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

Xiao-Wen Chang; Yingzi XU

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arXiv · 2401.15815

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

Xiao-Wen Chang·Yingzi XU

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Abstract

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.

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Xiao-Wen Chang, Yingzi XU. 2024-01-29. Success probability of the $L_0$-regularized box-constrained Babai point and column permutation strategies. https://arxiv.org/abs/2401.15815

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