Extremely massive MIMO (Multiple-Input Multiple-Output) is a crucial technology in wireless communication systems. By deploying a large number of antennas, extremely massive MIMO enables spatial diversity, but it also introduces significant computational complexity due to the large number of antennas involved in various processing tasks. One such task is precoding, where numerous improvements have been proposed in the literature. However, most existing methods assume spatially stationary channels and do not adequately account for the spatial non-stationarity that arises when the number of antennas increases. The randomized Kaczmarz algorithm (rKA) method and the sampling without replacement rKA (SwoR-rKA) method, that is an enhancement method of rKA, are proposed for the spatial non-stationarity downlink. The bit error ratio of rKA and SwoR-rKA are good at lower signal-to-noise ratio but the performances level off due to the residuals at higher signal-to-noise ratio, so the performances of bit error ratio are limited with the residuals. This paper focuses on reducing the residuals with the same or lower computational complexity. In the rKA method, the factors of precoding matrix are updated iteratively and a column to be updated is selected by a probability. The rKA method select each column at randomly and the SwoR-rKA tends to select a column corresponding to the channel in better condition. It, however, is not effective to update the column corresponding to good conditions because the columns corresponding to the good channels can be estimated to some extent with a small number of iterations. Our idea to improve the SwoR-rKA is that the policy to select a column to be updated is set that the columns corresponding to channels in bad condition tend to be selected. With this policy, all the columns corresponding to each channel are considered to reach a certain degree of estimation criteria. The result of computer simulation shows that proposed method defeats the original SwoR-rKA in view of bit error ratio performance with the same complexity, particularly at high signal-to-noise ratios of about 16 dB or more. The simulation results provide evidence of the effectiveness of the proposed approaches in mitigating the impact of spatial non-stationarity, leading to improved bit error ratio performance.
MIMO, regularized zero forcing, non-stationarity, precoding, randomized Kaczmarz algorithm
Cite this paper
Tatsuki Fukuda. (2023) Improvement of SwoR-rKA Precoding Method for Extremely Large-Scale MIMO With the Same Calculational Complexity. International Journal of Communications, 8, 6-14