# A Scalable Spatial-Temporal Correlated Non-Stationary Channel Fading Generation Method
## 5 Conclusions  
This paper has proposed a scalable spatial-temporal correlated non-stationary channel fading generation method, which is suitable for implementation on FPGA-based platforms. Based on the scalable system hardware architecture, a temporal-correlated fading generation method based on the improved CORDIC algorithm has been developed. It can expand the convergence domains of the e-exponent, logarithm, and square root functions, and the relative error is maintained at the \(10^{-4}\) level. In addition, a space-correlated fading generation method based on improved lower triangular matrix operations has been developed. By decomposing large-scale matrix operations into low-order matrix operations, it can reduce computational complexity and hardware resource consumption significantly.  
The measurement results confirm strong agreement between the statistical characteristics of the output fading and theoretical values. The PDF error for output fading is a  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Traditional Method in [27; 28]** & **Proposed Method** \\ \hline System clock & 160 M & 160 M \\ Channel sample rate & 312.5 K & 312.5 K \\ Slice LUTs & 59,315 (13.69\%) & 35,926 (8.29\%) \\ Registers & 65,543 (7.56\%) & 47,632 (5.49\%) \\ DSP & 461 (12.81\%) & 57 (1.58\%) \\ Block RAM & 196 (13.33\%) & 67 (4.55\%) \\ Resource utilization & 11.85\% & 4.98\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Hardware resource consumption of matrix operations.  
Figure 10: (**a**) Theoretical and (**b**) simulated values of sub-channel fading SCC at \(t=24\) s.  
mere 1.52%, and the time-domain envelopes closely match theoretical shapes, validating the correctness of the proposed hardware generation architecture. Meanwhile, the TCF and DPSD of the output fading at different time instances align with theoretical values, demonstrating the capability of the hardware generation architecture to support dynamic non-stationary channel simulations. Lastly, the average errors for SCF and SCC of the output fading are 1.47% and 1.86%, respectively, confirming the precise simulation of spatial-temporal correlations in MIMO channels. Furthermore, under identical conditions, the hardware resource consumption using the proposed method has been reduced by 6.87%. Specifically, the consumption of DSP resources has decreased by 11.23%, and the consumption of block RAM resources has decreased by 8.78%. This demonstrates that the proposed method effectively reduces hardware resource usage. In summary, the proposed method effectively and efficiently emulates spatial-temporal correlated non-stationary channel fading, and it can be applied to design, evaluate, and optimize MIMO-related communication technologies.  
Conceptualization, S.F. and Q.Z. ([PERSON]); funding acquisition, Q.Z. ([PERSON]); investigation, T.M. and B.H.; methodology, M.S. and Q.Z. ([PERSON]); software, S.F. and T.M.; supervision, Q.Z. ([PERSON]); validation, Q.Z. ([PERSON]) and T.M.; writing--original draft, S.F. and Q.Z. ([PERSON]); writing--review and editing, Y.D. and B.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China (No. 62271250), in part by Natural Science Foundation of Jiangsu Province (No. BK20211182), in part by the Key Technologies R&D Program of Jiangsu (Prospective and Key Technologies for Industry, BE2022067 and BE2022067-3), in part by the open research fund of National Mobile Communications Research Laboratory, Southeast University, (No. 2022D04), and in part by the Experimental technology research and development (SYJS202304Z).  
The data used to support the findings of this study are available from the corresponding author upon request.  
The authors declare no conflict of interest.