Renato L. G. Cavalcante

Tomasz Piotrowski, Rafail Ismayilov, Matthias Frey et al.

We introduce the concept of inverse feasibility for linear forward models as a tool to enhance OTA FL algorithms. Inverse feasibility is defined as an upper bound on the condition number of the forward operator as a function of its parameters. We analyze an existing OTA FL model using this definition, identify areas for improvement, and propose a new OTA FL model. Numerical experiments illustrate the main implications of the theoretical results. The proposed framework, which is based on inverse problem theory, can potentially complement existing notions of security and privacy by providing additional desirable characteristics to networks.

Mateusz Gabor, Tomasz Piotrowski, Renato L. G. Cavalcante

Deep equilibrium (DEQ) models are widely recognized as a memory efficient alternative to standard neural networks, achieving state-of-the-art performance in language modeling and computer vision tasks. These models solve a fixed point equation instead of explicitly computing the output, which sets them apart from standard neural networks. However, existing DEQ models often lack formal guarantees of the existence and uniqueness of the fixed point, and the convergence of the numerical scheme used for computing the fixed point is not formally established. As a result, DEQ models are potentially unstable in practice. To address these drawbacks, we introduce a novel class of DEQ models called positive concave deep equilibrium (pcDEQ) models. Our approach, which is based on nonlinear Perron-Frobenius theory, enforces nonnegative weights and activation functions that are concave on the positive orthant. By imposing these constraints, we can easily ensure the existence and uniqueness of the fixed point without relying on additional complex assumptions commonly found in the DEQ literature, such as those based on monotone operator theory in convex analysis. Furthermore, the fixed point can be computed with the standard fixed point algorithm, and we provide theoretical guarantees of its geometric convergence, which, in particular, simplifies the training process. Experiments demonstrate the competitiveness of our pcDEQ models against other implicit models.

Matthias Mehlhose, Guillermo Marcus, Daniel Schäufele et al.

In this feasibility study, we have implemented a recently proposed partially linear multiuser detection algorithm in reproducing kernel Hilbert spaces (RKHSs) on a GPU-accelerated platform. Partially linear multiuser detection, which combines the robustness of linear detection with the power of nonlinear methods, has been proposed for a massive connectivity scenario with the non-orthogonal multiple access (NOMA). This is a promising approach, but detecting payloads within a received orthogonal frequency division multiplexing (OFDM) radio frame requires the execution of a large number of inner product operations, which are the main computational burden of the algorithm. Although inner-product operations consist of simple kernel evaluations, their vast number poses a challenge in ultra-low latency (ULL) applications, because the time needed for computing the inner products might exceed the sub-millisecond latency requirement. To address this problem, this study demonstrates the acceleration of the inner-product operations through massive parallelization. The result is a GPU-accelerated real-time OFDM receiver that enables sub-millisecond latency detection to meet the requirements of 5th generation (5G) and beyond ultra-reliable and low latency communications (URLLC) systems. Moreover, the parallelization and acceleration techniques explored and demonstrated in this study can be extended to many other signal processing algorithms in Hilbert spaces, such as those based on projection onto convex sets (POCS) and adaptive projected subgradient method (APSM) algorithms. Experimental results and comparisons with the state-of-art confirm the effectiveness of our techniques.

Rafail Ismayilov, Renato L. G. Cavalcante, Sławomir Stańczak

We propose a method that combines fixed point algorithms with a neural network to optimize jointly discrete and continuous variables in millimeter-wave communication systems, so that the users' rates are allocated fairly in a well-defined sense. In more detail, the discrete variables include user-access point assignments and the beam configurations, while the continuous variables refer to the power allocation. The beam configuration is predicted from user-related information using a neural network. Given the predicted beam configuration, a fixed point algorithm allocates power and assigns users to access points so that the users achieve the maximum fraction of their interference-free rates. The proposed method predicts the beam configuration in a "one-shot" manner, which significantly reduces the complexity of the beam search procedure. Moreover, even if the predicted beam configurations are not optimal, the fixed point algorithm still provides the optimal power allocation and user-access point assignments for the given beam configuration.

Rafail Ismayilov, Renato L. G. Cavalcante, Sławomir Stańczak

We propose a deep learning-based method that uses spatial and temporal information extracted from the sub-6GHz band to predict/track beams in the millimeter-wave (mmWave) band. In more detail, we consider a dual-band communication system operating in both the sub-6GHz and mmWave bands. The objective is to maximize the achievable mutual information in the mmWave band with a hybrid analog/digital architecture where analog precoders (RF precoders) are taken from a finite codebook. Finding a RF precoder using conventional search methods incurs large signalling overhead, and the signalling scales with the number of RF chains and the resolution of the phase shifters. To overcome the issue of large signalling overhead in the mmWave band, the proposed method exploits the spatiotemporal correlation between sub-6GHz and mmWave bands, and it predicts/tracks the RF precoders in the mmWave band from sub-6GHz channel measurements. The proposed method provides a smaller candidate set so that performing a search over that set significantly reduces the signalling overhead compared with conventional search heuristics. Simulations show that the proposed method can provide reasonable achievable rates while significantly reducing the signalling overhead.

Tomasz J. Piotrowski, Renato L. G. Cavalcante, Mateusz Gabor

We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can be recognized as monotonic and (weakly) scalable mappings within the framework of nonlinear Perron-Frobenius theory. This fact enables us to provide conditions for the existence of fixed points of nonnegative neural networks having inputs and outputs of the same dimension, and these conditions are weaker than those recently obtained using arguments in convex analysis. Furthermore, we prove that the shape of the fixed point set of nonnegative neural networks with nonnegative weights and biases is an interval, which under mild conditions degenerates to a point. These results are then used to obtain the existence of fixed points of more general nonnegative neural networks. From a practical perspective, our results contribute to the understanding of the behavior of autoencoders, and we also offer valuable mathematical machinery for future developments in deep equilibrium models.

Daniyal Amir Awan, Renato L. G. Cavalcante, Slawomir Stanczak

Learning of the cell-load in radio access networks (RANs) has to be performed within a short time period. Therefore, we propose a learning framework that is robust against uncertainties resulting from the need for learning based on a relatively small training sample set. To this end, we incorporate prior knowledge about the cell-load in the learning framework. For example, an inherent property of the cell-load is that it is monotonic in downlink (data) rates. To obtain additional prior knowledge we first study the feasible rate region, i.e., the set of all vectors of user rates that can be supported by the network. We prove that the feasible rate region is compact. Moreover, we show the existence of a Lipschitz function that maps feasible rate vectors to cell-load vectors. With these results in hand, we present a learning technique that guarantees a minimum approximation error in the worst-case scenario by using prior knowledge and a small training sample set. Simulations in the network simulator NS3 demonstrate that the proposed method exhibits better robustness and accuracy than standard multivariate learning techniques, especially for small training sample sets.

Daniyal Amir Awan, Renato L. G. Cavalcante, Zoran Utkovski et al.

Cloud-radio access network (C-RAN) can enable cell-less operation by connecting distributed remote radio heads (RRHs) via fronthaul links to a powerful central unit. In conventional C-RAN, baseband signals are forwarded after quantization/ compression to the central unit for centralized processing to keep the complexity of the RRHs low. However, the limited capacity of the fronthaul is thought to be a significant bottleneck in the ability of C-RAN to support large systems (e.g. massive machine-type communications (mMTC)). Therefore, in contrast to the conventional C-RAN, we propose a learning-based system in which the detection is performed locally at each RRH and only the likelihood information is conveyed to the CU. To this end, we develop a general set-theoretic learningmethod to estimate likelihood functions. The method can be used to extend existing detection methods to the C-RAN setting.

Matthias Mehlhose, Daniyal Amir Awan, Renato L. G. Cavalcante et al.

Conventional multiuser detection techniques either require a large number of antennas at the receiver for a desired performance, or they are too complex for practical implementation. Moreover, many of these techniques, such as successive interference cancellation (SIC), suffer from errors in parameter estimation (user channels, covariance matrix, noise variance, etc.) that is performed before detection of user data symbols. As an alternative to conventional methods, this paper proposes and demonstrates a low-complexity practical Machine Learning (ML) based receiver that achieves similar (and at times better) performance to the SIC receiver. The proposed receiver does not require parameter estimation; instead it uses supervised learning to detect the user modulation symbols directly. We perform comparisons with minimum mean square error (MMSE) and SIC receivers in terms of symbol error rate (SER) and complexity.

Daniyal Amir Awan, Renato L. G. Cavalcante, Masahiro Yukawa et al.

Non-orthogonal multiple access (NOMA) has emerged as a promising radio access technique for enabling the performance enhancements promised by the fifth-generation (5G) networks in terms of connectivity, low latency, and high spectrum efficiency. In the NOMA uplink, successive interference cancellation (SIC) based detection with device clustering has been suggested. In the case of multiple receive antennas, SIC can be combined with the minimum mean-squared error (MMSE) beamforming. However, there exists a tradeoff between the NOMA cluster size and the incurred SIC error. Larger clusters lead to larger errors but they are desirable from the spectrum efficiency and connectivity point of view. We propose a novel online learning based detection for the NOMA uplink. In particular, we design an online adaptive filter in the sum space of linear and Gaussian reproducing kernel Hilbert spaces (RKHSs). Such a sum space design is robust against variations of a dynamic wireless network that can deteriorate the performance of a purely nonlinear adaptive filter. We demonstrate by simulations that the proposed method outperforms the MMSE-SIC based detection for large cluster sizes.

Martin Kasparick, Renato L. G. Cavalcante, Stefan Valentin et al.

In this paper, we address the problem of reconstructing coverage maps from path-loss measurements in cellular networks. We propose and evaluate two kernel-based adaptive online algorithms as an alternative to typical offline methods. The proposed algorithms are application-tailored extensions of powerful iterative methods such as the adaptive projected subgradient method and a state-of-the-art adaptive multikernel method. Assuming that the moving trajectories of users are available, it is shown how side information can be incorporated in the algorithms to improve their convergence performance and the quality of the estimation. The complexity is significantly reduced by imposing sparsity-awareness in the sense that the algorithms exploit the compressibility of the measurement data to reduce the amount of data which is saved and processed. Finally, we present extensive simulations based on realistic data to show that our algorithms provide fast, robust estimates of coverage maps in real-world scenarios. Envisioned applications include path-loss prediction along trajectories of mobile users as a building block for anticipatory buffering or traffic offloading.