Justification for Performance Loss Caused by Round-Off Errors in Massive MIMO Detector Based on QR Decomposition

In this letter, we propose a new approach to justify a round-off error’s impact on the accuracy of the linear multi-antenna receiver based on QR decomposition. The minimum mean square error (MMSE) detector employs this decomposition to implement the interference rejection combining (IRC) algorithm that requires the inversion of an interference + noise matrix. We suggested a stochastic approach to calculate the resulting round-off error that is significantly more accurate than the existing numerical bounds. 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 in many other applications of QR decomposition to examine the resulting roundoff inaccuracy.