Abstract: This paper examines the fairness-driven row selection process for randomized Kaczmarz (rKA) precoding within a Massive MIMO framework. The cubic complexity associated with regularized zero-forcing (RZF) motivates the use of iterative inversion-free solvers. We employ the Sainte-Laguë (SL) apportionment method to prioritize rows and introduce an efficient approach that integrates a unified count of floating-point operations (FLOPs) with observed iteration counts to project total computational effort. According to the convention where complex multiplication, addition, and division equate to 6, 2, and 9 FLOPs respectively, each iteration incurs a cost of 16Kj + 9FLOPs; when setting Kj = 16, including minimal selection overhead leads to approximately 275 FLOPs for the Sampling without Replacement rKA (SwoR-rKA) and D’Hondt-rKA (D-rKA), while SL-rKA sees around 270 FLOPs. Nevertheless, simulations targeting a bit error rate (BER) of $$10^{3}$$ at noise-to-power ratios (NTPs) of 25/30 dB reveal significantly fewer iterations needed for SL-rKA (19/18) in contrast to SwoR-rKA (69/68) and D-rKA (30/28). This indicates speedups compared to SwoR-rKA by factors of about 3.70 times and 3.85 times respectively. We investigate why these improvements predominantly stem from the ratio of iterations α, noting that savings per iteration serve as only a minor adjustment. Furthermore, we discuss how weakly dependent our findings are on system dimensions while containing potential effects arising from selection overheads. Our conclusions draw upon theoretical estimates substantiated by empirical observations. The paper also addresses sensitivity considerations, offers implementation recommendations, and identifies unresolved issues related to achieving rigorous assurances and validating on hardware systems.

Keywords: Massive MIMO, Precoding, rKA, RZF, Saint-Lague

Pages: 57-66