Optimizing Over-the-Air Computation in IRS-Aided C-RAN Systems

Over-the-air computation (AirComp) is an efficient solution to enable federated learning on wireless channels. AirComp assumes that the wireless channels from different devices can be controlled, e.g., via transmitter-side phase compensation, in order to ensure coherent on-air combining. Intelligent reflecting surfaces (IRSs) can provide an alternative, or additional, means of controlling channel propagation conditions. This work studies the advantages of deploying IRSs for AirComp systems in a large-scale cloud radio access network (C-RAN). In this system, worker devices upload locally updated models to a parameter server (PS) through distributed access points (APs) that communicate with the PS on finite-capacity fronthaul links. The problem of jointly optimizing the IRSs' reflecting phases and a linear detector at the PS is tackled with the goal of minimizing the mean squared error (MSE) of a parameter estimated at the PS. Numerical results validate the advantages of deploying IRSs with optimized phases for AirComp in C-RAN systems.Comment: to appear in Proc. IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 202

Optimized Amplify-and-Forward Relaying for Hierarchical Over-the-Air Computation

Over-the-air computation (AirComp) is an emerging wireless technique with wide applications (e.g., in distributed edge learning), which can swiftly compute functions of distributed data from different wireless devices (WDs) by exploiting the superposition property of wireless channels. Different from prior works focusing on the AirComp over one single cell in a small area, this paper considers a new hierarchical architecture to enable AirComp in a large area, in which a set of intermediate relays are exploited to help the fusion center to aggregate data from massive WDs for functional computation. In particular, we present a two-phase amplify-and-forward (AF) relaying design for hierarchical AirComp. In the first phase, the WDs simultaneously send their data to the relays, while in the second phase, the relays amplify the received signals and concurrently forward them to the fusion center for aggregation. Under this setup, we minimize the computation distortion measured by the mean squared error (MSE), by jointly optimizing the transmit coefficients at the WDs and relays and the de-noising factor at the fusion center, subject to their individual transmit power constraints. For the highly non-convex MSE minimization problem, we develop an alternating-optimization-based algorithm to obtain a high-quality solution. The optimized solution shows that for each WD, the phase of its transmit coefficient is opposite to that of the composite channel from the WD itself to the relays to the fusion center, such that they can be aligned at the fusion center, and its transmit power follows a regularized composite-channel-inversion structure to strike a balance between minimizing the signal misalignment error and the noise-induced error.Comment: As a starting point, this paper addresses AF relaying design for hierarchical AirComp in a large-scale network; 7 pages and 4 figure

Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws

For future Internet of Things (IoT)-based Big Data applications (e.g., smart cities/transportation), wireless data collection from ubiquitous massive smart sensors with limited spectrum bandwidth is very challenging. On the other hand, to interpret the meaning behind the collected data, it is also challenging for edge fusion centers running computing tasks over large data sets with limited computation capacity. To tackle these challenges, by exploiting the superposition property of a multiple-access channel and the functional decomposition properties, the recently proposed technique, over-the-air computation (AirComp), enables an effective joint data collection and computation from concurrent sensor transmissions. In this paper, we focus on a single-antenna AirComp system consisting of $K$ sensors and one receiver (i.e., the fusion center). We consider an optimization problem to minimize the computation mean-squared error (MSE) of the $K$ sensors' signals at the receiver by optimizing the transmitting-receiving (Tx-Rx) policy, under the peak power constraint of each sensor. Although the problem is not convex, we derive the computation-optimal policy in closed form. Also, we comprehensively investigate the ergodic performance of AirComp systems in terms of the average computation MSE and the average power consumption under Rayleigh fading channels with different Tx-Rx policies. For the computation-optimal policy, we prove that its average computation MSE has a decay rate of $O(1/\sqrt{K})$, and our numerical results illustrate that the policy also has a vanishing average power consumption with the increasing $K$, which jointly show the computation effectiveness and the energy efficiency of the policy with a large number of sensors.Comment: Paper accepted by IEEE Transactions on Wireless Communications. Copyright may be transferred without notice, after which this version may no longer be accessibl

Gradient Statistics Aware Power Control for Over-the-Air Federated Learning

Federated learning (FL) is a promising technique that enables many edge devices to train a machine learning model collaboratively in wireless networks. By exploiting the superposition nature of wireless waveforms, over-the-air computation (AirComp) can accelerate model aggregation and hence facilitate communication-efficient FL. Due to channel fading, power control is crucial in AirComp. Prior works assume that the signals to be aggregated from each device, i.e., local gradients have identical statistics. In FL, however, gradient statistics vary over both training iterations and feature dimensions, and are unknown in advance. This paper studies the power control problem for over-the-air FL by taking gradient statistics into account. The goal is to minimize the aggregation error by optimizing the transmit power at each device subject to peak power constraints. We obtain the optimal policy in closed form when gradient statistics are given. Notably, we show that the optimal transmit power is continuous and monotonically decreases with the squared multivariate coefficient of variation (SMCV) of gradient vectors. We then propose a method to estimate gradient statistics with negligible communication cost. Experimental results demonstrate that the proposed gradient-statistics-aware power control achieves higher test accuracy than the existing schemes for a wide range of scenarios.Comment: 30 pages, 8 figure

Robust Interference Management for SISO Systems with Multiple Over-the-Air Computations

In this paper, we consider the over-the-air computation of sums. Specifically, we wish to compute $M\geq 2$ sums $s_m=\sum_{k\in\mathcal{D}m}x_k$ over a shared complex-valued MAC at once with minimal mean-squared error ($\mathsf{MSE}$). Finding appropriate Tx-Rx scaling factors balance between a low error in the computation of $s_n$ and the interference induced by it in the computation of other sums $s_m$, $m\neq n$. In this paper, we are interested in designing an optimal Tx-Rx scaling policy that minimizes the mean-squared error $\max_{m\in[1:M]}\mathsf{MSE}_m$ subject to a Tx power constraint with maximum power $P$. We show that an optimal design of the Tx-Rx scaling policy $\left(\bar{\mathbf{a}},\bar{\mathbf{b}}\right)$ involves optimizing (a) their phases and (b) their absolute values in order to (i) decompose the computation of $M$ sums into, respectively, $M_R$ and $M_I$ ($M=M_R+M_I$) calculations over real and imaginary part of the Rx signal and (ii) to minimize the computation over each part -- real and imaginary -- individually. The primary focus of this paper is on (b). We derive conditions (i) on the feasibility of the optimization problem and (ii) on the Tx-Rx scaling policy of a local minimum for $M_w=2$ computations over the real ($w=R$) or the imaginary ($w=I$) part. Extensive simulations over a single Rx chain for $M_w=2$ show that the level of interference in terms of $\Delta D=|\mathcal{D}_2|-|\mathcal{D}_1|$ plays an important role on the ergodic worst-case $\mathsf{MSE}$. At very high $\mathsf{SNR}$, typically only the sensor with the weakest channel transmits with full power while all remaining sensors transmit with less to limit the interference. Interestingly, we observe that due to residual interference, the ergodic worst-case $\mathsf{MSE}$ is not vanishing; rather, it converges to $\frac{|\mathcal{D}_1||\mathcal{D}_2|}{K}$ as $\mathsf{SNR}\rightarrow\infty$

Hybrid Beamforming for Massive MIMO Over-the-Air Computation

Over-the-air computation (AirComp) has been recognized as a promising technique in Internet-of-Things (IoT) networks for fast data aggregation from a large number of wireless devices. However, as the number of devices becomes large, the computational accuracy of AirComp would seriously degrade due to the vanishing signal-to-noise ratio (SNR). To address this issue, we exploit the massive multiple-input multiple-output (MIMO) with hybrid beamforming, in order to enhance the computational accuracy of AirComp in a cost-effective manner. In particular, we consider the scenario with a large number of multi-antenna devices simultaneously sending data to an access point (AP) equipped with massive antennas for functional computation over the air. Under this setup, we jointly optimize the transmit digital beamforming at the wireless devices and the receive hybrid beamforming at the AP, with the objective of minimizing the computational mean-squared error (MSE) subject to the individual transmit power constraints at the wireless devices. To solve the non-convex hybrid beamforming design optimization problem, we propose an alternating-optimization-based approach. In particular, we propose two computationally efficient algorithms to handle the challenging receive analog beamforming problem, by exploiting the techniques of successive convex approximation (SCA) and block coordinate descent (BCD), respectively. It is shown that for the special case with a fully-digital receiver at the AP, the achieved MSE of the massive MIMO AirComp system is inversely proportional to the number of receive antennas. Furthermore, numerical results show that the proposed hybrid beamforming design substantially enhances the computation MSE performance as compared to other benchmark schemes, while the SCA-based algorithm performs closely to the performance upper bound achieved by the fully-digital beamforming

Energy-Efficient Federated Edge Learning with Joint Communication and Computation Design

This paper studies a federated edge learning system, in which an edge server coordinates a set of edge devices to train a shared machine learning model based on their locally distributed data samples. During the distributed training, we exploit the joint communication and computation design for improving the system energy efficiency, in which both the communication resource allocation for global ML parameters aggregation and the computation resource allocation for locally updating MLparameters are jointly optimized. In particular, we consider two transmission protocols for edge devices to upload ML parameters to edge server, based on the non orthogonal multiple access and time division multiple access, respectively. Under both protocols, we minimize the total energy consumption at all edge devices over a particular finite training duration subject to a given training accuracy, by jointly optimizing the transmission power and rates at edge devices for uploading MLparameters and their central processing unit frequencies for local update. We propose efficient algorithms to optimally solve the formulated energy minimization problems by using the techniques from convex optimization. Numerical results show that as compared to other benchmark schemes, our proposed joint communication and computation design significantly improves the energy efficiency of the federated edge learning system, by properly balancing the energy tradeoff between communication and computation.Comment: Submiited for possible publicatio

Distributed Machine Learning for Wireless Communication Networks: Techniques, Architectures, and Applications

Distributed machine learning (DML) techniques, such as federated learning, partitioned learning, and distributed reinforcement learning, have been increasingly applied to wireless communications. This is due to improved capabilities of terminal devices, explosively growing data volume, congestion in the radio interfaces, and increasing concern of data privacy. The unique features of wireless systems, such as large scale, geographically dispersed deployment, user mobility, and massive amount of data, give rise to new challenges in the design of DML techniques. There is a clear gap in the existing literature in that the DML techniques are yet to be systematically reviewed for their applicability to wireless systems. This survey bridges the gap by providing a contemporary and comprehensive survey of DML techniques with a focus on wireless networks. Specifically, we review the latest applications of DML in power control, spectrum management, user association, and edge cloud computing. The optimality, scalability, convergence rate, computation cost, and communication overhead of DML are analyzed. We also discuss the potential adversarial attacks faced by DML applications, and describe state-of-the-art countermeasures to preserve privacy and security. Last but not least, we point out a number of key issues yet to be addressed, and collate potentially interesting and challenging topics for future research