As data generation increasingly takes place on devices withouta wired connection, Machine Learning (ML) related traffic willbe ubiquitous in wireless networks. Many studies have shownthat traditional wireless protocols are highly inefficient or unsustainableto support ML, which creates the need for new wirelesscommunication methods. In this monograph, we give a comprehensivereview of the state-of-the-art wireless methods that arespecifically designed to support ML services over distributeddatasets. Currently, there are two clear themes within the literature,analog over-the-air computation and digital radio resourcemanagement optimized for ML. This survey gives an introductionto these methods, reviews the most important works, highlightsopen problems, and discusses application scenarios.

Motivated by the increasing computational capabilities of wireless devices, as well as unprecedented levels of user- and device-generated data, new distributed machine learning (ML) methods have emerged. In the wireless community, Federated Learning (FL) is of particular interest due to its communication efficiency and its ability to deal with the problem of non-IID data. FL training can be accelerated by a wireless communication method called Over-the-Air Computation (AirComp) which harnesses the interference of simultaneous uplink transmissions to efficiently aggregate model updates. However, since AirComp utilizes analog communication, it introduces inevitable estimation errors. In this paper, we study the impact of such estimation errors on the convergence of FL and propose retransmissions as a method to improve FL accuracy over resource-constrained wireless networks. First, we derive the optimal AirComp power control scheme with retransmissions over static channels. Then, we investigate the performance of Over-the-Air FL with retransmissions and find two upper bounds on the FL loss function. Numerical results demonstrate that the power control scheme offers significant reductions in mean squared error. Additionally, we provide simulation results on MNIST classification with a deep neural network that reveals significant improvements in classification accuracy for low-SNR scenarios.

Over-the-air computation (AirComp) has recently emerged as an efficient analog method for data acquisition from wireless sensor devices. In essence, AirComp exploits the signal superposition property of a multiple access channel to estimate functions of the transmitted data points. Unless devices are excluded from participation, state-of-the-art AirComp methods do not achieve unbiased function computation, thereby introducing systematic errors in the acquired function. In this paper, we propose a new AirComp scheme that employs retransmissions to achieve probabilistically unbiased function computation. We solve a power control problem that minimizes the bias subject to a peak transmission power constraint. We show that the optimal power control follows a greedy structure that maximizes the devices' contribution to the received function at every retransmission. Numerical results show that the proposed scheme can achieve unbiased function computation with a few retransmissions and drastically reduce the mean squared error in the function estimation compared to the current state-of-the-art.

Over-the-air computation (AirComp) is a promising wireless communication method for aggregating data from many devices in dense wireless networks. The fundamental idea of AirComp is to exploit signal superposition to compute functions of multiple simultaneously transmitted signals. However, the time-and phase-alignment of these superimposed signals have a significant effect on the quality of function computation. In this study, we analyze the AirComp problem for a system with unknown random time delays and phase shifts. We show that the classical matched filter does not produce optimal results, and generates bias in the function estimates. To counteract this, we propose a new filter design and show that, under a bound on the maximum time delay, it is possible to achieve unbiased function computation. Additionally, we propose a Tikhonov regularization problem that produces an optimal filter given a tradeoff between the bias and noise-induced variance of the function estimates. When the time delays are long compared to the length of the transmitted pulses, our filter vastly outperforms the matched filter both in terms of bias and mean-squared error (MSE). For shorter time delays, our proposal yields similar MSE as the matched filter, while reducing the bias.

We consider the problem of secure histogram es-timation, where n users hold private items xi from a size-d domain and a server aims to estimate the histogram of the user items. Previous results utilizing orthogonal communication schemes have shown that this problem can be solved securely with a total communication cost of O(n²log(d)) bits by hiding each item xi with a mask. In this paper, we offer a different approach to achieving secure aggregation. Instead of masking the data, our scheme protects individuals by aggregating their messages via a multiple-access channel. A naive communication scheme over the multiple-access channel requires d channel uses, which is generally worse than the O(n²1og(d)) bits communication cost of the prior art in the most relevant regime d >> n. Instead, we propose a new scheme that we call Over-the-Air Group Testing (AirG T) which uses group testing codes to solve the histogram estimation problem in O(n log(d)) channel uses. AirGT reconstructs the histogram exactly with a vanishing probability of error Perror= O(d-^T) that drops exponentially in the number of channel uses T.

We consider the problem of non-coherent over-the-air computation (AirComp), where $n$ devices carry high-dimensional data vectors of sparsity and the sum of these data vectors has to be computed at a receiver. Previous results on non-coherent AirComp generally require more than channel uses to compute functions of , where the extra redundancy is used to combat non-coherent signal aggregation. However, if the data vectors are sparse, this property can be exploited to offer significantly cheaper communication. In this paper, we propose to use random transforms to transmit lower-dimensional measures of the data vectors. These measures are communicated to the receiver using a majority vote (MV)-AirComp scheme, which estimates a bit-vector of the signs of the aggregated measures, i.e., . By leveraging 1-bit compressed sensing (1bCS) at the receiver, the real-valued and high-dimensional aggregate is estimated using and supplementary information about the random transform. We prove analytically that the proposed MVCS scheme estimates the aggregate data vector within a -norm ball of radius in channel uses. Moreover, we specify algorithms that leverage MVCS for histogram estimation and distributed machine learning. Finally, we provide numerical results that reveal the advantage of MVCS compared to the state-of-the-art.