Recently, the ChannelComp framework has proposed digital over-the-air computation by designing digital modulations that enable the computation of arbitrary functions. Unlike traditional analog over-the-air computation, which is restricted to nomographic functions, ChannelComp enables a broader range of computational tasks while maintaining compatibility with digital communication systems. This framework is intended for applications that favor local information processing over the mere acquisition of data. However, ChannelComp is currently designed for scalar function computation, while numerous data-centric applications necessitate vector-based computations, and it is susceptible to channel fading. In this work, we introduce a generalization of the ChannelComp framework, called VecComp, by integrating ChannelComp with multiple-antenna technology. This generalization not only enables vector function computation but also ensures scalability in the computational complexity, which increases only linearly with the vector dimension. As such, VecComp remains computationally efficient and robust against channel impairments, making it suitable for high-dimensional, data-centric applications. We establish a non-asymptotic upper bound on the mean squared error of VecComp, affirming its computation efficiency under fading channel conditions. Numerical experiments show the effectiveness of VecComp in improving the computation of vector functions and fading compensation over noisy and fading multiple-access channels.

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.

Abstract In this work, we consider a federated learning model in a wireless system with multiple base stations and inter‐cell interference. We apply a differentially private scheme to transmit information from users to their corresponding base station during the learning phase. We show the convergence behavior of the learning process by deriving an upper bound on its optimality gap. Furthermore, we define an optimization problem to reduce this upper bound and the total privacy leakage. To find the locally optimal solutions of this problem, we first propose an algorithm that schedules the resource blocks and users. We then extend this scheme to reduce the total privacy leakage by optimizing the differential privacy artificial noise. We apply the solutions of these two procedures as parameters of a federated learning system where each user is equipped with a classifier and communication cells have mostly fewer resource blocks than numbers of users. The simulation results show that our proposed scheduler improves the average accuracy of the predictions compared with a random scheduler. In particular, the results show an improvement of over 6%. Furthermore, its extended version with noise optimizer significantly reduces the amount of privacy leakage.

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 investigates efficient distributed training of a Federated Learning (FL) model over a wireless network of wireless devices. The communication iterations of the distributed training algorithm may be substantially deteriorated or even blocked by the effects of the devices’ background traffic, packet losses, congestion, or latency. We abstract the communication-computation impacts as an ‘iteration cost’ and propose a cost-aware causal FL algorithm (FedCau) to tackle this problem. We propose an iteration-termination method that trade-offs the training performance and networking costs. We apply our approach when workers use the slotted-ALOHA, carrier-sense multiple access with collision avoidance (CSMA/CA), and orthogonal frequency-division multiple access (OFDMA) protocols. We show that, given a total cost budget, the training performance degrades as either the background communication traffic or the dimension of the training problem increases. Our results demonstrate the importance of proactively designing optimal cost-efficient stopping criteria to avoid unnecessary communication-computation costs to achieve a marginal FL training improvement. We validate our method by training and testing FL over the MNIST and CIFAR-10 dataset. Finally, we apply our approach to existing communication efficient FL methods from the literature, achieving further efficiency. We conclude that cost-efficient stopping criteria are essential for the success of practical FL over wireless networks.

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 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.

In the resource management of wireless networks, Federated Learning has been used to predict handovers. However, non-independent and identically distributed data degrade the accuracy performance of such predictions. To overcome the problem, Federated Learning can leverage data clustering algorithms and build a machine learning model for each cluster. However, traditional data clustering algorithms, when applied to the handover prediction, exhibit three main limitations: the risk of data privacy breach, the fixed shape of clusters, and the non-adaptive number of clusters. To overcome these limitations, in this paper, we propose a three-phased data clustering algorithm, namely: generative adversarial network-based clustering, cluster calibration, and cluster division. We show that the generative adversarial network-based clustering preserves privacy. The cluster calibration deals with dynamic environments by modifying clusters. Moreover, the divisive clustering explores the different number of clusters by repeatedly selecting and dividing a cluster into multiple clusters. A baseline algorithm and our algorithm are tested on a time series forecasting task. We show that our algorithm improves the performance of forecasting models, including cellular network handover, by 43%.

Full-duplex communications have the potential to almost double the spectral efficiency. To realize such a potentiality, the signal separation at base station’s antennas plays an essential role. This article addresses the fundamentals of such separation by proposing a new smart antenna architecture that allows every antenna to be either shared or separated between uplink and downlink transmissions. The benefits of such architecture are investigated by an assignment problem to optimally assign antennas, beamforming and power to maximize the weighted sum spectral efficiency. We propose a near-to-optimal solution using block coordinate descent that divides the problem into assignment problems, which are NP-hard, a beamforming and power allocation problems. The optimal solutions for the beamforming and power allocation are established while near-to-optimal solutions to the assignment problems are derived by semidefinite relaxation. Numerical results indicate that the proposed solution is close to the optimum, and it maintains a similar performance for high and low residual self-interference powers. With respect to the usually assumed antenna separation technique and half-duplex transmission, the sum spectral efficiency gains increase with the number of antennas. We conclude that our proposed smart antenna assignment for signal separation is essential to realize the benefits of multiple antenna full-duplex communications.

Millimeter-wave using large-antenna arrays is a key technological component for the future cellular systems, where it is expected that hybrid beamforming along with quantized phase shifters will be used due to their implementation and cost efficiency. In this paper, we investigate the efficacy of full-duplex mmWave communication with hybrid beamforming using low-resolution phase shifters. We assume that the self-interference can be sufficiently cancelled by a combination of propagation domain and digital self-interference techniques, without any analog self-interference cancellation. We formulate the problem of joint self-interference suppression and downlink beamforming as a mixed-integer nonconvex joint optimization problem. We propose LowRes, a near-to-optimal solution using penalty dual decomposition. Numerical results indicate that LowRes using low-resolution phase shifters perform within 3% of the optimal solution that uses infinite phase shifter resolution. Moreover, even a single quantization bit outperforms half-duplex transmissions, respectively by 29% and 10% for both low and high residual self-interference scenarios, and for a wide range of practical antenna to radio-chain ratios. Thus, we conclude that 1-bit phase shifters suffice for full-duplex millimeter-wave communications, without requiring any additional new analog hardware.

To increase the spectral efficiency of wireless networks without requiring full-duplex capability of user devices, a potential solution is the recently proposed three-node full-duplex mode. To realize this potential, networks employing three-node full-duplex transmissions must deal with self-interference and user-to-user interference, which can be managed by frequency channel and power allocation techniques. Whereas previous works investigated either spectral efficient or fair mechanisms, a scheme that balances these two metrics among users is investigated in this paper. This balancing scheme is based on a new solution method of the multi-objective optimization problem to maximize the weighted sum of the per-user spectral efficiency and the minimum spectral efficiency among users. The mixed integer nonlinear nature of this problem is dealt by Lagrangian duality. Based on the proposed solution approach, a low-complexity centralized algorithm is developed, which relies on large scale fading measurements that can be advantageously implemented at the base station. Numerical results indicate that the proposed algorithm increases the spectral efficiency and fairness among users without the need of weighting the spectral efficiency. An important conclusion is that managing user-to-user interference by resource assignment and power control is crucial for ensuring spectral efficient and fair operation of full-duplex networks.

In cellular networks, the three-node full-duplex transmission mode has the potential to increase spectral efficiency without requiring full-duplex capability of users. Consequently, three-node full-duplex in cellular networks must deal with self-interference and user-to-user interference, which can be managed by power control and user-frequency assignment techniques. This paper investigates the problem of maximizing the sum spectral efficiency by jointly determining the transmit powers in a distributed fashion, and assigning users to frequency channels. The problem is formulated as a mixed-integer nonlinear problem, which is shown to be non-deterministic polynomial-time hard. We investigate a close-to-optimal solution approach by dividing the joint problem into a power control problem and an assignment problem. The power control problem is solved by Fast-Lipschitz optimization, while a greedy solution with guaranteed performance is developed for the assignment problem. Numerical results indicate that compared with the half-duplex mode, both spectral and energy efficiencies of the system are increased by the proposed algorithm. Moreover, results show that the power control and assignment solutions have important, but opposite roles in scenarios with low or high self-interference cancellation. When the self-interference cancellation is high, user-frequency assignment is more important than power control, while power control is essential at low self-interference cancellation.

A promising new transmission mode in cellular networks is the three-node full-duplex (FD) mode, which involves a base station with FD capability and two half-duplex user transmissions on the same frequency channel for uplink and downlink. The three-node FD mode can increase spectral efficiency, especially in the low transmit power regime, without requiring FD capability at user devices. However, when a large set of users are scheduled in this mode, self-interference at the base station and user-to-user interference can substantially hinder the potential gains of FD communications. This paper investigates the problem of grouping users to pairs and assigning frequency channels to each pair in a spectral efficient and fair manner. Specifically, the joint problem of user uplink/downlink frequency channel pairing and power allocation is formulated as a mixed integer nonlinear problem that is solved by a novel joint fairness assignment maximization algorithm. Realistic system-level simulations indicate that the spectral efficiency of the users having the lowest spectral efficiency is increased by the proposed algorithm, while a high ratio of connected users in different loads and self-interference levels is maintained.

Researches in Power Control (PC) schemes are fundamental to provide efficient algorithms and understand their behavior in Device-to-Device (D2D) scenario. The aim of the current study is to investigate Open Loop Power Control (OLPC), Closed Loop Power Control (CLPC) and indicate Soft Dropping Power Control (SDPC) like an alternative PC scheme to D2D communications underlaying a cellular network. We briefly review PC schemes, suggest a new point of dynamic offset compensation factor σ setting the issue in CLPC and evaluate its performance in terms of spectral and power efficiency. Results demonstrate that SDPC keeps a reasonable spectral efficiency and provides a gain of 70 % in power efficiency in relation Long Term Evolution (LTE) PC schemes for cellular communications, and the factor σ = 0.8 can modify the behavior of CLPC because increases the Signal to Interference-plus-Noise Ratio (SINR) of the worst users.

For systems with reuse factor less than one, the co- channel interference can drastically reduce the gain of primary networks, which limits the whole system performance. This paper exploits the selection of Downlink (DL) or Uplink (UL) band to be reused by a Device-to-Device (D2D) link. The band selected by the method is based on a radio distance metric, such as received power. Despite being a simple concept, results have shown that band selection can effectively mitigate the interference caused by D2D communications in a Long Term Evolution (LTE) network. Therefore, the coexistence of cellular and D2D communication modes becomes possible in time, frequency, and space.

Device-to-Device (D2D) communications underlying cellular networks are a way to increase the network capacity and potentially save the battery lifetime of closely located physical devices. However, D2D communications can generate significant interference to the cellular network when the same resources are shared by both systems. Therefore, the design of Power Control (PC) schemes is required to keep the interference under control, get energy-efficient transmissions and protect cellular devices. In this work, we investigated operating points of the Soft Dropping Power Control (SDPC) and Open-Loop Power Control (OLPC) schemes for energy efficiency of cellular and D2D communications in uplink OFDMA systems. Results indicate that the SDPC performs better for cellular links and OLPC provides higher gains for D2D links in terms of energy efficiency. While high values of pathloss compensation factor α have been widely used in OLPC studies for the LTE standard, α ∊ {0.4, 0.5} has provided high energy efficiency gains for D2D links. Also, by properly setting the parameters of the OLPC applied to D2D links in uplink and considering the most favorable scenario for sharing resources in all cells, the minimum cost for having spectral efficiency gains for D2D communications represents an impact of 11 % on the system spectral efficiency of cellular communications.