arXiv subjects

Renato Luis Garrido Cavalcante

Publications and source records attributed to Renato Luis Garrido Cavalcante.

12 recordsLinked to original sources

arXiv2026

Beyond the Use-and-then-Forget (UatF) Bound: Fixed Point Algorithms for Statistical Max-Min Power Control

We introduce mathematical tools and fixed point algorithms for optimal statistical max-min power control in cellular and cell-less massive MIMO systems. Unlike previous studies that rely on the use-and-then-forget (UatF) lower bound on Shannon achievable (ergodic) rates, our proposed framework can deal with alternative bounds that explicitly consider perfect or imperfect channel state information (CSI) at the decoder. In doing so, we address limitations of UatF-based power control algorithms, which inherit the shortcomings of the UatF bound. For example, the UatF bound can be overly conservative: in extreme cases, under fully statistical (nonadaptive) beamforming in zero-mean channels, the UatF bound produces trivial (zero) rate bounds. It also lacks scale invariance: a realization-dependent random scaling of the beamformers can change the bound drastically. In contrast, our framework is compatible with information-theoretic bounds that do not suffer from the above drawbacks. We illustrate the framework by solving a max-min power control problem considering a standard bound that exploits instantaneous CSI at the decoder.

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arXiv2026

Theoretical Validation of the Latent Optimally Partitioned-$\ell_2/\ell_1$ Penalty with Application to Angular Power Spectrum Estimation

This paper demonstrates that, in both theory and practice, the latent optimally partitioned (LOP)-$\ell_2/\ell_1$ penalty is effective for exploiting block-sparsity without knowledge of the concrete block structure. More precisely, we first present a novel theoretical result showing that the optimized block partition in the LOP-$\ell_2/\ell_1$ penalty satisfies a condition required for accurate recovery of block-sparse signals. Motivated by this result, we present a new application of the LOP-$\ell_2/\ell_1$ penalty to estimation of angular power spectrum, which is block-sparse with unknown block partition, in MIMO communication systems. Numerical simulations show that the proposed use of block-sparsity with the LOP-$\ell_2/\ell_1$ penalty significantly improves the estimation accuracy of the angular power spectrum.

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arXiv2026

Cellular, Cell-less, and Everything in Between: A Unified Framework for Utility Region Analysis in Wireless Networks

We introduce a unified framework for analyzing utility regions of wireless networks, with a focus on signal-to-interference-plus-noise-ratio (SINR) and achievable rate regions. The framework provides valuable insights into interference patterns of modern network architectures, including extremely large MIMO and cell-less networks. A central contribution is a simple characterization of feasible utility regions using the concept of spectral radius of nonlinear mappings. This characterization provides a powerful mathematical tool for wireless system design and analysis. For example, it allows us to generalize existing characterizations of the weak Pareto boundary using compact notation. It also allows us to derive tractable sufficient conditions for the identification of convex utility regions. This property is particularly important because, on the weak Pareto boundary, it guarantees that time sharing (or user grouping) cannot simultaneously improve the utilities of all users. Beyond geometrical insights, these sufficient conditions have two key implications. First, they identify a family of (weighted) sum-rate maximization problems that are inherently convex, thus paving the way for the development of efficient, provably optimal solvers for this family. Second, they provide justification for formulating sum-rate maximization problems directly in terms of achievable rates, rather than SINR levels. Our theoretical insights also motivate an alternative to the concept of favorable propagation in the massive MIMO literature -- one that explicitly accounts for self-interference and the beamforming strategy.

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arXiv2026

Sum-Rate Maximization via Convex Optimization Using Subgradient Projections Onto Nonlinear Spectral Radius Constraint Sets

We solve the (weighted) sum-rate maximization problem over the set of achievable rates characterized by a nonlinear spectral radius function. This set has been recently shown to be convex in some practically relevant settings in modern wireless networks, including cell-less networks. However, even under convexity, sum-rate maximization is challenging because the nonlinear spectral radius characterization of the achievable rate region is difficult to handle directly. We overcome this difficulty by exploiting subgradient projections onto the level sets of suitably reformulated spectral radius functions. Notably, the derived subgradient projection algorithm provably converges to the global optimum of the sum-rate maximization problem under the convexity condition. The efficacy of the proposed algorithm is illustrated in simulations for cell-less networks.

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arXiv2023

Characterization of the weak Pareto boundary of resource allocation problems in wireless networks -- Implications to cell-less systems

We establish necessary and sufficient conditions for a network configuration to provide utilities that are both fair and efficient in a well-defined sense. To cover as many applications as possible with a unified framework, we consider utilities defined in an axiomatic way, and the constraints imposed on the feasible network configurations are expressed with a single inequality involving a monotone norm. In this setting, we prove that a necessary and sufficient condition to obtain network configurations that are efficient in the weak Pareto sense is to select configurations attaining equality in the monotone norm constraint. Furthermore, for a given configuration satisfying this equality, we characterize a criterion for which the configuration can be considered fair for the active links. We illustrate potential implications of the theoretical findings by presenting, for the first time, a simple parametrization based on power vectors of achievable rate regions in modern cell-less systems subject to practical impairments.

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arXiv2022

Joint optimal beamforming and power control in cell-free massive MIMO

We derive a fast and optimal algorithm for solving practical weighted max-min SINR problems in cell-free massive MIMO networks. For the first time, the optimization problem jointly covers long-term power control and distributed beamforming design under imperfect cooperation. In particular, we consider user-centric clusters of access points cooperating on the basis of possibly limited channel state information sharing. Our optimal algorithm merges powerful power control tools based on interference calculus with the recently developed team theoretic framework for distributed beamforming design. In addition, we propose a variation that shows faster convergence in practice.

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arXiv2020

Hybrid data and model driven algorithms for angular power spectrum estimation

We propose two algorithms that use both models and datasets to estimate angular power spectra from channel covariance matrices in massive MIMO systems. The first algorithm is an iterative fixed-point method that solves a hierarchical problem. It uses model knowledge to narrow down candidate angular power spectra to a set that is consistent with a measured covariance matrix. Then, from this set, the algorithm selects the angular power spectrum with minimum distance to its expected value with respect to a Hilbertian metric learned from data. The second algorithm solves an alternative optimization problem with a single application of a solver for nonnegative least squares programs. By fusing information obtained from datasets and models, both algorithms can outperform existing approaches based on models, and they are also robust against environmental changes and small datasets.

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arXiv2020

Channel covariance estimation in multiuser massive MIMO systems with an approach based on infinite dimensional Hilbert spaces

We propose a novel algorithm to estimate the channel covariance matrix of a desired user in multiuser massive MIMO systems. The algorithm uses only knowledge of the array response and rough knowledge of the angular support of the incoming signals, which are assumed to be separated in a well-defined sense. To derive the algorithm, we study interference patterns with realistic models that treat signals as continuous functions in infinite dimensional Hilbert spaces. By doing so, we can avoid common and unnatural simplifications such as the presence of discrete signals, ideal isotropic antennas, and infinitely large antenna arrays. An additional advantage of the proposed algorithm is its computational simplicity: it only requires a single matrix-vector multiplication. In some scenarios, simulations show that the estimates obtained with the proposed algorithm are close to those obtained with standard estimation techniques operating in interference-free and noiseless systems.

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arXiv2018

Error Bounds for FDD Massive MIMO Channel Covariance Conversion with Set-Theoretic Methods

We derive novel bounds for the performance of algorithms that estimate the downlink covariance matrix from the uplink covariance matrix in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. The focus is on algorithms that use estimates of the angular power spectrum as an intermediate step. Unlike previous results, the proposed bounds follow from simple arguments in possibly infinite dimensional Hilbert spaces, and they do not require strong assumptions on the array geometry or on the propagation model. Furthermore, they are suitable for the analysis of set-theoretic methods that can efficiently incorporate side information about the angular power spectrum. This last feature enables us to derive simple techniques to enhance set-theoretic methods without any heuristic arguments. In particular, we show that the performance of a simple algorithm that requires only a simple matrix-vector multiplication cannot be improved significantly in some practical scenarios, especially if coarse information about the support of the angular power spectrum is available.

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arXiv2018

Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.

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arXiv2018

Fundamental properties of solutions to utility maximization problems in wireless networks

We introduce a unified framework for the study of the utility and the energy efficiency of solutions to a large class of weighted max-min utility maximization problems in interference-coupled wireless networks. In more detail, given a network utility maximization problem parameterized by a maximum power budget $\bar{p}$ available to network elements, we define two functions that map the power budget $\bar{p}$ to the energy efficiency and to the utility achieved by the solution. Among many interesting properties, we prove that these functions are continuous and monotonic. In addition, we derive bounds revealing that the solutions to utility maximization problems are characterized by a low and a high power regime. In the low power regime, the energy efficiency of the solution can decrease slowly as the power budget increases, and the network utility grows linearly at best. In contrast, in the high power regime, the energy efficiency typically scales as $Θ(1/\bar{p})$ as $\bar{p}\to\infty$, and the network utility scales as $Θ(1)$. We apply the theoretical findings to a novel weighted rate maximization problem involving the joint optimization of the uplink power and the base station assignment.

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arXiv2012

Base station selection for energy efficient network operation with the majorization-minimization algorithm

In this paper, we study the problem of reducing the energy consumption in a mobile communication network; we select the smallest set of active base stations that can preserve the quality of service (the minimum data rate) required by the users. In more detail, we start by posing this problem as an integer programming problem, the solution of which shows the optimal assignment (in the sense of minimizing the total energy consumption) between base stations and users. In particular, this solution shows which base stations can then be switched off or put in idle mode to save energy. However, solving this problem optimally is intractable in general, so in this study we develop a suboptimal approach that builds upon recent techniques that have been successfully applied to, among other problems, sparse signal reconstruction, portfolio optimization, statistical estimation, and error correction. More precisely, we relax the original integer programming problem as a minimization problem where the objective function is concave and the constraint set is convex. The resulting relaxed problem is still intractable in general, but we can apply the majorization-minimization algorithm to find good solutions (i.e., solutions attaining low objective value) with a low-complexity algorithm. In contrast to state-of-the-art approaches, the proposed algorithm can take into account inter-cell interference, is suitable for large-scale problems, and can be applied to heterogeneous networks (networks where base station consume different amounts of energy)

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