Research On Sparse Linear Inverse Problems Based On Adaptive-depth Neural Network And Its Application In Communication Systems

Sparse linear inverse problems,which mean recovering original sparse signals from observed samples when the measurement matrices are known,play important roles in various subjects and areas in reality.In communication systems,by using the sparse characteristics of wireless channels,compressive sensing theory and the sparse linear inverse algorithms in it realize signaling overhead reduction and user capacity expansion.Recently,the neural-network-based sparse linear inverse algorithms are widely researched due to their excellent reconstruction performances and fast convergence properties.However,these machine-learning-based approaches ignore a key characteristic in traditional iterative algorithms,where the numbers of iterations required for algorithm convergence are different for sparse signals with different sparsity levels.In general,the sparser signals have faster convergence rates.Current machine-learning-based algorithms use neural networks with fixed numbers of layers to recover signals with different sparsity levels,making the reconstruction process for signals with lower sparsity levels relatively slow and for signals with higher sparsity levels insufficient,which may not be able to maximize the computational efficiency.To overcome the drawbacks of current algorithms with fixed numbers of layers,this thesis conducts researches on sparse linear inverse problems based on adaptive-depth neural networks.The main works and innovation points of this thesis are as follows:(1)Regarding the problem that neural networks with fixed numbers of layers fail to satisfy sparse signals with all kinds of sparsity levels simultaneously,this thesis proposes to use an adaptive-depth neural network to dynamically assign computing resources for signals with different sparsity levels.Through theoretical analysis,this thesis compares the reconstruction error upper bound for fixed-layer scheme and adaptive-depth scheme.By introducing the adaptive computation time method(ACT)in computer vision field to sparse linear inverse problems,this thesis proposes an adaptive-depth sparse linear inverse algorithm based on ACT and corroborates the superiority of adaptive-depth scheme with synthetic experiments.(2)Regarding the drawbacks in ACT,this thesis proposes an adaptive-depth sparse linear inverse algorithm based on a continuous cost function(AD-CCF).Based on the original algorithm framework,this thesis makes some improvements in the network architecture and objective function.In terms of the network architecture,this thesis proposes to use an extra linear mapping matrix to take the advantage of sparse characteristics in signals,while for objective function,this thesis proposes to use a cost function consisted of continuous functions and the corresponding asymmetrical training-testing method,which is adopted to solve the incompletely-differentiable problem of the objective function in ACT.Compared to ACT which is required to train different neural networks for different average computing resources demands,the proposed AD-CCF method realizes dynamic adjustment of average computing resources with a set of fixed network parameters.This thesis validates the effectiveness of AD-CCF through synthetic experiments.(3)Regarding the situations where the sparsity levels of signals in massive machine-type random access are dynamically changing with the communication services and that in massive MIMO channel estimation are influenced by human movements,this thesis proposes to use adaptive-depth sparse linear inverse algorithms to further reduce the communication delay and improve the stability in communication systems.