Over-the-Air Computation Based on Balanced Number Systems for Federated Edge Learning

In this study, we propose a digital over-the-air computation (OAC) scheme for achieving continuous-valued (analog) aggregation for federated edge learning (FEEL). We show that the average of a set of real-valued parameters can be calculated approximately by using the average of the corresponding numerals, where the numerals are obtained based on a balanced number system. By exploiting this key property, the proposed scheme encodes the local stochastic gradients into a set of numerals. Next, it determines the positions of the activated orthogonal frequency division multiplexing (OFDM) subcarriers by using the values of the numerals. To eliminate the need for precise sample-level time synchronization, channel estimation overhead, and channel inversion, the proposed scheme also uses a non-coherent receiver at the edge server (ES) and does not utilize a pre-equalization at the edge devices (EDs). We theoretically analyze the MSE performance of the proposed scheme and the convergence rate for a non-convex loss function. To improve the test accuracy of FEEL with the proposed scheme, we introduce the concept of adaptive absolute maximum (AAM). Our numerical results show that when the proposed scheme is used with AAM for FEEL, the test accuracy can reach up to 98% for heterogeneous data distribution.Comment: Accepted for publication in IEEE Transactions on Wireless Communications. arXiv admin note: substantial text overlap with arXiv:2209.1100

Wireless Federated kk-Means Clustering with Non-coherent Over-the-Air Computation

In this study, we propose using an over-the-air computation (OAC) scheme for the federated k-means clustering algorithm to reduce the per-round communication latency when it is implemented over a wireless network. The OAC scheme relies on an encoder exploiting the representation of a number in a balanced number system and computes the sum of the updates for the federated k-means via signal superposition property of wireless multiple-access channels non-coherently to eliminate the need for precise phase and time synchronization. Also, a reinitialization method for ineffectively used centroids is proposed to improve the performance of the proposed method for heterogeneous data distribution. For a customer-location clustering scenario, we demonstrate the performance of the proposed algorithm and compare it with the standard k-means clustering. Our results show that the proposed approach performs similarly to the standard k-means while reducing communication latency.Comment: This work has been accepted for presentation at IEEE MILCOM 202

Majority Vote Computation With Complementary Sequences for Distributed UAV Guidance

This study introduces a novel non-coherent over-the-air computation (OAC) scheme aimed at achieving reliable majority vote (MV) calculations in fading channels. The proposed approach relies on modulating the amplitude of the elements of complementary sequences (CSs) based on the sign of the parameters to be aggregated. Notably, our method eliminates the reliance on channel state information at the nodes, rendering it compatible with time-varying channels. To demonstrate the efficacy of our approach, we employ it in a scenario where an unmanned aerial vehicle (UAV) is guided by distributed sensors, relying on the MV computed using our proposed scheme. The experimental results confirm the superiority of our approach, as evidenced by a significant reduction in computation error rates in fading channels, particularly with longer sequence lengths. Meanwhile, we ensure that the peak-to-mean-envelope power ratio of the transmitted orthogonal frequency division multiplexing signals remains within or below 3 dB.Comment: This work has been accepted for presentation at IEEE MILCOM 202

Over-the-Air Computation over Balanced Numerals

In this study, a digital over-the-air computation (OAC) scheme for achieving continuous-valued gradient aggregation is proposed. It is shown that the average of a set of real-valued parameters can be calculated approximately by using the average of the corresponding numerals, where the numerals are obtained based on a balanced number system. By using this property, the proposed scheme encodes the local gradients into a set of numerals. It then determines the positions of the activated orthogonal frequency division multiplexing (OFDM) subcarriers by using the values of the numerals. To eliminate the need for a precise sample-level time synchronization, channel estimation overhead, and power instabilities due to the channel inversion, the proposed scheme also uses a non-coherent receiver at the edge server (ES) and does not utilize a pre-equalization at the edge devices (EDs). Finally, the theoretical mean squared error (MSE) performance of the proposed scheme is derived and its performance for federated edge learning (FEEL) is demonstrated.Comment: 6 pages, 3 figures, Accepted to GLOBECOM'2022 Workshops: Workshop on Wireless Communications for Distributed Intelligenc

Hybrid 3D Localization for Visible Light Communication Systems

In this study, we investigate hybrid utilization of angle-of-arrival (AOA) and received signal strength (RSS) information in visible light communication (VLC) systems for 3D localization. We show that AOA-based localization method allows the receiver to locate itself via a least squares estimator by exploiting the directionality of light-emitting diodes (LEDs). We then prove that when the RSS information is taken into account, the positioning accuracy of AOA-based localization can be improved further using a weighted least squares solution. On the other hand, when the radiation patterns of LEDs are explicitly considered in the estimation, RSS-based localization yields highly accurate results. In order to deal with the system of nonlinear equations for RSS-based localization, we develop an analytical learning rule based on the Newton-Raphson method. The non-convex structure is addressed by initializing the learning rule based on 1) location estimates, and 2) a newly developed method, which we refer as random report and cluster algorithm. As a benchmark, we also derive analytical expression of the Cramer-Rao lower bound (CRLB) for RSS-based localization, which captures any deployment scenario positioning in 3D geometry. Finally, we demonstrate the effectiveness of the proposed solutions for a wide range of LED characteristics and orientations through extensive computer simulations.Comment: Submitted to IEEE/OSA Journal of Lightwave Technology (10 pages, 14 figures