On the Success Probability of the $L_{0}$-regularized Box-constrained Babai Point

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 and the monotonicity of the ratio of the two success probabilities. Finally a bound on the success probability of the
$L_{0}$
-regularized Babai point is derived.