Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermin...Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.展开更多
In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization me...In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.展开更多
This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates ...This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with multi-antenna.We develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders alternately.For the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the WSR.For the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent method.Numerical results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works.展开更多
基金Supported by the National Natural Science Foundation ofChina(No.61271240)Jiangsu Province Natural Science Fund Project(No.BK2010077)Subject of Twelfth Five Years Plans in Jiangsu Second Normal University(No.417103)
文摘Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.
基金supported by the National Natural Science Foundation of China under Grant No.61973291。
文摘In this work,a novel gradient descent method based on event-triggered strategy has been proposed,which involves integer and fractional order iteration.Firstly,the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked.Based on this result,a fractional order iteration approach has been developed by modelling the system with fractional order dynamics.Secondly,to reduce the comsumption of computation,a feedback based event-triggered mechanism has been introduced to the gradient descent method.The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method,and Zeno behavior is proved to be avoided simultaneously.Lastly,the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.
基金supported by National Natural Science Foundation of China(No.61771005)
文摘This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with multi-antenna.We develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders alternately.For the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the WSR.For the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent method.Numerical results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works.
