Numerical Error Analysis of MIMO Detector Based on Cholesky Factorization

In this letter, we propose a new approach to justify a roundoff error’s impact on the accuracy of the linear multi-antenna receiver based on Cholesky decomposition. This decomposition is used in the minimum mean square error (MMSE) algorithm to invert the interference-plus-noise matrix. We suggest a stochastic approach to calculate the resulting roundoff error of a low-bitwidth MMSE detection that employs a quantized channel estimate and an inaccurate interference-plus-noise matrix inversion. The proposed method allows for a detailed roundoff analysis of the linear detection. It was validated in realistic scenarios using a standard half-precision format. Experimental data show that our method predicts errors that are quite similar to those obtained from simulations. The suggested method can be used to study how quantization noise and other sources of error (such as channel estimation, interpolation, and interference-plus-noise matrix sampling) affect the accuracy of detection.