We consider the success probability of the $L_0$-regularized box-constrained Babai point, which is a suboptimal solution to the $L_0$-regularized box-constrained integer least squares problem and can be used for MIMO detection. First, we derive formulas for the success probability of both $L_0$-regularized and unregularized box-constrained Babai points. Then we investigate the properties of the $L_0$-regularized box-constrained Babai point, including the optimality of the regularization parameter, the monotonicity of its success probability, and the monotonicity of the ratio of the two success probabilities. A bound on the success probability of the $L_0$-regularized Babai point is derived. After that, we analyze the effect of the LLL-P permutation strategy on the success probability of the $L_0$-regularized Babai point. Then we propose some success probability based column permutation strategies to increase the success probability of the $L_0$-regularized box-constrained Babai point. Finally, we present numerical tests to confirm our theoretical results and to show the advantage of the $L_0$ regularization and the effectiveness of the proposed column permutation algorithms compared to existing strategies.

翻译：本文研究了$L_0$正则化盒约束Babai点的成功概率，该点是$L_0$正则化盒约束整数最小二乘问题的次优解，可用于MIMO检测。首先，我们推导了正则化与非正则化盒约束Babai点成功概率的公式。随后研究了$L_0$正则化盒约束Babai点的性质，包括正则化参数的最优性、其成功概率的单调性以及两种成功概率比值的单调性。我们推导了$L_0$正则化Babai点成功概率的一个上界。接着，分析了LLL-P置换策略对$L_0$正则化Babai点成功概率的影响。然后，提出若干基于成功概率的列置换策略以提高$L_0$正则化盒约束Babai点的成功概率。最后通过数值实验验证了理论结果，并展示了相比现有策略，$L_0$正则化的优势及所提列置换算法的有效性。