Robotic fleets such as unmanned aerial and ground vehicles have been widely used for routine inspections of static environments, where the areas of interest are known and planned in advance. However, in many applications, such areas of interest are unknown and should be identified online during exploration. Thus, this paper considers the problem of simultaneous exploration, inspection of unknown environments and then real-time communication to a mobile ground control station to report the findings. The heterogeneous robots are equipped with different sensors, e.g., long-range lidars for fast exploration and close-range cameras for detailed inspection. Furthermore, global communication is often unavailable in such environments, where the robots can only communicate with each other via ad-hoc wireless networks when they are in close proximity and free of obstruction. This work proposes a novel planning and coordination framework (SLEI3D) that integrates the online strategies for collaborative 3D exploration, adaptive inspection and timely communication (via the intermittent or proactive protocols). To account for uncertainties w.r.t. the number and location of features, a multi-layer and multi-rate planning mechanism is developed for inter-and-intra robot subgroups, to actively meet and coordinate their local plans. The proposed framework is validated extensively via high-fidelity simulations of numerous large-scale missions with up to 48 robots and 384 thousand cubic meters. Hardware experiments of 7 robots are also conducted. Project website is available at https://junfengchen-robotics.github.io/SLEI3D/.

To tackle the challenge of data heterogeneity in federated learning (FL), personalized FL has been proposed to maximize individual utility (model performance) by customizing personalized models for clients. Considering the significance ofindividual rationality, existing works have formulated clients' participation decisions problem ashedonicgames. However, they assume that clients can participate in only one collaborative coalition, constraining players' attempts to join multiple coalitions. Different from prior works, we approach personalized FL from the perspective of hedonicoverlapping coalition formation(OCF) games where rational clients can join multiple coalitions and generate their personalized model by weighting the local and coalition models. Nevertheless, the key challenge in analyzing the game is how to achieve a stable coalition structure where no clients would deviate from the current structure. This leads to our main question:what does a stable OCF structure look like?To address this problem, we first investigate the linear FL models for theoretical insights. Then, we design a heuristic algorithm for achieving anindividually stableOCF structure. Experimental results demonstrate the feasibility of our algorithm for both linear and non-linear models, and show that our mechanism can improve the personalized model performance by up to 19% over existing methods.

In federated learning (FL), distributed users collaboratively train a neural network model under the coordination of a central server. However, time-varying client availability, coupled with non-independent and non-identically distributed (non-IID) datasets, leads to a biased convergence. In this work, we prove the convergence of FL under time-varying client availability. The theoretical result shows that biased convergence occurs when available client distribution does not algin with the client population distribution. To address this challenge, we propose a pricing-based incentive mechanism to encourage clients to adjust their availability. First, we model the strategic interactions among clients as a non-cooperative game under an arbitrary pricing scheme. We prove that this game is a potential game and its equilibrium can be found through optimization. Second, we derive an optimal pricing scheme for large client populations and propose a bi-level optimization algorithm using Particle Swarm Optimization (PSO) for general scenarios. Through analysis of client availability evolution, we prove the effectiveness of our scheme in mitigating biased convergence. Experimental results using real-world client availability dataset show that our approach addresses time-varying client availability issue, achieving up to 99.5% improvement over benchmarks and enhancing FL convergence rates by up to 2.49 times.

Federated Unlearning (FU) enables the removal of specific clients' data influence from trained models. However, in non-IID settings, removing clients creates critical side effects: remaining clients with similar data distributions suffer disproportionate performance degradation, while the global model's stability deteriorates. These vulnerable clients then have reduced incentives to stay in the federation, potentially triggering a cascade of withdrawals that further destabilize the system. To address this challenge, we develop a theoretical framework that quantifies how data heterogeneity impacts unlearning outcomes. Based on these insights, we model FU as a Stackelberg game where the server strategically offers payments to retain crucial clients based on their contribution to both unlearning effectiveness and system stability. Our rigorous equilibrium analysis reveals how data heterogeneity fundamentally shapes the trade-offs between system-wide objectives and client interests. Our approach improves global stability by up to 6.23%, reduces worst-case client degradation by 10.05%, and achieves up to 38.6% runtime efficiency over complete retraining.

The rapid growth of AI-generated content (AIGC) services has created an urgent need for effective prompt pricing strategies, yet current approaches overlook users' strategic two-step decision-making process in selecting and utilizing generative AI models. This oversight creates two key technical challenges: quantifying the relationship between user prompt capabilities and generation outcomes, and optimizing platform payoff while accounting for heterogeneous user behaviors. We address these challenges by introducing prompt ambiguity, a theoretical framework that captures users' varying abilities in prompt engineering, and developing an Optimal Prompt Pricing (OPP) algorithm. Our analysis reveals a counterintuitive insight: users with higher prompt ambiguity (i.e., lower capability) exhibit non-monotonic prompt usage patterns, first increasing then decreasing with ambiguity levels, reflecting complex changes in marginal utility. Experimental evaluation using a character-level GPT-like model demonstrates that our OPP algorithm achieves up to 31.72 % improvement in platform payoff compared to existing pricing mechanisms, validating the importance of user-centric prompt pricing in AIGC services.

Federated Foundation Models (FedFMs) represent a distributed learning paradigm that fuses general competences of foundation models as well as privacy-preserving capabilities of federated learning. This combination allows the large foundation models and the small local domain models at the remote clients to learn from each other in a teacher-student learning setting. This paper provides a comprehensive summary of the ten challenging problems inherent in FedFMs, encompassing foundational theory, utilization of private data, continual learning, unlearning, Non-IID and graph data, bidirectional knowledge transfer, incentive mechanism design, game mechanism design, model watermarking, and efficiency. The ten challenging problems manifest in five pivotal aspects: “Foundational Theory,” which aims to establish a coherent and unifying theoretical framework for FedFMs. “Data,” addressing the difficulties in leveraging domain-specific knowledge from private data while maintaining privacy; “Heterogeneity,” examining variations in data, model, and computational resources across clients; “Security and Privacy,” focusing on defenses against malicious attacks and model theft; and “Efficiency,” highlighting the need for improvements in training, communication, and parameter efficiency. For each problem, we offer a clear mathematical definition on the objective function, analyze existing methods, and discuss the key challenges and potential solutions. This in-depth exploration aims to advance the theoretical foundations of FedFMs, guide practical implementations, and inspire future research to overcome these obstacles, thereby enabling the robust, efficient, and privacy-preserving FedFMs in various real-world applications.

Local Differential Privacy (LDP) is a mechanism used to protect training privacy in Federated Learning (FL) systems, typically by introducing noise to data and local models. However, in real-world distributed edge systems, the non-independent and identically distributed nature of data means that clients in FL systems experience varying sensitivities to LDP-introduced noise. This disparity leads to fairness issues, potentially discouraging marginal clients from contributing further. In this paper, we explore how to enhance client-level performance fairness under LDP conditions. We model an FL system with LDP and formulate the problem PriFair using regularization, which assigns varied noise amplitudes to clients based on federated analytics. Additionally, we develop PriFairFed, a Tikhonov regularization-based algorithm that eliminates variable dependencies and optimizes variables alternately, while also offering a theoretical privacy guarantee. We further experimented with the algorithm on a real-world system with 20 Raspberry Pi clients, showing up to a 73.2% improvement in client-level fairness compared to existing state-of-the-art approaches, while maintaining a comparable level of privacy.

Federated learning (FL) has garnered increased attention in the field of distributed machine learning and privacy computing. In the FL setup, effective and efficient unlearning algorithms are required to remove the impact of specific training data from the trained model, called federated unlearning. However, traditional machine unlearning algorithms face limitations in FL systems because the client data is private and even non-IID. In this paper, we propose a new federated unlearning algorithm called FednP. Our approach involves dividing the client set into subsets using multiple different partitions. We then train constituent models for each client subset within these partitions using existing FL algorithms and aggregate the results of constituent models for predictions. With multiple partitions, FednP limits the influence of the data to be erased within its belonging subsets, while it also improves the accuracy of the aggregated prediction. Based on the multiple-partition framework, we design partition creation methods to effectively enhance the prediction accuracy. Furthermore, we propose a cost reduction method to reduce the cost of training/retraining. Our extensive experiments on various datasets and model architectures demonstrate that FednP improves prediction accuracy while well-controls the additional cost.

We present FedSM, a Federated Spectrum Management architecture to increase channel utilization (CU) and reduce latency, while protecting users’ data privacy. We employ hedonic coalition formation game for spectrum allocation. Within each coalition, we design a bandit learning algorithm to share spectra and adjust resource usage. Preliminary simulation results show FedSM increases CU to 93.51% and reduces latency to 248.68 ms compared to three privacy-preserving dynamic spectrum management architectures.

Federated Learning (FL) algorithms commonly sample a random subset of clients to address the straggler issue and improve communication efficiency. While recent works have proposed various client sampling methods, they have limitations in joint system and data heterogeneity design, which may not align with practical heterogeneous wireless networks. In this work, we advocate a new independent client sampling strategy to minimize the wall-clock training time of FL, while considering data heterogeneity and system heterogeneity in both communication and computation. We first derive a new convergence bound for non-convex loss functions with independent client sampling and then propose an adaptive bandwidth allocation scheme. Furthermore, we propose an efficient independent client sampling algorithm based on the upper bounds on the convergence rounds and the expected per-round training time, to minimize the wall-clock time of FL, while considering both the data and system heterogeneity. Experimental results under practical wireless network settings with real-world prototype demonstrate that the proposed independent sampling scheme substantially outperforms the current best sampling schemes under various training models and datasets.

Federated learning (FL) has recently received more and more attention in the joint field of distributed machine learning (ML) and privacy computing. Similar to the traditional ML systems, there exists the need of effective and efficient unlearning algorithms to unlearn certain training data from the FL model. The traditional machine unlearning algorithms have limitations for the FL systems, since the data of clients are both private and non-IID. In this paper, we propose a new algorithm for federated unlearning called FedUMP to improve the model performance and accelerate the unlearning process. Its main idea is to first create multiple different client partition strategies, each of which divides the clients into several subsets. Then we independently train subset models for all client subsets and aggregate the results of subset models for predictions. Furthermore, we propose a retraining acceleration method to reduce the time consumption with multiple partitions, and a partition strategy design method to search for good partition strategies efficiently. Extensive experiments on various datasets and model architectures demonstrate that FedUMP improves both model performance and unlearning speed.

In federated learning (FL), distributed users collaboratively train a neural network model under the coordination of a central server. However, during the training process, clients often exhibit time-varying availability and have non-independent and non-identically distributed (non-IID) datasets. This results in system-induced bias, as models trained by the available clients do not accurately represent the entire population, which includes both available and unavailable clients. To address this bias, we propose a pricing-based incentive mechanism to encourage clients to adjust their availability. First, we model the strategic interaction among a large number of FL clients as a non-cooperative game under an arbitrary pricing scheme. We demonstrate that this game is a potential game, and its equilibrium can be found by solving an optimization problem. Second, based on equilibrium analysis, we derive an optimal pricing scheme for scenarios with a large client population. For general scenarios with any number of clients, we propose a bi-level optimization algorithm that utilizes Particle Swarm Optimization (PSO) to determine the optimal pricing scheme. This algorithm can effectively handles the intricate correlation between the equilibrium and pricing scheme. Our experimental results, based on real-world client availability datasets, highlight the effectiveness of our proposed incentive mechanism in mitigating system-induced bias, with improvements of up to 99.5% compared to the uniform pricing benchmark. Furthermore, this mechanism enhances the FL convergence rate by up to 3.43 times.

In this demo, we introduce FedCampus, a privacy-preserving mobile application for smart campus with federated learning (FL) and federated analytics (FA). FedCampus enables cross-platform on-device FL/FA for both iOS and Android, supporting continuously models and algorithms deployment (MLOps). Our app integrates privacy-preserving processed data via differential privacy (DP) from smartwatches, where the processed parameters are used for FL/FA through the FedCampus backend platform. We distributed 100 smartwatches to volunteers at Duke Kunshan University and have successfully completed a series of smart campus tasks featuring capabilities such as sleep tracking, physical activity monitoring, personalized recommendations, and heavy hitters. Our project is opensourced at https://github.com/FedCampus/FedCampus_Flutter. See the FedCampus video at https://youtu.be/k5iu46IjA38.

A proper mechanism design can help federated learning (FL) to achieve good social welfare by coordinating self-interested clients through the learning process. However, existing mechanisms neglect the network effects of client participation, leading to suboptimal incentives and social welfare. This paper addresses this gap by exploring network effects in FL incentive mechanism design. We establish a theoretical model to analyze FL model performance and quantify the impact of network effects on heterogeneous client participation. Our analysis reveals the non-monotonic nature of FL network effects. To leverage such effects, we propose a model trading and sharing (MTS) framework that allows clients to obtain FL models through participation or purchase. To tackle heterogeneous clients' strategic behaviors, we further design a socially efficient model trading and sharing (SEMTS) mechanism. Our mechanism achieves social welfare maximization solely through customer payments, without additional incentive costs. Experimental results on an FL hardware prototype demonstrate up to 148.86% improvement in social welfare compared to existing mechanisms.

We present a privacy-preserving room occupancy estimation method using federated analytics of Bluetooth Low Energy (BLE) packets. By processing data locally and reporting only aggregated device counts, our approach preserves user privacy while achieving 95% accuracy in occupancy prediction. This method provides a cost-effective alternative to traditional sensing technologies like PIR and mmWave, balancing privacy, accuracy, and ease of deployment. Future work will expand testing to multi-room setups and enhance privacy measures. Code URL: https://github.com/Johnnybyzhang/BLE-capture

Federated learning (FL) provides a collaborative paradigm for distributedly training a global model while protecting clients' privacy. In addition to communication bottlenecks and non-i.i.d. data distributions, the FL framework introduces two fundamental economic challenges: first, clients are self-interested and strategic in practice, requiring specific incentives to participate in FL; second, each client can misreport its private information to its advantage. Although existing studies have proposed economic mechanisms, they are often restricted to a “binary” participation scenario, leading to communication overheads or biased models due to client heterogeneity. In this paper, we first analyze the convergence bound under arbitrary client sampling probability with a varying number of clients. Then, we consider an optimal mechanism design problem: the FL convergence bound minimization subject to budget constraint, incentive compatibility, and individual rationality. We derive the optimal sampling probability function in a close form. To overcome the unknown prior distribution challenge, we introduce a prior-independent mechanism design, and show how it gradually learns cost distributions by exploiting the incentive compatibility property. We perform extensive experiments and show that, while outperforming the uniform sampling scheme, two proposed schemes (prior-based and prior-independent ones) perform closely to the ideal complete information upper bound.

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence analysis of FL have focused on unbiased client sampling, e.g., sampling uniformly at random, which suffers from slow wall-clock time for convergence due to high degrees of system heterogeneity (e.g., diverse computation and communication capacities) and statistical heterogeneity (e.g., unbalanced and non-i.i.d. data). This paper aims to design an adaptive client sampling algorithm for FL over wireless networks that tackles both system and statistical heterogeneity to minimize the wall-clock convergence time. We obtain a new tractable convergence bound for FL algorithms with arbitrary client sampling probability. Based on the bound, we analytically establish the relationship between the total learning time and sampling probability with an adaptive bandwidth allocation scheme, which results in a non-convex optimization problem. We design an efficient algorithm for learning the unknown parameters in the convergence bound and develop a low-complexity algorithm to approximately solve the non-convex problem. Our solution reveals the impact of system and statistical heterogeneity parameters on the optimal client sampling design. Moreover, our solution shows that as the number of sampled clients increases, the total convergence time first decreases and then increases because a larger sampling number reduces the number of rounds for convergence but results in a longer expected time per-round due to limited wireless bandwidth. Experimental results from both hardware prototype and simulation demonstrate that our proposed sampling scheme significantly reduces the convergence time compared to several baseline sampling schemes. Notably, for EMNIST dataset, our scheme in hardware prototype spends 71% less time than the baseline uniform sampling for reaching the same target loss.

Incentive mechanism is crucial for federated learning (FL) when rational clients do not have the same interests in the global model as the server. However, due to system heterogeneity and limited budget, it is generally impractical for the server to incentivize all clients to participate in all training rounds (known as full participation). The existing FL incentive mechanisms are typically designed by stimulating a fixed subset of clients based on their data quantity or system resources. Hence, FL is performed only using this subset of clients throughout the entire training process, leading to a biased model because of data heterogeneity. This paper proposes a game-theoretic incentive mechanism for FL with randomized client participation, where the server adopts a customized pricing strategy that motivates different clients to join with different participation levels (probabilities) for obtaining an unbiased and high-performance model. Each client responds to the server's monetary incentive by choosing its best participation level, to maximize its profit based on not only the incurred local cost but also its intrinsic value for the global model. To effectively evaluate clients' contribution to the model performance, we derive a new convergence bound which analytically predicts how clients' arbitrary participation levels and their heterogeneous data affect the model performance. By solving a non-convex optimization problem, our analysis reveals that the intrinsic value leads to the interesting possibility of bi-directional payment between the server and clients. Experimental results using real datasets on a hardware prototype demonstrate the superiority of our mechanism in achieving higher model performance for the server as well as higher profits for the clients.

In this paper, we propose FedRos, a Federated Reinforcement Learning based multi-robot system, which enables networked robots collaboratively to train a shared model without sharing their private sensing data. Firstly, we present the FedRos pipeline that embeds the Webots robotics simulator. We then highlight features of FedRos, including its compatibility with the state-of-the-art Federated Learning and Reinforcement Learning algorithms and its sim-to-real viability. Lastly, we present benchmark experiments to show the effectiveness of FedRos.11Jianwei Huang and Bing Luo are co-corresponding authors of this paper. This work is supported by the National Natural Science Foundation of China (Project 62271434), Shenzhen Science and Technology Program (Project JCY120210324120011032), Guangdong Basic and Applied Basic Research Foundation (Project 2021B1515120008), Shenzhen Key Lab of Crowd Intelligence Empowered Low-Carbon Energy Network (No. ZDSYS20220606100601002), and the Shenzhen Institute of Artificial Intelligence and Robotics for Society. Video of FedRos demo: https://youtube/oDVpB6eo6qs

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server’s communication bandwidth is limited. Recent works on the convergence analysis of FL have focused on unbiased client sampling, e.g., sampling uniformly at random, which suffers from slow wall-clock time for convergence due to high degrees of system heterogeneity and statistical heterogeneity. This paper aims to design an adaptive client sampling algorithm that tackles both system and statistical heterogeneity to minimize the wall-clock convergence time. We obtain a new tractable convergence bound for FL algorithms with arbitrary client sampling probabilities. Based on the bound, we analytically establish the relationship between the total learning time and sampling probabilities, which results in a non-convex optimization problem for training time minimization. We design an efficient algorithm for learning the unknown parameters in the convergence bound and develop a low-complexity algorithm to approximately solve the non-convex problem. Experimental results from both hardware prototype and simulation demonstrate that our proposed sampling scheme significantly reduces the convergence time compared to several baseline sampling schemes. Notably, our scheme in hardware prototype spends 73% less time than the uniform sampling baseline for reaching the same target loss.

Federated learning (FL) is a distributed learning paradigm that enables a large number of devices to collaboratively learn a model without sharing their raw data. Despite its practical efficiency and effectiveness, the iterative on-device learning process incurs a considerable cost in terms of learning time and energy consumption, which depends crucially on the number of selected clients and the number of local iterations in each training round. In this paper, we analyze how to design adaptive FL that optimally chooses these essential control variables to minimize the total cost while ensuring convergence. Theoretically, we analytically establish the relationship between the total cost and the control variables with the convergence upper bound. To efficiently solve the cost minimization problem, we develop a low-cost sampling-based algorithm to learn the convergence related unknown parameters. We derive important solution properties that effectively identify the design principles for different metric preferences. Practically, we evaluate our theoretical results both in a simulated environment and on a hardware prototype. Experimental evidence verifies our derived properties and demonstrates that our proposed solution achieves near-optimal performance for various datasets, different machine learning models, and heterogeneous system settings.

Federated learning (FL) is a distributed learning paradigm that enables a large number of mobile devices to collaboratively learn a model under the coordination of a central server without sharing their raw data. Despite its practical efficiency and effectiveness, the iterative on-device learning process (e.g., local computations and global communications with the server) incurs a considerable cost in terms of learning time and energy consumption, which depends crucially on the number of selected clients and the number of local iterations in each training round. In this paper, we analyze how to design adaptive FL in mobile edge networks that optimally chooses these essential control variables to minimize the total cost while ensuring convergence. We establish the analytical relationship between the total cost and the control variables with the convergence upper bound. To efficiently solve the cost minimization problem, we develop a low-cost sampling-based algorithm to learn the convergence related unknown parameters. We derive important solution properties that effectively identify the design principles for different optimization metrics. Practically, we evaluate our theoretical results both in a simulated environment and on a hardware prototype. Experimental evidence verifies our derived properties and demonstrates that our proposed solution achieves near-optimal performance for different optimization metrics for various datasets and heterogeneous system and statistical settings.

We derive new optimal power allocation solutions for a distributed antenna system with orthogonal frequency division multiplexing (DAS-OFDM), in which K remote radio heads (RRHs) allocate power over N subchannels with both in-dividual RRH and total system power constraints. The individual RRH constraints may be necessary due to hardware limitations, while the total power constraint allows the system to limit the overall energy consumption for cost and/or green environmental factors. In order to obtain some insight on the optimal power allocation, we focus on a simple two-RRH case in this paper. The resulting optimal power allocation solution has an interesting sparse feature: Among N subchannels, at most 1 subchannel can be allocated power for joint transmission by the two RRHs, and the rest of the subchannels must be served by a single RRH. A novel subchannel rearrangement scheme is presented to identify the possible joint-transmission subchannel, as well as which RRH the remaining subchannels are associated with. Numerical results are presented to verify our theoretical results.

This paper analyzes the optimal energy beamforming solution for a multiple-input single-output wireless power transfer (WPT) system over frequency-selective fading channels with joint total and individual antenna power constraints. To maximize the total harvested energy, we derive the optimal co-phasing power allocation rule which reveals that all K antennas will participate in energy beamforming with T<; K antennas transmitting with their maximum individual powers due to the total power constraint. We prove that optimally no more than T+1 subchannels are selected for power allocation. We highlight that the optimal power allocation solution can be efficiently obtained based on the corresponding low- complexity dual problem. Our proposed power allocation algorithm generalizes previous solutions considering only total or individual power constraints. Numerical examples verify our theoretical results and show the impact of the joint total and individual power constraints on the average harvested power.

This paper analyzes the optimal transmission strategy and power allocation for a distributed wireless power transfer (WPT) system operating over frequency-selective fading channels. We consider K coordinated energy transmitters (CETs) coherently transmitting energy to a single user over N > K subchannels with individual power constraints. To maximize the total harvested energy, we derive the optimal co-phasing power allocation rule which has the following properties: 1) For any given subchannel, if the optimal power allocation of one CET is zero, then the power allocated by all the other K - 1 CETs to that subchannel is also zero (i.e., the subchannel is inactive); 2) For the non-zero power subchannels, the optimal power allocation obeys a proportionality principle that establishes a relationship between the powers allocated by all K CETs to all active subchannels. Based on this property, we prove that the optimal distributed WPT strategy is for all CETs to select no more than K subchannels. This is in sharp contrast to wireless information transmission where more than K subchannels may be used for capacity maximization. Numerical examples verify our theoretical results and show the performance gains of our proposed scheme compared to two benchmark schemes.

This paper derives the optimal power allocation for a coordinated orthogonal frequency-division multiplexing (OFDM) transmission system in which K coordinated transmission points (CTPs) coherently transmit and allocate power across N subchannels under both total and individual power constraints. In maximizing the system capacity, previous works showed that, under a total power constraint, the optimal transmission strategy is a maximum-ratio transmission (MRT) for CTPs with a waterfilling type of power allocation solution for the subchannels. For CTPs with both total and individual power constraints, we derive a new optimal co-phasing power allocation with the following property: For any given subchannel, if the optimal power allocation of one CTP is zero, then the power allocation of all the other K - 1 CTPs on that subchannel must also be zero; otherwise, the non-zero power allocation on all CTPs must follow a proportional principle which establishes the relationship between the optimal power allocation for all subchannels and all CTPs. This property highlights that the optimal power allocation for CTPs with individual power constraints is different from waterfilling and MRT, as more power is not necessarily allocated to the subchannels with better channel conditions. Numerical results are presented to verify our theoretical findings.

This paper considers an orthogonal frequency division multiplexing (OFDM) coordinated transmission system in which K coordinated transmission points (CTPs) coherently transmit and allocate power across N subchannels under individual power constraints. In maximizing the system capacity, we derive an optimal co-phasing power allocation solution with the following property: For any subchannel, if the power allocation of one CTP is zero, then the power allocation of all the other CTPs must be zero. Otherwise, the non-zero power allocation of all CTPs follows a proportional rule establishing a relationship between the power allocation for all the subchannels and CTPs. This highlights that the optimal power allocation is different from classical waterfilling and maximum ratio transmission (MRT), as more power is not necessarily allocated to the subchannels with better channel conditions. Based on this property and our derived solution, we successfully reduce the constrained optimization problem with NK variables into an unconstrained one with only K variables, which simplifies computation significantly. Numerical results are presented to verify our theoretical findings.

Recently, two cooperative transmission strategies, Coordinated Multi-Point (CoMP) and wireless relaying, are widely expected to be deployed in future LTE-Advanced (LTE-A) systems to improve the coverage of high data rates and cell-edge throughput. Motivated by the common cooperative diversity feature, in this paper we propose a novel OFDM-based relay system with coordinated wireless backhaul (CoMP backhaul), in which two cooperative base stations (CBS) simultaneously transmit information to an infrastructure-based cell-edge relay node (RN), so as to enhance the rate of backhaul link, as well as improve the end to end (e2e) throughput. In order to maximize the achievable e2e rate, a new Co-Phasing waterfilling power allocation scheme is developed for the multi-carrier CoMP backhaul. Meanwhile, with Taylor series expansion, a simplified iterative Co-Phasing waterfilling (ICPWF) algorithm is proposed to seek the optimal power allocation solutions. Numerical results are presented to verify the optimality of the derived scheme and to show e2e throughput gains over non-coordinated schemes.

It is known that traditional water-filling provides a closed form solution for capacity maximization in frequency-selective block fading channels or multicarrier system with adaptive modulation. This waterfilling solution is derived from a maximum mutual information argument with single transmission point. Motivated by the new technology of coordinated multiple point (CoMP) transmission , a new closed form solution named as joint-waterfilling is derived for a multicarrier system with multiple coordinated transmission point (CTP) [2]. However, like traditional waterfilling, to utilize this joint-waterfilling in practical system, an important issue is the complex transmitter and receiver design, such as variable-rate variable-power MQAM modulation and coding. In this paper we investigate a new constant-power joint-waterfilling scheme for a coordinated transmission system, in which two constant power levels are used across a properly chosen subset of subchannels. A rigorous worst-case performance bound of the constant-power joint-waterfilling is given based on the \emph{duality gap} analysis. Furthermore, a low-complexity constant-power adaptation algorithm is also developed. Numerical simulation result shows that the proposed constant-power joint-waterfilling has a negligible performance loss compared with true joint-waterfilling.

In this paper, we investigate a new power allocation scheme for a multi-user orthogonal frequency division multiplex (OFDM) system, in which two cooperative power sources (CPS) coordinately transmit their power to multiple orthogonal subchannels. In order to maximize the sum rate, a closed form solution is obtained by analytical derivation. Based on the derived solution, we present a novel joint optimal power allocation scheme named as joint water-filling (Jo-WF) which has a remarkably simple nature. Furthermore, a new iterative Jo-WF algorithm is also proposed. Motivated by the regular theoretical derivation of the two-CPS case, we subsequently extend the closed form solution of Jo-WF into arbitrary K-CPS case. Numerical simulation results verify that, compared to traditional non-cooperative water-filling (WF) and equal power allocation (EPA), the proposed Jo-WF scheme provides a significant sum rate gain.