The explosive growth of distributed data generation — spanning data centers, sensor networks, massive IoT, and edge learning places an unsustainable burden on modern infrastructure, where the energy and latency costs of moving raw data often outstrip those of processing it. While analog over-the-air computation (OAC) promises a solution by exploiting the natural superposition of wireless waveforms to aggregate data in-channel, it remains fragile against noise and fundamentally incompatible with the ubiquitous digital hardware that powers all modern communication systems.

This thesis introduces a digital-native framework that unifies communication and computation at the physical layer. Rather than treating channel interference as an obstacle, we engineer the geometry of digital constellations so that the superposition of signals directly yields the desired function value. This paradigm shift transforms the communication link from a passive data pipe into an active computational engine, applicable to any multiple-access channel—whether wired or wireless—without requiring the decoding of individual inputs.

We generalize this framework along three axes to ensure scalability and reliability across diverse network environments. First, we develop noise-aware constellation designs that optimize inter-symbol geometry for non-Gaussian and heavy-tailed interference, ensuring robustness beyond standard Euclidean metrics. Second, we introduce a sampling-based reduction strategy that leverages the symmetry of aggregation functions to cut design complexity by orders of magnitude, enabling deployment in massive-scale networks. Third, we extend the framework to vector-valued computation, utilizing spatial degrees of freedom to perform complex, multi-dimensional aggregations in a single transmission shot without relying on perfect channel state information.

Finally, to bridge the gap to immediate deployment, we present a closed-form algebraic coding scheme for exact summation. The proposed solution integrates seamlessly with standard quadrature amplitude modulation, eliminating the need for complex optimization and offering a plug-and-play solution for digital aggregation. We validate these contributions through the lens of Federated Edge Learning, demonstrating that computation-by-communication is not only feasible using standard digital protocols but significantly outperforms traditional orthogonal transmission. Collectively, these works prove that computation-by-communication is not only feasible on digitally modulated signals but superior to analog alternatives, paving the way for the next generation of compute-aware networks, enabling energy efficient, scalable, and robust intelligence across any digital infrastructure.

Recently, over-the-air computation (AirComp) leverages the superposition property of wireless channels to enable efficient function computation over a multiple access channel (MAC). However, existing digital AirComp methods either rely on single-symbol modulation, which limits flexibility and robustness, or on multi-symbol extensions that suffer from high complexity or approximation errors. To overcome these limitations, we propose a new multi-symbol modulation framework, termed sequential modulation for AirComp (SeMAC), which encodes each input into a sequence of symbols with distinct constellation diagrams across multiple time slots. This approach increases design flexibility and robustness against channel noise. Specifically, the modulation design is formulated as a non-convex optimization problem and efficiently solved through a successive convex approximation (SCA) combined with stochastic subgradient descent (SSD). For fixed modulation formats, we further develop SeMAC with power adaptation (SeMAC-PA) to adjusts transmit power and phase while preserving the modulation structure. Notably, numerical results show that SeMAC improves computation accuracy by up to 14 dB compared to the existing methods for computing nonlinear functions such as the product function.

To meet the growing demands for connectivity and reliability in cellular networks, it is essential to ensure reliable quality of service (QoS) guarantees for end users. The integration of predictive QoS (pQoS) in cellular networks enables proactive fulfillment of QoS requirements for a diverse range of applications, including intelligent transportation systems. This study presents a pQoS framework in cellular networks, particularly for connected vehicles, that divides the road into segments, clusters them, and assigns a pQoS model to each cluster. By implementing this framework, we mitigate the concept drift of the pQoS model induced by variations in the propagation environment and interference. Each predictive cluster model is locally trained on vehicles traveling within the cluster boundaries using federated learning. A significant challenge is balancing the trade-off between the number of clusters, prediction accuracy, and communication overhead for updating local models. This trade-off suggests the novel problem of performing a joint optimization of the training and number of clusters. To address such difficult optimization, we propose an iterative approximate solution using proximal alternative minimization for which we provide convergence guarantees. Ultimately, by evaluations with real-world data, our numerical findings reveal that our proposed clustered predictive model reduces the mean absolute percentage error by 8%, and the mean absolute error by 7%, compared to conventional predictive approaches proposed by prior studies.

In this paper, we consider the ChannelComp framework, where multiple transmitters aim to compute a function of their values at a common receiver while using digital modulations over a multiple access channel. ChannelComp provides a general framework for computation by designing digital constellations for over-the-air computation. Currently, ChannelComp uses a symbol-level encoding. However, encoding repeated transmissions of the same symbol and performing the function computation using the corresponding received sequence may significantly improve the computation performance and reduce the encoding complexity. In this paper, we propose a new scheme where each transmitter repeats the transmission of the same symbol over multiple time slots while encoding such repetitions and designing constellation diagrams to minimize computational errors. We formally model such a scheme by an optimization problem, whose solution jointly identifies the constellation diagram and the repetition code. We call the proposed scheme Repetition for Multiple Access Computing (ReMAC). To manage the computational complexity of the optimization, we divide it into two tractable subproblems. We verify the performance of ReMAC by numerical experiments. The simulation results reveal that ReMAC can reduce the computation error in noisy and fading channels by approximately up to 4.5 dB compared to standard ChannelComp, particularly for the max function.

Communication and computation are traditionally treated as separate entities, allowing for individual optimizations. However, many applications focus on local information's functionality rather than the information itself. For such cases, harnessing interference for computation in a multiple access channel through digital over-the-air computation can notably increase the computation, as established by the ChannelComp method. However, the coding scheme originally proposed in ChannelComp may suffer from high computational complexity because it is general and is not optimized for specific modulation categories. Therefore, this study considers a specific category of digital modulations for over-the-air computations, quadrature amplitude modulation (QAM) and pulse-amplitude modulation (PAM), for which we introduce a novel coding scheme called SumComp. Furthermore, we derive a mean squared error (MSE) analysis for SumComp coding in the computation of the arithmetic mean function and establish an upper bound on the mean absolute error (MAE) for a set of nomographic functions. Simulation results are presented to affirm the superior performance of SumComp coding compared to traditional analog over-the-air computation and the original coding in ChannelComp approaches in terms of both MSE and MAE over a noisy multiple access channel. Specifically, SumComp coding shows at least 10 dB improvements for computing arithmetic and geometric mean on the normalized MSE for low noise scenarios.

The Internet of Things interconnects billions of devices and forms a vast network where users sporadically transmit short messages through multi-path wireless channels. These channels are characterized by the superposition of a small number of scaled and delayed copies of Dirac spikes. At the receiver, the observed signal is a sum of these convolved signals, and the task is to find the amplitudes, continuous-indexed delays, and transmitted messages from a single signal. This task is inherently ill-posed without additional assumptions on the channel or messages. In this work, we assume the channel exhibits sparsity in the delay domain and that independent and identically distributed random linear encoding is applied to the messages at the devices. Leveraging these assumptions, we propose a semidefinite programming optimization capable of simultaneously recovering both messages and the delay parameters of the channels from only a single received signal. Our theoretical analysis establishes that the required number of samples at the receiver scales proportionally to the sum-product of sparsity and message length of all users, aligning with the degrees of freedom in the lifting-type optimization frameworks. Numerical experiments confirm the efficacy of the proposed method in accurately estimating closely-spaced delay parameters and recovering messages.

Over-the-air computation (AirComp) leverages the signal superposition characteristic of wireless multiple-access channels (MACs) to perform mathematical computations. Initially introduced to enhance communication reliability in interference channels and wireless sensor networks (WSNs), AirComp has more recently found applications in task-oriented communications like wireless distributed learning and in wireless control systems. Its adoption aims to address latency challenges arising from an increased number of edge devices or Internet of Things (IoT) devices accessing the constrained wireless spectrum. This article is the first one to focus on the physical layer (PHY) of these systems. We present a unified framework, 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.

In this paper, we consider the ChannelComp frame-work, which facilitates the computation of desired functions by multiple transmitters over a common receiver using digital mod-ulations across a multiple access channel. While ChannelComp currently offers a broad framework for computation by designing digital constellations for over-the-air computation and employing symbol-level encoding, encoding the repeated transmissions of the same symbol and using the corresponding received sequence may significantly improve the computation performance and reduce the encoding complexity. In this paper, we propose an enhancement involving the encoding of the repetitive transmission of the same symbol at each transmitter over multiple time slots and the design of constellation diagrams, with the aim of minimizing computational errors. We frame this enhancement as an optimization problem, which jointly identifies the constellation diagram and the channel code for repetition, which we call ReChCompCode. To manage the computational complexity of the optimization, we divide it into two tractable subproblems. Through numerical experiments, we evaluate the performance of ReChCompCode. The simulation results reveal that ReCh-CompCode can reduce the computation error by approximately up to 30 dB compared to standard ChannelComp, particularly for product functions.

In this work, we investigate federated edge learning over a fading multiple access channel. To alleviate the communication burden between the edge devices and the access point, we introduce a pioneering digital over-the-air computation strategy employing q-ary quadrature amplitude modulation, culminating in a low latency communication scheme. Indeed, we propose a new federated edge learning framework in which edge devices use digital modulation for over-the-air uplink transmission to the edge server while they have no access to the channel state information. Furthermore, we incorporate multiple antennas at the edge server to overcome the fading inherent in wireless communication. We analyze the number of antennas required to mitigate the fading impact effectively. We prove a non-asymptotic upper bound for the mean squared error for the proposed federated learning with digital over-the-air uplink transmissions under both noisy and fading conditions. Leveraging the derived upper bound, we characterize the convergence rate of the learning process of a non-convex loss function in terms of the mean square error of gradients due to the fading channel. Furthermore, we substantiate the theoretical assurances through numerical experiments concerning mean square error and the convergence efficacy of the digital federated edge learning framework. Notably, the results demonstrate that augmenting the number of antennas at the edge server and adopting higher-order modulations improve the model accuracy up to 60%.

Over-the-air computation (AirComp) is a well-known technique by which several wireless devices transmit by analog amplitude modulation to achieve a sum of their transmit signals at a common receiver. The underlying physical principle is the superposition property of the radio waves. Since such superposition is analog and in amplitude, it is natural that AirComp uses analog amplitude modulations. Unfortunately, this is impractical because most wireless devices today use digital modulations. It would be highly desirable to use digital communications because of their numerous benefits, such as error correction, synchronization, acquisition of channel state information, and widespread use. However, when we use digital modulations for AirComp, a general belief is that the superposition property of the radio waves returns a meaningless overlapping of the digital signals. In this paper, we break through such beliefs and propose an entirely new digital channel computing method named ChannelComp, which can use digital as well as analog modulations. We propose a feasibility optimization problem that ascertains the optimal modulation for computing arbitrary functions over-the-air. Additionally, we propose pre-coders to adapt existing digital modulation schemes for computing the function over the multiple access channel. The simulation results verify the superior performance of ChannelComp compared to AirComp, particularly for the product functions, with more than 10 dB improvement of the computation error.