Reference [23] derived approximate expressions for the system interruption probability and channel capacity in a system where both the sensing transmission signal and the interference signal experience \(k\)-\(\mu\) shadow fading under given conditions such as signal-to-noise ratio. These expressions are expressed in known hypergeometric functions and can be easily calculated numerically. However, while most of these studies evaluate channel transmission quality in specific scenarios through the analysis of system interruption probability, average bit error rate, and channel capacity based on \(k\)-\(\mu\) distribution and \(k\)-\(\mu\) shadow distribution, they do not provide effective channel model parameter estimation methods by assuming the range of critical channel parameters such as \(k\) and \(\mu\), making it difficult to provide adjustment strategies for communication system transmission scheme design and performance analysis optimization through accurate channel estimation and CQI quantization in practical scenarios, thus affecting system generality. In the existing research on \(k\)-\(\mu\) parameter estimators, [PERSON] et al. [24] proposed closed-form expressions for \(k\)-\(\mu\) parameters, and [PERSON] et al. further analyzed the asymptotic validity of this estimator [25]. However, our experiments have shown that this estimator is inefficient and prone to errors in estimation, which means the method in [24] has a higher probability of error when estimating channel parameters. [25] includes transcendental functions that incorporate special functions such as gamma and hypergeometric functions,which means that they cannot be solved analytically, but only through numerical methods. Additionally, a maximum likelihood-based \(\alpha\)-\(\eta\)-\(\mu\) distribution parameter estimator was proposed in [26] for inferring the characteristics of signal amplitude distribution. However, this study's conclusion is not a closed-form expression, and the algorithm's complexity is high. To address these issues, this paper proposes a new \(k\)-\(\mu\) parameter estimator for the communication system's \(k\)-\(\mu\) fading channel model, providing theoretical support for distinguishing fading channel types. The main contributions of this paper are as follows: First, two mathematical models containing the unknown parameters \(k\) and \(\mu\) are established using the moment-generating function. Second, three \(k\)-\(\mu\) parameter moment estimators based on the \(k\)-\(\mu\) fading model are derived, resulting in corresponding closed-form expressions for parameter estimation. The complexity and estimation accuracy of the estimator are analyzed. Finally, simulation analysis is performed on different parameters, ensuring high-precision and effective estimation of \(k\) and \(\mu\) parameters under different \(k\)-value conditions. The structure of this paper is organized as follows: In Section 2, we introduce the \(k\)-\(\mu\) distribution-based fading channel model and the existing estimators. In Section 3, we provide the derivation process for three moment-based estimators. In Section 4, we utilize Monte Carlo simulation to generate test data and compare the computational complexity and estimation accuracy of the three moment-based estimators proposed in this paper with the estimator proposed by [PERSON]. We also discuss the applicability of each estimator in different scenarios.