## 5 Conclusions  
The paper introduces a novel and efficient methodology for estimating multiple parameters in the \(k\)-\(\mu\) fading channel model. Two sets of solutions are derived using moment-generating functions based on second-, fourth-, and sixth-order moments. Three sets of closed-form solutions are designed for estimating the \(k\) and \(\mu\) parameters based on the previously derived solutions. Performance analysis of the proposed parameter estimators using simulation results demonstrates strong consistency between theoretical and estimated values. The proposed parameter estimators address some of the shortcomings of existing estimators through simulation and comparison, including large estimation errors, susceptibility to errors, and fragility to noise interference. The estimators can calculate \(k\) and \(\mu\) parameters based on the envelope and SNR signals. The work presents a mathematically tractable framework for estimating characteristic parameters of wireless channels in small-scale environments. It is expected to allow for real-time and accurate analysis of complex scenarios, such as moving targets, time-varying conditions, or non-line-of-sight (NLOS) extreme communication, based on \(k\)-\(\mu\) fading channel model parameters. Simulation results demonstrate that the proposed parameter estimator \(\hat{k}\)-\(\hat{\mu}_{\Delta}\) is appropriate for low latency and limited resource overhead communication scenarios, and the other estimator \(\hat{k}\)-\(\hat{\mu}_{\text{B}}\) is suitable for scenarios with poor channel quality, numerous obstacles between antennas, or no LOS communication path available (\(k\) approaches zero, NLOS communication scenarios).  
Conceptualization, Z.F. and J.T.; formal analysis, Z.J. and D.H.; investigation, Z.J., X.L., P.F. and D.H.; methodology, Z.F. and J.T.; project administration, J.T.; supervision, X.L. and P.F.; validation, Z.F., Z.J. and J.T.; visualization, Z.J., P.F. and D.H.; writing--original draft, Z.F, Z.J. and J.T.; writing--review and editing, Z.F., X.L., P.F., D.H. and J.T. All authors have read and agreed to the published version of the manuscript.  
Figure 5: Impact analysis of estimator performance based on different SNR conditions: (**a**) The power delay spectrum and PDF values of parameters \(k\) and \(\mu\) when \(N=8500\); (**b**) The power delay spectrum and PDF values of parameters \(k\) and \(\mu\) when \(N=8000\); (**c**) The power delay spectrum and PDF values of parameters \(k\) and \(\mu\) when \(N=5000\); (**d**) The power delay spectrum and PDF values of parameters \(k\) and \(\mu\) when \(N=2600\); (**e**) The power delay spectrum and PDF values of parameters \(k\) and \(\mu\) when \(N=1000\).  
**Funding:** This research was funded by the CAEP Foundation under Grant CX20200010, National Natural Science Foundation of China under grant number 61871084, and National Natural Science Foundation of China under grant number 62271109.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.