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.

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.

This paper presents a novel distributed computing framework, DCbMF (Distributed Computing by Matrix Factorization), for the efficient computation of linearly separable functions. Our framework operates within a multicast network of interconnected computing nodes to compute a set of output functions from input data through an efficient three-step process - Map, Shuffle, and Reduce. We cast the computation procedure as a sparse matrix factorization problem to achieve efficient communication and computation. To this end, we formulate an ℓ0 optimization problem that seeks to minimize the number of nonzero elements in each matrix factor. Due to the intractability of ℓ0 minimization, we turn to a relaxed ℓ1 formulation of the problem. We devise a modified alternating direction method of multipliers to solve the biconvex optimization problem and prove the convergence of our algorithm to a stationary solution. The numerical experiments show that DCbMF outperforms similar computing frameworks for linearly separable function computation, achieving a substantial reduction in communication overhead by 98% while maintaining the same computation cost. Notably, leveraging sparse matrix factorization and alternating optimization highlights a fundamental tradeoff between compu-tation and communication costs and paves the way for scalable and efficient distributed computing applications.

In this paper, we investigate the problem of recovering the frequency components of a mixture of K complex sinusoids from a random subset of N equally-spaced time-domain samples. Because of the random subset, the samples are effectively non-uniform. Besides, the frequency values of each of the K complex sinusoids are assumed to vary continuously within a given range. For this problem, we propose a two-step strategy: (i) we first lift the incomplete set of uniform samples (unavailable samples are treated as missing data) into a structured matrix with missing entries, which is potentially low-rank; then (ii) we complete the matrix using a weighted nuclear minimization problem. We call the method a weighted lifted-structured (WLi) low-rank matrix recovery. Our approach can be applied to a range of matrix structures such as Hankel and double-Hankel, among others, and provides improvement over the unweighted existing schemes such as EMaC and DEMaC. We provide theoretical guarantees for the proposed method, as well as numerical simulations in both noiseless and noisy settings. Both the theoretical and the numerical results confirm the superiority of the proposed approach.

Resource allocation and multiple access schemes are instrumental for the success of communication networks, which facilitate seamless wireless connectivity among a growing population of uncoordinated and non-synchronized users. In this paper, we present a novel random access scheme that addresses one of the most severe barriers of current strategies to achieve massive connectivity and ultra reliable and low latency communications for 6G. The proposed scheme utilizes wireless channels’ angular continuous group-sparsity feature to provide low latency, high reliability, and massive access features in the face of limited time-bandwidth resources, asynchronous transmissions, and preamble errors. Specifically, a reconstruction-free goal oriented optimization problem is proposed which preserves the angular information of active devices and is then complemented by a clustering algorithm to assign active users to specific groups. This allows to identify active stationary devices according to their line of sight angles. Additionally, for mobile devices, an alternating minimization algorithm is proposed to recover their preamble, data, and channel gains simultaneously, enabling the identification of active mobile users. Simulation results show that the proposed algorithm provides excellent performance and supports a massive number of devices. Moreover, the performance of the proposed scheme is independent of the total number of devices, distinguishing it from other random access schemes. The proposed method provides a unified solution to meet the requirements of machine-type communications and ultra reliable and low latency communications, making it an important contribution to the emerging 6G networks.

The imminent Internet of Things, fueled by 6G networks and machine learning technologies, is set to shift wireless communication to machine-centric paradigms, revolutionizing sectors such as healthcare or industrial automation through efficient data handling. However, this connectivity boom poses challenges, including straining existing communication systems due to increased data traffic and computational demands.

Over-the-air computation (OAC) presents a feasible solution, allowing the summation of transmitted signals at a common receiver through analog amplitude modulation. Designed to enable concurrent data collection and computation at the network edge, OAC seeks to lessen the central system burden, reducing latency and energy usage while enabling real-time analytics. This approach is particularly beneficial for federated learning, a machine learning technique that operates across decentralized devices. However, OAC's dependence on analog communication poses notable challenges, including signal distortion during transmission and the limited availability of devices supporting analog modulations. Digital modulation is a preferable alternative, recognized for its excellent channel correction capabilities and broad acceptance in modern wireless devices. Nevertheless, its integration into OAC is perceived as a significant hurdle, with overlapping digitally modulated signals threatening the fundamental concept of simultaneous data collection and computation.

The first part of the thesis provides an overview of communication systems, specifically focusing on the relevant OAC methodologies for analog and digital parts and their application in ML, particularly in training federated learning models. Subsequently, an exhaustive literature review concerning analog OAC techniques is undertaken, identifying existing limitations within this domain. The central thrust of our research is then introduced, proposing an innovative digital OAC approach along with a fresh perspective on the communication systems models designed for executing the computation. The chapter concludes with a summary of the principal contributions of each paper included within the thesis.

In the second part, we introduce ChannelComp, a groundbreaking computing approach compatible with current digital communication systems, including smartphones and IoT devices. A detailed analysis of ChannelComp's functions reveals how it enables digital modulation schemes to perform computations, addressing a critical gap in previous research. Moreover, introducing pre-coders designed for function computation over the multiple access channel, combined with a feasibility optimization problem framework, allows for seamless integration with current systems. Compared to OAC, restricted to analog modulations, ChannelComp exhibits broader computational capabilities and adherence to strict computation time constraints, thus showcasing its robust potential for future massive machine-type communications. This innovative method signifies a promising direction toward sustainable and efficient future wireless communication.

Den nära förestående Internet of Things, drivet av 6G-nätverk och maskininlärningsteknologier, är på väg att förändra trådlös kommunikation till maskincentrerade paradigm, revolutionerande sektorer som hälso- och sjukvård samt industriell automatisering genom effektiv datahantering. Dock medför denna uppkopplingsboom utmaningar, inklusive påfrestningar på befintliga kommunikationssystem på grund av ökad datatrafik och beräkningsbehov.

Over-the-air-beräkning (OAC) framstår som en genomförbar lösning, genom att tillåta summering av överförda signaler hos en gemensam mottagare genom analog amplitudmodulering. Utformad för att möjliggöra samtidig datainsamling och beräkning vid nätverkskanten, strävar OAC efter att minska den centrala systembelastningen, minska latens och energiförbrukning samtidigt som det möjliggör realtidsanalys. Denna metod är särskilt fördelaktig för federerad inlärning, en maskininlärningsteknik som fungerar över decentraliserade enheter. Dock medför OAC:s beroende av analog kommunikation märkbara utmaningar, inklusive signal distortion under överföring och begränsad tillgänglighet av enheter som stöder analoga moduleringar. Digital modulering är ett föredraget alternativ, erkänt för dess utmärkta kanalkorrigeringsegenskaper och bred acceptans i moderna trådlösa enheter. Trots detta uppfattas dess integration i OAC som ett betydande hinder, med överlappande digitalt modulerade signaler som hotar den grundläggande konceptet med samtidig datainsamling och beräkning.

Den första delen av avhandlingen ger en översikt över kommunikationssystem, med särskilt fokus på relevanta OAC-metodiker för analoga och digitala delar och deras tillämpning i ML, särskilt vid träning av federerade inlärningsmodeller. Därefter genomförs en omfattande litteraturöversikt angående analoga OAC-tekniker, där befintliga begränsningar inom detta område identifieras. Forskningens centrala drivkraft introduceras sedan, med förslag på en innovativ digital OAC-metod tillsammans med ett nytt perspektiv på kommunikationssystemmodeller utformade för att utföra beräkningen. Kapitlet avslutas med en sammanfattning av de huvudsakliga bidragen från varje artikel inkluderad i avhandlingen.

I den andra delen introducerar vi ChannelComp, en ny och banbrytande beräkningsmetod som är kompatibel med nuvarande digitala kommunikationssystem, inklusive smartphones och IoT-enheter. En detaljerad analys av ChannelComp:s funktioner avslöjar hur den möjliggör digitala moduleringsscheman för att utföra beräkningar, vilket adresserar en kritisk lucka i tidigare forskning. Dessutom möjliggör introduktionen av förkodare utformade för funktionsberäkning över den fleraccessa kanalen, kombinerat med ett ramverk för genomförbarhetsoptimeringsproblem, en sömlös integration med nuvarande system. Jämfört med OAC, begränsad till analoga moduleringar, uppvisar ChannelComp bredare beräkningsmöjligheter och efterlevnad av strikta beräkningstidsbegränsningar, vilket visar dess robusta potential för framtida massiva maskintypkommunikationer. Denna innovativa metod signalerar en lovande riktning mot hållbar och effektiv framtida trådlös kommunikation.

Over-the-air computation (AirComp) is a known technique in which wireless devices transmit values by analog amplitude modulation so that a function of these values is computed over the communication channel at a common receiver. The physical reason is the superposition properties of the electromagnetic waves, which naturally return sums of analog values. Consequently, the applications of AirComp are almost entirely restricted to analog communication systems. However, the use of digital communications for over-the-air computations would have several benefits, such as error correction, synchronization, acquisition of channel state information, and easier adoption by current digital communication systems. Nevertheless, a common belief is that digital modulations are generally unfeasible for computation tasks because the overlapping of digitally modulated signals returns signals that seem to be meaningless for these tasks. This paper breaks through such a belief and proposes a fundamentally new computing method, named ChannelComp, for performing over-the-air computations by any digital modulation. In particular, we propose digital modulation formats that allow us to compute a wider class of functions than AirComp can compute, and we propose a feasibility optimization problem that ascertains the optimal digital modulation for computing functions over-the-air. The simulation results verify the superior performance of ChannelComp in comparison to AirComp, particularly for the product functions, with around 10 dB improvement of the computation error.

We consider the problem of gridless blind deconvolution and demixing (GB2D) in scenarios where multiple users communicate messages through multiple unknown channels, and a single base station (BS) collects their contributions. This scenario arises in various communication fields, including wireless communications, the Internet of Things, over-the-air computation, and integrated sensing and communications. In this setup, each user's message is convolved with a multi-path channel formed by several scaled and delayed copies of Dirac spikes. The BS receives a linear combination of the convolved signals, and the goal is to recover the unknown amplitudes, continuous-indexed delays, and transmitted waveforms from a compressed vector of measurements at the BS. However, without prior knowledge of the transmitted messages and channels, GB2D is highly challenging and intractable in general. To address this issue, we assume that each user's message follows a distinct modulation scheme living in a known low-dimensional subspace. By exploiting these subspace assumptions and the sparsity of the multipath channels for different users, we transform the nonlinear GB2D problem into a matrix tuple recovery problem from a few linear measurements. To achieve this, we propose a semidefinite programming optimization that exploits the specific low-dimensional structure of the matrix tuple to recover the messages and continuous delays of different communication paths from a single received signal at the BS. Finally, our numerical experiments show that our proposed method effectively recovers all transmitted messages and the continuous delay parameters of the channels with sufficient samples.