Research On Over-the-air Computation In Mobile Edge Networks

Thanks to the rapid development of information and communication technology and the continuous upgrading of artificial intelligence applications,the future 6G wireless communication network is envisioned to provide ultra-high-speed,ultra-reliable,and lowlatency communication with massive devices,and further support vertical intelligent applications,such as autonomous driving,smart cities,industrial automation,smart medical,and other applications.However,in the existing edge network,the constrained network resources are hard to satisfy the massive access and data processing requirements for largescale devices.At the same time,the existing communication network architecture is built in a separated manner for communication and computing,and thus cannot be satified with the strong coupling property of sensing,transmission,and processing from those intelligent applications.To solve the above problems,this thesis focuses on the over-the-air computation(Air Comp)technology in mobile edge networks,in which we investigate the integration of communication,computation,and intelligence,to conduct in-depth research on the technological breakthroughs and its applications.Firstly,this thesis considers the power control problem in highly reliable Air Comp over wireless fading channel,based on which we jointly optimize the transmission power at edge devices and the signal scaling factor(called denoising factor)at edge servers to minimize the computation error subject to the average power constraint of edge devices.Due to the coupling of optimization variables,the formulated problem is non-convex,and difficult to obtain the optimal solution directly.To solve this problem,a threshold-based optimal power control structure is proposed for static channel case,in which the transmission power strategy is determined by a quality coefficient.For the time-varying channel case,an optimal power control strategy with regularized channel inversion structure is proposed to achieve a performance balance between reducing signal misalignment error and suppressing noiseinduced error.Simulation results validate that the proposed power control policy can achieve the remarkable performance in reducing the distortion of Air Comp.Secondly,we consider a multi-cell Air Comp network subject to the inter-cell interference,and investigate the cooperative interference management and power control optimization.First,a centralized multi-cell joint power control scheme is proposed for the scenario with a centralized controller among edge servers.By minimizing the mean squared error(MSE)of the multi-cell Air Comp network,we inverstigate the Air Comp performance trade-off between different cells via characterizing the Pareto boundary of the multi-cell MSE region.Next,we consider the other scenario of distributed power control,e.g.,when there lacks a centralized controller,in which we introduce a set of interference temperature(IT)constraints to represent the total inter-cell interference power between a specific pair of cells.Therefore,each edge server can optimize the transmission power of its associated devices based on only a set of IT constraints for adjacent cells,to minimize its MSE.By optimizing the IT level,another distributed power control method is proposed to characterize the Pareto boundary of multicell MSE region equivalent to the centralized power control method.Simulation results shows that the proposed cooperative interference management and power control optimization scheme can significantly reduce the MSE of multi-cell Ai Comp networks.Thirdly,in order to support intelligent applications,we further consider the implementation of Air Comp in federated edge learning(FEEL),enabling the so-called overthe-air federated edge learning(Air-FEEL).According to its implementations,namely overthe-air federated stochastic gradient descent(Air-Fed SGD)and over-the-air federated averaging(Air-Fed Avg),we first analyze the fundamental perforamnce trade-off between the Air Comp and machine learning,based on which we design the joint management of learning hyper-parameters and resource allocation to improve learning performance:This thesis investigates the transmission power control to enhance the learning performance of Air-Fed SGD.We first analyze the convergence behavior of Air-Fed SGD(in terms of the optimality gap)subject to aggregation errors at different communication rounds.It is revealed that if the aggregation estimates are unbiased,then the training algorithm would converge exactly to the optimal point with mild conditions;while if they are biased,then the algorithm would converge with an error floor determined by the accumulated estimate bias over communication rounds.Next,building upon the convergence results,we optimize the power control to directly minimize the derived optimality gaps under the cases without and with unbiased aggregation constraints,subject to a set of average and maximum power constraints at individual edge devices.We transform both problems into convex forms,and obtain their structured optimal solutions,both appearing in a form of regularized channel inversion,by using the Lagrangian duality method.Finally,numerical results show that the proposed power control policies achieve significantly faster convergence for Air-Fed SGD.Then,we consider the transmission power control optimization in Air-Fed Avg.Towards this end,we first analyze the convergence behavior(in terms of the optimality gap)of AirFed Avg with aggregation errors(of global model updates)at different outer iterations.Then,to enhance the training accuracy,we minimize the optimality gap by jointly optimizing the transmission power control at edge devices and the denoising factors at edge server,subject to a series of power constraints at individual edge devices.Furthermore,to accelerate the training speed,we also minimize the training latency of Air-Fed Avg with a given targeted optimality gap,in which learning hyper-parameters including the numbers of outer iterations and local training epochs are optimized jointly with the power control.Finally,numerical results show that the proposed transmission power control policy achieves significantly faster convergence speed for Air-Fed Avg.It is also shown that the Air-Fed Avg achieves an order-of-magnitude shorter training latency than the conventional Fed Avg with digital orthogonal multiple access(OMA-Fed Avg).