Abstract: To solve the rank-deficient problem in the underdetermined Multiple-Input Multiple-Output (underdetermined MIMO) systems, this paper proposed the ordering λ-Generalized Sphere Decoding (λ-GSD) algorithm based on reliability measurement. The proposed algorithm transformed the rank-deficient channel matrix into the full-column-ranked one, and adopted a new ordering strategy based on reliability measurement, and then sorted the sub-optimal values of the Minimum Mean Square Error （MMSE） algorithm in a descending order and made the first point as the initial value of the λ-GSD algorithm to reduce the initial search radius. Meanwhile, the decreasing rate of the radius was accelerated with an exponential converging in the algorithm. The simulation results indicate that the proposed algorithm can approach the optimum maximum-likelihood decoding performance and has a lower average operation time than the original λ-GSD algorithm.

Key words: underdetermined MIMO systems, multi-user detection, λ-generalized sphere decoding, reliability measurement, minimum mean square error

摘要： 针对欠定多输入多输出(MIMO)系统中信道矩阵非满秩的问题，提出基于可靠性度量排序的λ-广义球形解码(λ-GSD)算法。该算法将信道矩阵直接转换成满秩矩阵，然后采用基于可靠性度量的排序策略，将排序后由最小均方误差算法得到的次优解作为λ-广义球形解码算法的初始值，减小了初始搜索半径，同时对球形解码算法搜索半径的收缩进行了指数收敛加速处理。仿真结果表明，所提算法同最大似然检测算法和原λ-GSD算法相比较，能获得相同的误符号率性能，而平均运算时间比原λ-GSD算法有明显降低。

关键词: 欠定多输入多输出系统, 多用户检测, 广义球形解码, 可靠性度量, 最小均方误差