A Joint Learning and Communications Framework for Federated Learning Over Wireless Networks

Mingzhe ChenZhaohui YangW. SaadChangchuan YinH. PoorShuguang Cui

article2019IEEE Transactions on Wireless Communications1,469 citations2023 IEEE Marconi Prize Paper Award in Wireless Communications

Develops an analytical framework for wireless federated learning that derives the mathematical impact of channel packet errors on convergence and jointly optimizes user selection, transmit power, and resource allocation to minimize model loss.

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Federated learning enables mobile devices to collaboratively train artificial intelligence models using local data, protecting user privacy and avoiding the massive bandwidth costs of centralizing raw datasets. However, deploying federated learning over commercial wireless cellular networks introduces operational challenges. Wireless channels suffer from interference, packet transmission errors, latency, and limited spectrum and battery energy. When device updates are corrupted or dropped, the accuracy and convergence speed of the shared machine learning model degrade significantly. Addressing these communication bottlenecks is essential for making decentralized intelligence practical on mobile and edge devices.

The main objective of the article is to establish and evaluate a joint learning and communication framework that minimizes machine learning training loss over wireless networks by systematically optimizing user selection, wireless resource allocation, and device transmit power.

To achieve this, the article analyzes a cellular uplink network where distributed devices transmit local model updates to a central base station using orthogonal frequency division multiple access. The authors derive a closed-form mathematical expression for the expected convergence rate of the federated learning algorithm under packet transmission errors. Using this theoretical convergence bound, they simplify the training loss minimization problem into a bipartite matching formulation that strictly enforces per-round transmission delay and device energy limits. The base station determines optimal device transmit powers analytically and allocates wireless resource blocks using the standard Hungarian matching algorithm. The framework is validated through numeric simulations using synthetic linear regression tasks and image classification on the MNIST handwritten digit dataset across varying user counts and bandwidth allocations.

The findings show that wireless impairments create a quantifiable performance gap between practical federated learning and idealized error-free training, but this gap can be minimized through joint network and learning optimization. In image identification tests, the proposed joint framework improves model accuracy by up to 1.4% compared to optimal user selection with random resource allocation, by 3.5% compared to standard wireless federated learning with random user selection, and by 4.1% compared to conventional wireless resource management that minimizes packet errors without considering machine learning parameters. The theoretical convergence rate closely aligns with simulation results, exhibiting less than a 9% discrepancy. Furthermore, the analysis demonstrates that while increasing user participation supplies more data to improve model quality, performance gains plateau once the base station receives sufficient data samples (e.g., beyond approximately 30 samples per user in linear regression), meaning network managers do not need to schedule every device in every round.

These results indicate that treating wireless network management and machine learning design as separate domains leads to suboptimal artificial intelligence performance. Cellular operators and edge computing architects can implement learning-aware scheduling at the base station to achieve higher prediction accuracy and faster model convergence without requiring additional hardware or spectral bandwidth. By accounting for device sample counts, channel reliability, and local energy constraints simultaneously, network operators reduce operational risks such as training stalls, battery drain, and excessive latency in time-sensitive edge applications.

Organizations deploying federated learning over wireless infrastructure should integrate joint user selection and resource allocation algorithms into base station schedulers. Operators should prioritize scheduling devices that possess both high data quality and favorable channel conditions to maximize learning efficiency per round. Further development should focus on deploying small-scale field pilots in live cellular networks and extending the framework to handle non-orthogonal multiple access, asynchronous model updates, and multi-cell interference environments.

The primary analytical derivations rely on standard convex optimization assumptions regarding the loss functions and assume that corrupted packets are discarded rather than retransmitted. Nevertheless, simulation results on non-convex convolutional neural networks confirm that the optimization framework remains robust and effective in practical deep learning scenarios, providing high confidence in the operational conclusions.

Beijing University of Posts and Telecommunications Future Network of Intelligence Institute King's College London Princeton University Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Virginia Tech bandwidth base stations closed-form expression federated learning wireless networks joint learning and communications framework

arXiv: 1909.07972 mzchen0/Wireless-FL

Paper: Communication-Efficient Learning of Deep Networks from Decentralized Data, H. B. McMahan et al. (2016). Introduces the foundational FederatedAveraging algorithm that the source adapts and mathematically analyzes over wireless cellular networks.
Paper: Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge, Takayuki Nishio et al. (2018). Establishes client selection protocols under heterogeneous compute and communication deadlines in mobile edge networks, directly preceding the source's joint resource optimization.
Paper: Federated Optimization: Distributed Machine Learning for On-Device Intelligence, Jakub Konečný et al. (2016). Provides the foundational formulation of federated optimization across decentralized, communication-constrained mobile devices.
Paper: Adaptive Federated Learning in Resource Constrained Edge Computing Systems, Shiqiang Wang et al. (2018). Derives convergence bounds for federated learning under resource constraints to dynamically control local computation versus communication rounds.
Paper: Federated Learning: Strategies for Improving Communication Efficiency, Jakub Konečný et al. (2016). Explores compression and structured updates to overcome uplink communication bottlenecks in federated learning.
Paper: Federated Optimization in Heterogeneous Networks, Tian Li et al. (2018). Presents theoretical and algorithmic solutions (FedProx) to manage systems and statistical heterogeneity across edge devices.
Paper: Federated Learning with Non-IID Data, Yue Zhao et al. (2018). Quantifies the accuracy degradation and weight divergence of federated averaging when client data is non-IID.

Paper: Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization, Jianyu Wang et al. (2020). Extends federated optimization under device heterogeneity by introducing FedNova to correct for objective inconsistency caused by unequal local updates.
Paper: SCAFFOLD: Stochastic Controlled Averaging for Federated Learning, Sai Praneeth Karimireddy et al. (2019). Proposes SCAFFOLD to overcome client drift and improve convergence guarantees under heterogeneous client participation and non-IID data.
Paper: Adaptive Federated Optimization, Sashank Reddi et al. (2020). Generalizes federated optimization by incorporating server-side adaptive optimization methods to accelerate convergence.
Paper: Personalized Federated Learning with Moreau Envelopes, Canh T. Dinh et al. (2020). Builds on edge federated learning by formulating bi-level optimization with Moreau envelopes for personalized client models.
Paper: Ditto: Fair and Robust Federated Learning Through Personalization, Tian Li et al. (2020). Extends federated learning frameworks to simultaneously achieve fairness, robustness, and personalization on heterogeneous edge devices.
Paper: Ensemble Distillation for Robust Model Fusion in Federated Learning, Tao Lin et al. (2020). Develops ensemble distillation to achieve model fusion across heterogeneous client architectures without relying on parameter averaging.
Paper: Federated Learning on Non-IID Data Silos: An Experimental Study, Qinbin Li et al. (2021). Provides a comprehensive experimental benchmark comparing advanced federated learning algorithms under realistic non-IID data silo conditions.

Cover for A Joint Learning and Communications Framework for Federated Learning Over Wireless Networks

Abstract

In this paper, the problem of training federated learning (FL) algorithms over a realistic wireless network is studied. In the considered model, wireless users execute an FL algorithm while training their local FL models using their own data and transmitting the trained local FL models to a base station (BS) that generates a global FL model and sends the model back to the users. Since all training parameters are transmitted over wireless links, the quality of training is affected by wireless factors such as packet errors and the availability of wireless resources. Meanwhile, due to the limited wireless bandwidth, the BS needs to select an appropriate subset of users to execute the FL algorithm so as to build a global FL model accurately. This joint learning, wireless resource allocation, and user selection problem is formulated as an optimization problem whose goal is to minimize an FL loss function that captures the performance of the FL algorithm. To seek the solution, a closed-form expression for the expected convergence rate of the FL algorithm is first derived to quantify the impact of wireless factors on FL. Then, based on the expected convergence rate of the FL algorithm, the optimal transmit power for each user is derived, under a given user selection and uplink resource block (RB) allocation scheme. Finally, the user selection and uplink RB allocation is optimized so as to minimize the FL loss function.

Topics

bandwidth base stations closed-form expression federated learning genetic selection optimization optimization problems transmit power uplink user selection

Keywords

federated learning wireless networks joint learning and communications framework random resource allocation edge computing gradient descent uplink data rate wireless channel

I Introduction
I-A Related Works
I-B Contributions
II System Model and Problem Formulation
II-A Machine Learning Model
II-B Transmission Model
II-C Packet Error Rates
II-D Energy Consumption Model
II-E Problem Formulation
III Analysis of the FL Convergence Rate
IV Optimization of FL Training Loss
IV-A Optimal Transmit Power
IV-B Optimal Uplink Resource Block Allocation
IV-C Implementation and Complexity
V Simulation Results and Analysis
V-A FL for Linear Regression
V-B FL for Handwritten Digit Identification
VI Conclusion
VI-A Proof of Theorem
VI-B Proof of Proposition
References

Knowls

Knowl 1 — Upper Bound on Expected Convergence Rate of Wireless Federated Learning
theoretical result
Consider a federated learning (FL) system executed over an orthogonal frequency division multiple access (OFDMA) wireless cellular network with a base station (BS) and a set $\mathcal{U}$ of $U$ users. Let $K_i$ be the number of training samples at user $i$ , $K = \sum_{i=1}^U K_i$ , $a_i \in \{0, 1\}$ be the indicator of whether user $i$ is selected ( $a_i = 1$ ) or not ( $a_i = 0$ ), $r_i$ be the resource block (RB) allocation vector for user $i$ , and $P_i$ be its transmit power. Let $q_i(r_i, P_i)$ denote user $i$ 's uplink packet error rate.

Assume the global loss function $F(g) = \frac{1}{K}\sum_{i=1}^U \sum_{k=1}^{K_i} f(g, x_{ik}, y_{ik})$ is $L$ -smooth and $\mu$ -strongly convex, and local gradients satisfy $\|\nabla f(g_t, x_{ik}, y_{ik})\|^2 \le \zeta_1 + \zeta_2 \|\nabla F(g_t)\|^2$ for non-negative constants $\zeta_1, \zeta_2$ . Using a gradient descent update step with learning rate $\lambda = 1/L$ , the expected suboptimality gap of the global model $g_{t+1}$ after $t+1$ communication rounds satisfies the upper bound:

$\mathbb{E}\left[F(g_{t+1}) - F(g^*)\right] \le A^t \mathbb{E}\left[F(g_0) - F(g^*)\right] + \frac{2\zeta_1}{LK} \sum_{i=1}^U K_i \left(1 - a_i + a_i q_i(r_i, P_i)\right) \frac{1 - A^t}{1 - A}$

where $g^*$ is the optimal global model in an error-free centralized setting, $g_0$ is the initial model, and the convergence factor $A$ is defined as:

$A = 1 - \frac{\mu}{L} + \frac{4\mu\zeta_2}{LK} \sum_{i=1}^U K_i \left(1 - a_i + a_i q_i(r_i, P_i)\right)$

When packet transmission is error-free ( $q_i = 0$ ) and all users participate ( $a_i = 1$ ), the second additive gap term vanishes and the rate reduces to the standard linear convergence bound $\mathbb{E}\left[F(g_{t+1}) - F(g^*)\right] \le (1 - \mu/L)^t \mathbb{E}\left[F(g_0) - F(g^*)\right]$ .
Knowl 2 — Global Model Aggregation under Wireless Packet Transmission Errors
model/method
In a wireless federated learning system with $U$ distributed users and one base station (BS), each selected user $i$ trains its local parameter vector $w_i$ and transmits it over an assigned wireless uplink resource block (RB). Due to channel fading, noise, and co-channel interference, the uplink transmission of $w_i$ (transmitted as a single packet) experiences packet errors verified via cyclic redundancy check (CRC).

The global FL model $g(a, P, R)$ aggregated at the BS at each round is defined as:

$g(a, P, R) = \frac{\sum_{i=1}^U K_i a_i w_i C(w_i)}{\sum_{i=1}^U K_i a_i C(w_i)}$

where:
- $K_i$ is the number of local data samples collected by user $i$ .
- $a_i \in \{0, 1\}$ is the user selection variable ( $a_i = 1$ if user $i$ is selected, $a_i = 0$ otherwise).
- $C(w_i) \in \{0, 1\}$ is the packet reception indicator, modeled as a Bernoulli random variable where $C(w_i) = 1$ with probability $1 - q_i(r_i, P_i)$ (correct reception) and $C(w_i) = 0$ with probability $q_i(r_i, P_i)$ (packet error).
- $q_i(r_i, P_i) = \sum_{n=1}^R r_{i,n} q_{i,n}$ is the packet error rate experienced by user $i$ , with $r_{i,n} \in \{0, 1\}$ indicating allocation of RB $n \in \{1, \dots, R\}$ , and $q_{i,n} = \mathbb{E}_{h_i}\left[1 - \exp\left(-\frac{m(I_n + B^U N_0)}{P_i h_i}\right)\right]$ , where $P_i$ is user transmit power, $h_i$ is the channel gain, $I_n$ is inter-cell interference on RB $n$ , $B^U$ is the RB bandwidth, $N_0$ is noise power spectral density, and $m$ is a waterfall threshold.
When a packet contains errors ( $C(w_i) = 0$ ), the BS discards the local update without requesting retransmission and updates the global model using only the correctly received updates.
Knowl 3 — Joint Learning, User Selection, and Resource Allocation Optimization Problem
model/method
The joint optimization of user selection $a = [a_1, \dots, a_U]$ , transmit power $P = [P_1, \dots, P_U]$ , and uplink resource block (RB) allocation $R = [r_1, \dots, r_U]$ to minimize the global federated learning training loss under wireless delay and energy constraints is formulated as:

$\min_{a, P, R} \frac{1}{K} \sum_{i=1}^U \sum_{k=1}^{K_i} f(g(a, P, R), x_{ik}, y_{ik})$

$\text{s.t.} \quad a_i, r_{i,n} \in \{0, 1\}, \quad \forall i \in \mathcal{U}, \; n = 1, \dots, R$

$\sum_{n=1}^R r_{i,n} = a_i, \quad \forall i \in \mathcal{U}$

$l_i^U(r_i, P_i) + l_i^D \le \gamma_T, \quad \forall i \in \mathcal{U}$

$e_i(r_i, P_i) \le \gamma_E, \quad \forall i \in \mathcal{U}$

$\sum_{i \in \mathcal{U}} r_{i,n} \le 1, \quad \forall n = 1, \dots, R$

$0 \le P_i \le P_{\max}, \quad \forall i \in \mathcal{U}$

where:
- $K = \sum_{i=1}^U K_i$ is the total dataset size across all users $\mathcal{U}$ , and $(x_{ik}, y_{ik})$ denotes data sample $k$ of user $i$ .
- $l_i^U(r_i, P_i) = \frac{Z(w_i)}{c_i^U(r_i, P_i)}$ is the uplink transmission delay with data size $Z(w_i)$ bits and rate $c_i^U(r_i, P_i) = \sum_{n=1}^R r_{i,n} B^U \mathbb{E}_{h_i}\left[\log_2\left(1 + \frac{P_i h_i}{I_n + B^U N_0}\right)\right]$ .
- $l_i^D = \frac{Z(g)}{c_i^D}$ is the downlink transmission delay with rate $c_i^D = B^D \mathbb{E}_{h_i}\left[\log_2\left(1 + \frac{P_B h_i}{I^D + B^D N_0}\right)\right]$ , where $B^D$ is downlink bandwidth, $P_B$ is BS transmit power, and $I^D$ is interference from other BSs.
- $e_i(r_i, P_i) = \varsigma \omega_i \vartheta^2 Z(w_i) + P_i l_i^U(r_i, P_i)$ is user $i$ 's total energy consumption per round (local computing plus uplink transmission), with CPU frequency $\vartheta$ , compute cycles per bit $\omega_i$ , and hardware energy coefficient $\varsigma$ .
- $\gamma_T$ and $\gamma_E$ denote the per-round latency and energy consumption limits, and $P_{\max}$ is the maximum user transmit power.
Knowl 4 — Optimal Transmit Power Allocation for Wireless FL Users
theoretical result
Given an assigned uplink resource block (RB) allocation vector $r_i$ for user $i$ , the per-round energy consumption $e_i(r_i, P_i) = \varsigma \omega_i \vartheta^2 Z(w_i) + \frac{P_i Z(w_i)}{c_i^U(r_i, P_i)}$ is strictly monotonically increasing with respect to transmit power $P_i > 0$ . Because the packet error rate $q_i(r_i, P_i)$ strictly decreases as transmit power increases, minimizing the FL loss gap requires maximizing transmit power up to the energy constraint $e_i(r_i, P_i) \le \gamma_E$ and the device power ceiling $P_{\max}$ .

The optimal transmit power $P_i^*(r_i)$ of user $i$ is uniquely given by:

$P_i^*(r_i) = \min\{P_{\max}, P_{i, \gamma_E}\}$

where $P_{i, \gamma_E}$ is the unique positive root of the equality:

$\varsigma \omega_i \vartheta^2 Z(w_i) + \frac{P_{i, \gamma_E} Z(w_i)}{c_i^U(r_i, P_{i, \gamma_E})} = \gamma_E$

with $Z(w_i)$ being the local model size in bits, $c_i^U(r_i, P_i)$ the uplink data rate on the assigned RB, $\vartheta$ the user CPU clock frequency, $\omega_i$ the required CPU cycles per bit, and $\varsigma$ the device chip energy coefficient.
Knowl 5 — Asymptotic FL Loss Simplification and Bipartite Matching Reformulation
model/method
In the asymptotic regime ( $t \to \infty$ ) where the convergence coefficient satisfies $A < 1$ (such that $A^t \to 0$ ), minimizing the expected convergence gap $\frac{2\zeta_1}{LK}\sum_{i=1}^U K_i(1 - a_i + a_i q_i(r_i, P_i^*))\frac{1}{1-A}$ reduces to minimizing $\sum_{i=1}^U K_i\left(1 - \sum_{n=1}^R r_{i,n} + \sum_{n=1}^R r_{i,n} q_{i,n}\right)$ .

This optimization problem is equivalently mapped to a minimum weight bipartite matching problem on the graph $\mathcal{A} = (\mathcal{U} \times \mathcal{R}, \mathcal{E})$ , where $\mathcal{U}$ represents the set of $U$ users, $\mathcal{R}$ represents the set of $R$ orthogonal resource blocks, and $\mathcal{E}$ is the set of user-RB candidate edges. The weight $\psi_{in}$ assigned to edge $\chi_{in}$ connecting user $i$ and RB $n$ is defined as:

$\psi_{in} = \begin{cases} K_i (q_{i,n} - 1), & \text{if } l_i^U(r_{i,n}, P_i^*) + l_i^D \le \gamma_T \text{ and } e_i(r_{i,n}, P_i^*) \le \gamma_E, \\ 0, & \text{otherwise} \end{cases}$

where $K_i$ is user $i$ 's dataset size, $q_{i,n}$ is the packet error rate over RB $n$ , $l_i^U$ and $l_i^D$ are uplink and downlink delays, and $e_i$ is energy consumption. If delay or energy constraints cannot be met when assigning RB $n$ to user $i$ , setting $\psi_{in} = 0$ prevents matching.

The global minimum is solved via the Hungarian algorithm with a worst-case computational complexity of $\mathcal{O}(U^2 R)$ and best-case complexity of $\mathcal{O}(UR)$ . The resulting matching yields the optimal RB allocation $R^*$ and optimal user selection $a_i^* = \sum_{n=1}^R r_{i,n}^*$ .
Knowl 6 — Condition on Gradient Variance Bound for Convergence of Wireless FL
theoretical result
Let the local sample loss gradients satisfy $\|\nabla f(g_t, x_{ik}, y_{ik})\|^2 \le \zeta_1 + \zeta_2 \|\nabla F(g_t)\|^2$ with constants $\zeta_1, \zeta_2 \ge 0$ . Under learning rate $\lambda = 1/L$ , strong convexity parameter $\mu$ , and Lipschitz constant $L$ , to guarantee convergence of the wireless federated learning algorithm (i.e., ensuring the convergence contraction parameter $A < 1$ ), the parameter $\zeta_2$ must strictly satisfy:

$0 < \zeta_2 < \frac{K}{\max_{P, R} 4 \sum_{i=1}^U K_i q_i(r_i, P_i)}$

where $K = \sum_{i=1}^U K_i$ is the total dataset size across all $U$ users, and $q_i(r_i, P_i)$ is the packet error rate of user $i$ under transmit power vector $P$ and resource block allocation matrix $R$ .
Knowl 7 — Joint User Selection, Resource Allocation, and Transmit Power Optimization Algorithm
algorithm
The joint federated learning and wireless resource allocation framework determines the optimal user selection vector $a^*$ , RB allocation matrix $R^*$ , and user transmit power vector $P^*$ to minimize global FL loss while respecting per-round latency and energy budgets.
Input: Uplink rates $c_i^U(r_i, P_i)$ , downlink rates $c_i^D$ , model data size $Z(w_i)$ , packet error rates $q_i(r_i, P_i)$ for all $i \in \mathcal{U}$ , delay limit $\gamma_T$ , energy limit $\gamma_E$
Output: Optimal user selection $a^*$ , RB allocation matrix $R^*$ , transmit power vector $P^*$
1: for each user $i \in \mathcal{U}$ and each RB $n \in \{1, \dots, R\}$ do
2: Calculate optimal transmit power $P_i^*(r_{i,n}) = \min\{P_{\max}, P_{i, \gamma_E}\}$
3: Compute delay $l_i^U(r_{i,n}, P_i^*) + l_i^D$ and energy $e_i(r_{i,n}, P_i^*)$
4: if $l_i^U + l_i^D \le \gamma_T$ and $e_i \le \gamma_E$ then
5: Set edge weight $\psi_{in} = K_i (q_{i,n} - 1)$
6: else
7: Set edge weight $\psi_{in} = 0$
8: end if
9: end for
10: Solve the bipartite matching problem with weight matrix $[\psi_{in}]$ using the Hungarian algorithm to obtain optimal RB assignment $R^*$
11: Set optimal user selection $a_i^* = \sum_{n=1}^R r_{i,n}^*$ for each user $i \in \mathcal{U}$
12: Set optimal transmit power $P_i^* = P_i^*(r_i^*)$ for each user $i \in \mathcal{U}$
13: Execute FL training rounds using $a^*$ , $R^*$ , and $P^*$
The BS centralized execution requires $\mathcal{O}(UR)$ evaluations to set up the bipartite graph weights and $\mathcal{O}(U^2 R)$ operations in the worst case to solve the Hungarian assignment.
Knowl 8 — Global and Local Loss Function Assumptions for Wireless FL Convergence
assumption
Let $F(g) = \frac{1}{K}\sum_{i=1}^U \sum_{k=1}^{K_i} f(g, x_{ik}, y_{ik})$ denote the global empirical loss function over model parameters $g$ , where $K = \sum_{i=1}^U K_i$ . The theoretical convergence analysis of the wireless FL framework rests on four mathematical assumptions:
1. Uniform Lipschitz Continuous Gradient: The gradient $\nabla F(g)$ is Lipschitz continuous with constant $L > 0$ : $\|\nabla F(g_{t+1}) - \nabla F(g_t)\| \le L \|g_{t+1} - g_t\|$
2. Strong Convexity: $F(g)$ is strongly convex with parameter $\mu > 0$ : $F(g_{t+1}) \ge F(g_t) + (g_{t+1} - g_t)^T \nabla F(g_t) + \frac{\mu}{2}\|g_{t+1} - g_t\|^2$
3. Twice Continuous Differentiability: $F(g)$ is twice-continuously differentiable, which implies: $\mu I \preceq \nabla^2 F(g) \preceq L I$ where $I$ is the identity matrix.
4. Bounded Gradient Dissimilarity: For all users $i$ and samples $k$ , local sample gradients satisfy: $\|\nabla f(g_t, x_{ik}, y_{ik})\|^2 \le \zeta_1 + \zeta_2 \|\nabla F(g_t)\|^2$ where $\zeta_1, \zeta_2 \ge 0$ are non-negative constants.
Knowl 9 — Empirical Performance and Accuracy Gains of Wireless FL Framework
empirical result
The proposed joint learning and communications framework is evaluated on linear regression (fitting $y = -2x + 1 + 0.4n$ , $n \sim \mathcal{N}(0, 1)$ using a 20-neuron feedforward neural network) and MNIST handwritten digit identification (50-neuron FNN and CNN, cross-entropy loss) in a circular cell of radius $r = 500$ m with $U = 15$ users and $R \in [3, 15]$ resource blocks.

Key simulation parameters include user transmit power limit $P_{\max} = 0.01$ W, BS power $P_B = 1$ W, downlink bandwidth $B^D = 20$ MHz, uplink RB bandwidth $B^U = 1$ MHz, noise density $N_0 = -174$ dBm/Hz, delay limit $\gamma_T = 500$ ms, energy limit $\gamma_E = 0.003$ J, $\vartheta = 10^9$ Hz, $\varsigma = 10^{-27}$ , and $\omega_i = 40$ cycles/bit.

Key empirical findings include:
- Accuracy Gains: In MNIST handwritten digit identification with $R = 9$ RBs, the proposed algorithm improves classification accuracy by up to 1.4% over an optimal user selection baseline with random RB allocation, by up to 3.5% over standard FL with random user selection and random RB allocation, and by up to 4.1% over a wireless optimization baseline that minimizes sum packet error rates while ignoring FL parameters.
- CNN Generalization: On non-convex CNN training with MNIST, the proposed algorithm correctly classifies 30 out of 36 sample digits compared to 27 out of 36 for standard FL with random selection and resource allocation.
- Theoretical Validation: The theoretical asymptotic convergence gap matches empirical simulation values with less than 9% difference across varying user counts.

Coverage note — Intermediate algebraic proof steps for Theorem 1 in Appendix A and Proposition 2 in Appendix B were omitted in accordance with the requirement to exclude proof derivations.

References

1.M. Chen, Z. Yang, W. Saad, C. Yin, H. V. Poor, and S. Cui, “Performance optimization of federated learning over wireless networks,” in Proc. IEEE Global Commun. Conf., Waikoloa, HI, USA, December 2019.
2.M. Chen, U. Challita, W. Saad, C. Yin, and M. Debbah, “Artificial neural networks-based machine learning for wireless networks: A tutorial,” IEEE Commun. Surveys Tut., vol. 21, no. 4, pp. 3039–3071, Fourthquarter 2019.
3.Y. Sun, M. Peng, Y. Zhou, Y. Huang, and S. Mao, “Application of machine learning in wireless networks: Key techniques and open issues,” IEEE Commun. Surveys Tut., vol. 21, no. 4, pp. 3072–3108, Fourthquarter 2019.
4.Y. Liu, S. Bi, Z. Shi, and L. Hanzo, “When machine learning meets big data: A wireless communication perspective,” IEEE Veh. Technol. Mag., vol. 15, no. 1, pp. 63–72, March 2020.
5.K. Bonawitz, H. Eichner, W. Grieskamp, D. Huba, A. Ingerman, V. Ivanov, C. M. Kiddon, J. Konecny, S. Mazzocchi, B. McMahan, T. V. Overveldt, D. Petrou, D. Ramage, and J. Roselander, “Towards federated learning at scale: System design,” in Proc. Systems and Machine Learning Conference, Stanford, CA, USA, 2019.
6.V. Smith, C. K. Chiang, M. Sanjabi, and A. S. Talwalkar, “Federated multi-task learning,” in Proc. Advances in Neural Information Processing Systems, Long Beach, CA, USA, Dec. 2017.
7.X. Wang, Y. Han, C. Wang, Q. Zhao, X. Chen, and M. Chen, “In-edge AI: Intelligentizing mobile edge computing, caching and communication by federated learning,” IEEE Netw., vol. 33, no. 5, pp. 156–165, Sep. 2019.
8.W. Saad, M. Bennis, and M. Chen, “A vision of 6G wireless systems: Applications, trends, technologies, and open research problems,” IEEE Netw., vol. 34, no. 3, pp. 134–142, May 2020.
9.E. Jeong, S. Oh, J. Park, H. Kim, M. Bennis, and S. L. Kim, “Multi-hop federated private data augmentation with sample compression,” in Proc. International Joint Conference on Artificial Intelligence Workshop on Federated Machine Learning for User Privacy and Data Confidentiality, Macao, China, Aug. 2019.
10.Z. Yang, M. Chen, W. Saad, C. S. Hong, and M. Shikh-Bahaei, “Energy efficient federated learning over wireless communication networks,” arXiv preprint arXiv:1911.02417, 2019.
11.T. Li, A. K. Sahu, A. Talwalkar, and V. Smith, “Federated learning: Challenges, methods, and future directions,” IEEE Signal Process. Mag., vol. 37, no. 3, pp. 50–60, May 2020.
12.J. Konećnȃ y, H. B. McMahan, D. Ramage, and P. Richtárik, “Federated optimization: Distributed machine learning for ` on-device intelligence,” arXiv preprint arXiv:1610.02527, Oct. 2016.
13.H. B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Proc. Conf. Machine Learning Research, Fort Lauderdale, FL, USA, Apr. 2017.
14.M. Chen, O. Semiari, W. Saad, X. Liu, and C. Yin, “iterated echo state learning for minimizing breaks in presence in wireless virtual reality networks,” IEEE Trans. Wireless Commun., vol. 19, no. 1, pp. 177–191, Jan. 2020.
15.J. Konećnȃ y, B. McMahan, and D. Ramage, “iterated optimization: Distributed optimization beyond the datacenter,” ` arXiv preprint arXiv:1511.03575, Nov. 2015.
16.S. Samarakoon, M. Bennis, W. Saad, and M. Debbah, “Distributed federated learning for ultra-reliable low-latency vehicular communications,” IEEE Trans. Commun., vol. 68, no. 2, pp. 1146–1159, Feb. 2020.
17.S. Ha, J. Zhang, O. Simeone, and J. Kang, “iterated federated computing in wireless networks with straggling devices and imperfect CSI,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Paris, France, Jul. 2019.
18.O. Habachi, M. A. Adjif, and J. P. Cances, “iterated uplink grant for NOMA: A federated learning based approach,” arXiv preprint arXiv:1904.07975, Mar. 2019.
19.J. Park, S. Samarakoon, M. Bennis, and M. Debbah, “iterated network intelligence at the edge,” Proc. IEEE, vol. 107, no. 11, pp. 2204–2239, Nov. 2019.
20.Q. Zeng, Y. Du, K. Huang, and K. K. Leung, “iterated-efficient radio resource allocation for federated edge learning,” in Proc. IEEE Int. Conf. Commun. Workshop, Dublin, Ireland, Jun. 2020.
21.S. Wang, T. Tuor, T. Salonidis, K. K. Leung, C. Makaya, T. He, and K. Chan, “iterated federated learning in resource constrained edge computing systems,” IEEE J. Sel. Areas Commun., vol. 37, no. 6, pp. 1205–1221, June 2019.
22.Z. Zhao, C. Feng, H. H. Yang, and X. Luo, “iterated-learning-enabled intelligent fog radio access networks: Fundamental theory, key techniques, and future trends,” IEEE Wireless Commun., vol. 27, no. 2, pp. 22–28, April 2020.
23.T. T. Vu, D. T. Ngo, N. H. Tran, H. Q. Ngo, M. N. Dao, and R. H. Middleton, “iterated-free massive MIMO for wireless federated learning,” IEEE Tans. Wireless Commun., to appear, 2020.
24.N. H. Tran, W. Bao, A. Zomaya, N. Minh N.H., and C. S. Hong, “iterated learning over wireless networks: Optimization model design and analysis,” in Proc. IEEE Int. Conf. Compt. Commun., Paris, France, April 2019.
25.M. Chen, H. V. Poor, W. Saad, and S. Cui, “Convergence time optimization for federated learning over wireless networks,” arXiv preprint arXiv:2001.07845, 2020.
26.H. H. Yang, Z. Liu, T. Q. S. Quek, and H. V. Poor, “iterated policies for federated learning in wireless networks,” IEEE Tans. Commun., vol. 68, no. 1, pp. 317–333, Jan. 2020.
27.S. Bi, J. Lyu, Z. Ding, and R. Zhang, “iterated radio maps for wireless resource management,” IEEE Wireless Commun., vol. 26, no. 2, pp. 133–141, April 2019.
28.C. Hennig and M. Kutlukaya, “iterated thoughts about the design of loss functions,” Revstat Stat. J., vol. 5, no. 1, pp. 19–39, March 2007.
29.J. Konecny, H. B. McMahan, F. X. Yu, P. Richtarik, A. Theertha Suresh, and D. Bacon, “iterated learning: Strategies for improving communication efficiency,” in Proc. NIPS Workshop on Private Multi-Party Machine Learning, Barcelona, Spain, Dec. 2016.
30.Y. Xi, A. Burr, J. Wei, and D. Grace, “iterated general upper bound to evaluate packet error rate over quasi-static fading channels,” IEEE Tans. Wireless Commun., vol. 10, no. 5, pp. 1373–1377, May 2011.
31.Y. Pan, C. Pan, Z. Yang, and M. Chen, “iterated allocation for D2D communications underlaying a NOMA-based cellular network,” IEEE Wireless Commun. Lett., vol. 7, no. 1, pp. 130–133, Feb 2018.
32.M. P. Friedlander and M. Schmidt, “iterated deterministic-stochastic methods for data fitting,” SIAM J. Sci. Comput., vol. 34, no. 3, pp. A1380–A1405, May 2012.
33.M. Mahdian and Q. Yan, “iterated bipartite matching with random arrivals: An approach based on strongly factor-revealing LPs,” in Proc. ACM Symposium on Theory of Computing, San Jose, California, USA, June 2011.
34.R. Jonker and T. Volgenant, “iterated the Hungarian assignment algorithm,” Oper. Res. Lett., vol. 5, no. 4, pp. 171–175, 1986.
35.N. Landman K. Moore and J. Khim, “iterated maximum matching algorithm,” https://brilliant.org/wiki/ hungarian-matching/.
36.Y. LeCun, “iterated MNIST database of handwritten digits,” http://yann.lecun.com/exdb/mnist/.
37.S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.

Citation

MLA

Chen, M., et al. “A Joint Learning and Communications Framework for Federated Learning over Wireless Networks”. arXiv, 2019, http://arxiv.org/abs/1909.07972v4.

APA

Chen, M., Yang, Z., Saad, W., Yin, C., Poor, H. V., & Cui, S. (2019). A Joint Learning and Communications Framework for Federated Learning over Wireless Networks. arXiv. http://arxiv.org/abs/1909.07972v4

Chicago

Chen, M., Z. Yang, W. Saad, C. Yin, H. V. Poor, and S. Cui. 2019. “A Joint Learning and Communications Framework for Federated Learning over Wireless Networks”. arXiv. http://arxiv.org/abs/1909.07972v4.

Harvard

Chen, M. et al. (2019) “A Joint Learning and Communications Framework for Federated Learning over Wireless Networks”, arXiv [Preprint]. Available at: http://arxiv.org/abs/1909.07972v4.

Vancouver

1. Chen M, Yang Z, Saad W, Yin C, Poor HV, Cui S (2019) A Joint Learning and Communications Framework for Federated Learning over Wireless Networks. arXiv

BibTeX

@article{chen2019joint,
  title = {A Joint Learning and Communications Framework for Federated Learning over Wireless Networks},
  author = {Chen, Mingzhe and Yang, Zhaohui and Saad, Walid and Yin, Changchuan and Poor, H. Vincent and Cui, Shuguang},
  year = {2019},
  journal = {arXiv},
  url = {http://arxiv.org/abs/1909.07972v4},
  eprint = {1909.07972}
}

Metadata:arXiv

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A Joint Learning and Communications Framework for Federated Learning Over Wireless Networks

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Knowls

Knowl 1 — Upper Bound on Expected Convergence Rate of Wireless Federated Learning

Knowl 2 — Global Model Aggregation under Wireless Packet Transmission Errors

Knowl 3 — Joint Learning, User Selection, and Resource Allocation Optimization Problem

Knowl 4 — Optimal Transmit Power Allocation for Wireless FL Users

Knowl 5 — Asymptotic FL Loss Simplification and Bipartite Matching Reformulation

Knowl 6 — Condition on Gradient Variance Bound for Convergence of Wireless FL

Knowl 7 — Joint User Selection, Resource Allocation, and Transmit Power Optimization Algorithm

Knowl 8 — Global and Local Loss Function Assumptions for Wireless FL Convergence

Knowl 9 — Empirical Performance and Accuracy Gains of Wireless FL Framework

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