals are capable of achieving promising results in terms of mean square error and bit error rate at low computational complexity, and in the case of semi-blind algorithms, using much less training data. [less ▲] Detailed reference viewed: 95 (7 UL)Convex Combination of Constraint Vectors for Set-membership Affine Projection Algorithms ; Alves Martins, Wallace ; et al in Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2019, May) Set-membership affine projection (SM-AP) adaptive filters have been increasingly employed in the context of online data-selective learning. A key aspect for their good performance in terms of both ... [more ▼] Set-membership affine projection (SM-AP) adaptive filters have been increasingly employed in the context of online data-selective learning. A key aspect for their good performance in terms of both convergence speed and steady-state mean-squared error is the choice of the so-called constraint vector. Optimal constraint vectors were recently proposed relying on convex optimization tools, which might some- times lead to prohibitive computational burden. This paper proposes a convex combination of simpler constraint vectors whose performance approaches the optimal solution closely, utilizing much fewer computations. Some illustrative examples confirm that the sub-optimal solution follows the accomplishments of the optimal one. [less ▲] Detailed reference viewed: 107 (14 UL)Achievable Data Rate of DCT-based Multicarrier Modulation Systems ; Alves Martins, Wallace ; et al in IEEE Transactions on Wireless Communications (2019), 18(3), 1739-1749 This paper aims at studying the achievable data rate of discrete cosine transform (DCT)-based multicarrier modulation (MCM) systems. To this end, a general formulation is presented for the full ... [more ▼] This paper aims at studying the achievable data rate of discrete cosine transform (DCT)-based multicarrier modulation (MCM) systems. To this end, a general formulation is presented for the full transmission/reception process of data in Type-II even DCT and Type-IV even DCT-based systems. The paper focuses on the use of symmetric extension (SE) and zero padding (ZP) as redundancy methods. Furthermore, three cases related to the channel order and the length of the redundancy are studied. In the first case, the channel order is less than or equal to the length of the redundancy. In the second and third cases, the channel order is greater than the length of the redundancy; the interference caused by the channel impulse response is calculated, and theoretical expressions for their powers are derived. These expressions allow studying the achievable data rate of DCT-based MCM systems, besides enabling the comparison with the conventional MCM based on the discrete Fourier Transform. [less ▲] Detailed reference viewed: 92 (5 UL)Normalized LMS Algorithm and Data-selective Strategies for Adaptive Graph Signal Estimation ; Alves Martins, Wallace in Signal Processing (2019) This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive ... [more ▼] This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive filtering framework, the resulting GS estimation technique converges faster than the least-mean-squares (LMS) algorithm while being less complex than the recursive least-squares (RLS) algorithm, both recently recast as adaptive estimation strategies for the GS framework. Detailed steady-state mean-squared error and deviation analyses are provided for the proposed NLMS algorithm, and are also employed to complement previous analyses on the LMS and RLS algorithms. Additionally, two different time-domain data-selective (DS) strategies are proposed to reduce the overall computational complexity by only performing updates when the input signal brings enough innovation. The parameter setting of the algorithms is performed based on the analysis of these DS strategies, and closed formulas are derived for an accurate evaluation of the update probability when using different adaptive algorithms. The theoretical results predicted in this work are corroborated with high accuracy by numerical simulations. [less ▲] Detailed reference viewed: 166 (23 UL) |
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