In this paper, we propose a new approach to justify a round-off error impact on the accuracy of the linear least squares (LS) solution using Cholesky decomposition. This decomposition is widely employed to inverse a matrix in the linear detector of the Multi-User multi-antenna receiver. The proposed stochastic bound is much closer to actual errors than other numerical bounds. It was tested with a half-precision format and validated in realistic scenarios. Experimental results demonstrate our approach predicts errors very close to those achieved by simulations. The proposed approach can be employed to analyze the resulting round-off error in many other applications.

翻译：本文提出了一种新方法，用于论证舍入误差对使用Cholesky分解的线性最小二乘（LS）解精度的影响。该分解被广泛应用于多用户多天线接收机线性检测器中的矩阵求逆。所提出的随机界限比其他数值界限更接近实际误差。该方法在半精度格式下进行了测试，并在实际场景中得到了验证。实验结果表明，我们的方法预测的误差与仿真结果非常接近。该方案可用于分析许多其他应用中的舍入误差。