Predictive Demodulation for Chaotic Communications

Chaotic signals offer promising characteristics for wireless communications due to their wideband nature, low cross-correlation, and sensitivity to initial conditions. Although classical chaotic modulation schemes like Chaos Shift Keying (CSK) can theoretically match the performance of traditional modulation techniques (i.e., bit error rate), practical challenges, such as the difficulty in generating accurate signal replicas at the receiver, limit their effectiveness. Besides, chaotic signals are often considered unpredictable despite their deterministic nature. In this paper, we challenge this view by introducing a novel modulation scheme for chaotic communications that leverages the deterministic behavior of chaotic signals. The proposed approach eliminates the need for synchronized replicas of transmitted waveforms at the receiver. Moreover, to enhance noise robustness, we employ M-ary Frequency Shift Keying (FSK) modulation on the chaotic samples. Experimental results show that the proposed scheme significantly outperforms CSK when perfect replicas are unavailable, with the best performance achieved for low-order modulations, and resulting in minimal delay increase.

Frequency Modulation for Task-Oriented Communications and Multiple Access

In the context of task-oriented communications we advocate the development of waveforms for Federated Edge Learning (FEEL). Over-the-air computing (AirComp) has emerged as a communication scheme that allows to compute a function out of distributed data and can be applied to FEEL. However, the design of modulations for AirComp is still in its infancy and most of the literature ignores this topic. In this work we employ frequency modulation (FM) and type based multiple access (TMBA) for FEEL and demonstrate its advantages with respect to the state of the art in terms of convergence and peak-to-average power ratio (PAPR).

Waveforms for Computing Over the Air

Over-the-air computation (AirComp) leverages the signal-superposition characteristic of wireless multiple access channels to perform mathematical computations. Initially introduced to enhance communication reliability in interference channels and wireless sensor networks, AirComp has more recently found applications in task-oriented communications, namely, for wireless distributed learning and in wireless control systems. Its adoption aims to address latency challenges arising from an increased number of edge devices or IoT devices accessing the constrained wireless spectrum. This paper focuses on the physical layer of these systems, specifically on the waveform and the signal processing aspects at the transmitter and receiver to meet the challenges that AirComp presents within the different contexts and use cases.

Log-FSK: A Frequency Modulation for Over-the-Air Computing

In this study we introduce Logarithmic Frequency Shift Keying (Log-FSK), a novel frequency modulation for over-the-air computing (AirComp). Log-FSK leverages non-linear signal processing to produce AirComp in the frequency domain, this is, the maximum frequency of the received signal corresponds to the sum of the individual transmitted frequencies. The demodulation procedure relies on the inverse Discrete Cosine Transform (DCT) and the extraction of the maximum frequency component. We provide the theoretical performance in terms of error probability and mean squared error. To demonstrate its practicality, we present specific applications and experimental results showcasing the effectiveness of Log-FSK AirComp within linear Wireless Sensor Networks (WSN). Our experiments show that Log-FSK outperforms linear AirComp, implemented with double sideband (DSB), when working above the threshold SNR.

Adaptive function approximation based on the Discrete Cosine Transform (DCT)

This paper studies the cosine as basis function for the approximation of univariate and continuous functions without memory. This work studies a supervised learning to obtain the approximation coefficients, instead of using the Discrete Cosine Transform (DCT). Due to the finite dynamics and orthogonality of the cosine basis functions, simple gradient algorithms, such as the Normalized Least Mean Squares (NLMS), can benefit from it and present a controlled and predictable convergence time and error misadjustment. Due to its simplicity, the proposed technique ranks as the best in terms of learning quality versus complexity, and it is presented as an attractive technique to be used in more complex supervised learning systems. Simulations illustrate the performance of the approach. This paper celebrates the 50th anniversary of the publication of the DCT by Nasir Ahmed in 1973.

LoRa Modulation for Split Learning

We design a task-oriented communication design for Split learning (SL). Specifically, we propose to use a variant of the Long Range (LoRa) modulation and an orthogonal chirp division multiplexing (OCDM) access scheme. As we implement an Expressive Neural Network (ENN), this is, an architecture with adaptive activation functions (AAF), the modulation is also suited for the computing side of the problem. The cosine nature of the modulation matches the Discrete Cosine Transform (DCT) model used to implement the AAFs. We also propose a variant of the waveform to control the transmission bandwidth. Our results show that scheme achieves high accuracy up to -15 dB in the presence of additive white Gaussian noise (AWGN), and up to -12.5 dB in the case of Rayleigh fading.

ENN: A Neural Network with DCT-Adaptive Activation Functions

The expressiveness of neural networks highly depends on the nature of the activation function, although these are usually assumed predefined and fixed during the training stage. In this paper we present Expressive Neural Network (ENN), a novel architecture in which the non-linear activation functions are modeled using the Discrete Cosine Transform (DCT) and adapted using backpropagation during training. This parametrization keeps the number of trainable parameters low, is appropriate for gradient-based schemes, and adapts to different learning tasks. This is the first non-linear model for activation functions that relies on a signal processing perspective, providing high flexibility and expressiveness to the network. We contribute with insights in the explainability of the network at convergence by recovering the concept of bump, this is, the response of each activation function in the output space to provide insights. Finally, through exhaustive experiments we show that the model can adapt to classification and regression tasks. The performance of ENN outperforms state of the art benchmarks, providing up to a 40\% gap in accuracy in some scenarios.

Over the Air Computing for Satellite Networks in 6G

6G and beyond networks will merge communication and computation capabilities in order to adapt to changes. As they will consist of many sensors gathering information from its environment, new schemes for managing these large amounts of data are needed. For this purpose, we review Over the Air (OTA) computing in the context of estimation and detection. For distributed scenarios, such as a Wireless Sensor Network, it has been proven that a separation theorem does not necessarily hold, whereas analog schemes may outperform digital designs. We outline existing gaps in the literature, evincing that current state of the art requires a theoretical framework based on analog and hybrid digital-analog schemes that will boost the evolution of OTA computing. Furthermore, we motivate the development of 3D networks based on OTA schemes, where satellites function as sensors. We discuss its integration within the satellite segment, delineate current challenges and present a variety of use cases that benefit from OTA computing in 3D networks.

DCT-based Air Interface Design for Function Computation

With the integration of communication and computing, it is expected that part of the computing is transferred to the transmitter side. In this paper we address the general problem of Frequency Modulation (FM) for function approximation through a communication channel. We exploit the benefits of the Discrete Cosine Transform (DCT) to approximate the function and design the waveform. In front of other approximation schemes, the DCT uses basis of controlled dynamic, which is a desirable property for a practical implementation. Furthermore, the proposed modulation allows to recover both the measurement and the function in a single transmission. Our experiments show that this scheme outperforms the double side-band (DSB) modulation in terms of mean squared error (MSE). This can also be implemented with an agnostic receiver, in which the function is unknown to the receiver. Finally, the proposed modulation is compatible with some of the existing transmission technologies for sensor networks.

Frequency Modulation Aggregation for Federated Learning

Federated edge learning (FEEL) is a framework for training models in a distributed fashion using edge devices and a server that coordinates the learning process. In FEEL, edge devices periodically transmit model parameters to the server, which aggregates them to generate a global model. To reduce the burden of transmitting high-dimensional data by many edge devices, a broadband analog transmission scheme has been proposed. The devices transmit the parameters concurrently using a linear analog modulation, which are aggregated by the superposition nature of the wireless medium. However, linear analog modulations incur in an excessive power consumption for edge devices and are not suitable for current digital wireless systems. To overcome this issue, in this paper we propose a digital frequency broadband aggregation. The scheme integrates a Multiple Frequency Shift Keying (MFSK) at the transmitters and a type-based multiple access (TBMA) at the receiver. Using concurrent transmission, the server can recover the type (i.e., a histogram) of the transmitted parameters and compute any aggregation function to generate a shared global model. We provide a extensive analysis of the communication scheme in an AWGN channel and compare it with linear analog modulations. Our experimental results show that the proposed scheme achieves the same performance, although it requires 14 dB less in peak-to-average power ratio (PAPR) than linear analog modulations.