In the massive Multiple-Input Multiple-Output（MIMO） system

when the number of users is comparable（or equal） to the number of Base Station（BS） antennas

the performance of the linear detection algorithm is not ideal. We start with nonlinear detection and propose a greedy sphere decoding algorithm based on Lattice Reduction（LR）. Lenstra-Lenstra-Lovasz algorithm assisted QR decomposition is proposed to obtain orthogonal bases

which then combines the improved sphere decoding algorithm with the greedy strategy. The search tree nodes are reduced more efficiently by searching the smallest Partial Euclidean Distance（PED） as the root node. Simulation results show that the proposed algorithm has the characteristics of low complexity and fast convergence. Compared with linear algorithms

the proposed algorithm has a 3～10 dB performance improvement when the system bit error rate is 10

-4

. Moreover

the algorithm reduces the complexity of the recently proposed LR-K-Best algorithm to a certain extent

and has high engineering application value.