On the Success Probability of Three Detectors for the Box-Constrained Integer Linear Model

This paper is concerned with detecting an integer parameter vector inside a box from linear model that corrupted noise following the Gaussian distribution. One of commonly used detectors maximum likelihood detector, which obtained by solving box-constrained least squares problem, NP-hard. Two other popular are rounding and Babai due to their high efficiency implementation. In this paper, we first present formulas for success probabilities (the correct detection) these three two different situations: deterministic uniformly distributed over constraint box. Then, give simple examples respectively show probability detector can be larger than latter when deterministic, prove always not Some relations between results constrained ordinary cases presented, bounds on easily computed, developed. Finally, simulation provided illustrate our main theoretical findings.