Dynamic User Activity And Data Detection For Grant-free NOMA Via Weighted L?{2,1} Minimization

Recently,the grant-free Non-Orthogonal Multiple Access(NOMA)has received widespread attention in reducing signaling overhead and transmission delay in the massive machine type communications(m MTC).In the grant-free NOMA system,detecting user activity and data(UAD)accurately is a very challenging problem.Compressed sensing(CS)is considered as an effective way to solve this problem because it can accurately reconstruct the signal through a small amount of sampling.However,the detection performance of existing methods based on CS in actual dynamic scenes is not yet ideal.This paper proposes to use the weighted(?)_2,1-norm minimization(WL21M)method to solve the UAD detection problem in dynamic scenes.The main research contents and contributions of this paper are as follows:(1)This article carried out an average recoverability analysis of the WL21M problem.By extending the average recoverability analysis results of the classic the(?)_2,1-norm minimization problem to the WL21M problem,the exact recovery conditions are established for the WL21M.Then,the average recoverability of the WL21M problem is analyzed by calculating the probability that the recovery condition is established.The analysis shows that the WL21M method can improve the signal detection performance through the combination of proper weighting and intrinsic time correlation.(2)This paper proposes a aollaborative hierarchical match pursuit(C-HiMP)algorithm to solve the problem of dynamic user UAD detection in the grant-free NOMA.In the C-HiMP,the WL21M problems are solved in the subspaces spanned by all of the components in the hierarchical estimated support sets,where the weights are collaboratively updated by the solutions in previous time slots so that an attractive self-correction capacity is obtained.At the same time,because the estimated support set in each time slot is not necessarily nested or increased,the solution to the WL21M problem has lower computational complexity.Finally,the simulation results of the C-HiMP algorithm show that,compared with several latest CS-based detection algorithms,the proposed C-HiMP algorithm can significantly improve the performance in terms of detection accuracy and computational complexity.(3)In order to further improve the computational efficiency of the C-HiMP,this paper proposes a fast collaborative hierarchical match pursuit(F-C-HiMP)algorithm based on the augmented lagrangian methods(ALM)of WL21M.The C-HiMP algorithm uses the original WL21M,which wastes the running time of the algorithm.The existing ALM method can formulate the WL21M problem as a linear program and solve it quickly.Therefore,this paper studies the ALM form of WL21M and proposes the F-C-HiMP algorithm.In the F-C-HiMP algorithm,under the condition of the initial unit weight and a wide range of stopping iterations,the signal is pre-estimated through ALM to determine the support and weight.Then,the signal is detected accurately by ALM in the subspace of the support set index under the condition of a strictly stopping iterations.Finally,the simulation results of the F-C-HiMP algorithm show that,compared with several of the fastest CS-based detection algorithms and the proposed C-HiMP algorithm,the F-C-HiMP algorithm not only has a high detection accuracy,but also has a very low computational complexity.