Although the existing sphere decoding algorithm of the spatial modulation systems can greatly reduce the computational complexity of the maximum-likelihood (ML) detection

due to its loose updating radii and slow convergence

the level of computational complexity reduction is still very limited

especially in high-order modulation systems. To solve the problem

the statistical distribution is used in this paper to estimate the redundancy in the updating radii of the existing algorithm

and two improved sphere decoding algorithms are proposed. Theoretical analysis and simulation results show that the improved algorithms can greatly reduce the computational complexity of the traditional sphere decoding while achieving the same performance with ML detection

which have great theoretical and practical significance.