The DCT Neuron for Estimation and Compensation of Amplitude Distortions in OFDM Systems

We present a receiver-side framework for identifying amplitude distortions in frequency-selective OFDM channels. The core novelty is the use of the DCT Neuron, a compact adaptive processor based on the discrete cosine transform (DCT), to characterize the channel's nonlinear response, leveraging its properties for highly efficient estimation. Operating directly in the time domain, the method builds an accurate signal model and tracks channel variations adaptively, achieving reliable identification with as few as two OFDM symbols. The learned nonlinear response can then be exploited for predistortion and iterative decoding, enabling low-complexity, real-time adaptive compensation of complex responses in multicarrier systems.

Efficient Neural Networks with Discrete Cosine Transform Activations

In this paper, we extend our previous work on the Expressive Neural Network (ENN), a multilayer perceptron with adaptive activation functions parametrized using the Discrete Cosine Transform (DCT). Building upon previous work that demonstrated the strong expressiveness of ENNs with compact architectures, we now emphasize their efficiency, interpretability and pruning capabilities. The DCT-based parameterization provides a structured and decorrelated representation that reveals the functional role of each neuron and allows direct identification of redundant components. Leveraging this property, we propose an efficient pruning strategy that removes unnecessary DCT coefficients with negligible or no loss in performance. Experimental results across classification and implicit neural representation tasks confirm that ENNs achieve state-of-the-art accuracy while maintaining a low number of parameters. Furthermore, up to 40% of the activation coefficients can be safely pruned, thanks to the orthogonality and bounded nature of the DCT basis. Overall, these findings demonstrate that the ENN framework offers a principled integration of signal processing concepts into neural network design, achieving a balanced trade-off between expressiveness, compactness, and interpretability.

Robust Over-the-Air Computation with Type-Based Multiple Access

This paper utilizes the properties of type-based multiple access (TBMA) to investigate its effectiveness as a robust approach for over-the-air computation (AirComp) in the presence of Byzantine attacks, this is, adversarial strategies where malicious nodes intentionally distort their transmissions to corrupt the aggregated result. Unlike classical direct aggregation (DA) AirComp, which aggregates data in the amplitude of the signals and are highly vulnerable to attacks, TBMA distributes data over multiple radio resources, enabling the receiver to construct a histogram representation of the transmitted data. This structure allows the integration of classical robust estimators and supports the computation of diverse functions beyond the arithmetic mean, which is not feasible with DA. Through extensive simulations, we demonstrate that robust TBMA significantly outperforms DA, maintaining high accuracy even under adversarial conditions, and showcases its applicability in federated learning (FEEL) scenarios. Additionally, TBMA reduces channel state information (CSI) requirements, lowers energy consumption, and enhances resiliency by leveraging the diversity of the transmitted data. These results establish TBMA as a scalable and robust solution for AirComp, paving the way for secure and efficient aggregation in next-generation networks.

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).

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.

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.

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.

LoRa-based Over-the-Air Computing for Sat-IoT

Satellite Internet of Things (Sat-IoT) is a novel framework in which satellites integrate sensing, communication and computing capabilities to carry out task-oriented communications. In this paper we propose to use the Long Range (LoRa) modulation for the purpose of estimation in a Sat-IoT scenario. Then we realize that the collisions generated by LoRa can be harnessed in an Over-the-Air Computing (AirComp) framework. Specifically, we propose to use LoRa for Type-based Multiple Access (TBMA), a semantic-aware scheme in which communication resources are assigned to different parameters, not users. Our experimental results show that LoRa-TBMA is suitable as a massive access scheme, provides large gains in terms of mean squared error (MSE) and saves scarce satellite communication resources (i.e., power, latency and bandwidth) with respect to orthogonal multiple access schemes. We also analyze the satellite scenarios that could take advantage of the LoRa-TBMA scheme. In summary, that angular modulations, which are very useful in satellite communications, can also benefit from AirComp.