Success probability of the L_0-regularized box-constrained Babai point and column permutation strategies

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.