## 2 \(k\)-\(\mu\) Fading Channel Models  
In wireless communication systems, the received signal at the receiver can be represented as [27]  
\[y(t)=x(t)\otimes h(t)+n(t) \tag{1}\]  
where \(x(t)\) is the transmit signal, \(h(t)\) is the channel impulse response (CIR) signal, and \(n(t)\) is the noise. The CIR signal describes the energy attenuation and time delay of countless electromagnetic waves that undergo optical phenomena such as reflection and diffraction in the channel, and then arrive at the receiver. Energy attenuation and time delay are two uncorrelated random variables that follow different probability distributions. Various channel fading models (such as Rice, _Nakagami-M_, etc.) use statistical methods to describe the energy attenuation random variable. Assuming that a known frequency-domain signal \(X(f)\) is transmitted from the transmitter and undergoes multipath fading, the received signal filtered at the receiver can be represented in the frequency domain as \(Y(f)=X(f)\cdot H(f)+N(f)\). The estimated channel state information (CSI) obtained from it is \(\hat{H}(f)=X^{-1}(f)\cdot[Y(f)-N(f)]\), which is the channel frequency response (CFR). By performing the inverse Fourier transform on \(\hat{H}(f)\), the channel impulse response (CIR) can be obtained and denoted as \(\hat{h}(t)\), and \(r=|h(t)|\). The classical Rician channel model assumes that the obstacles in the channel follow a uniform distribution, and it defines the signal that arrives at the receiver as a cluster; there is no time correlation between each electromagnetic wave, and the energy fading of the electromagnetic wave obeys a normal distribution and the phase follows a uniform distribution. However, under practical scenario conditions, the electromagnetic waves that arrive at the receiver will be time-dependent because of the non-uniform distribution of the obstacles in the channel, and the CIR will show multiple energy peaks in the experimental data. According to the multiple-cluster effects of the transmitted electromagnetic waves arriving at the receiving end, the electromagnetic waves can be divided into a set of clusters; the number of clusters is denoted by \(\mu\), and each cluster is individually subject to the Rice distribution. This new method for modeling electromagnetic waves was first proposed by [PERSON] [10] and is called the \(k\)-\(\mu\) fading distribution model. The cumulative electrical frequency amplitude (envelope) of the \(\mu\) clusters of electromagnetic waves that arrive at the receiver satisfies the following physical model [24]. \[r^{2}=\sum_{i=1}^{\mu}\left(p_{i}+x_{i}\right)^{2}+\sum_{i=1}^{\mu}\left(q_{i}+y _{i}\right)^{2} \tag{2}\]  
where \(r^{2}\) is the instantaneous power of the carrier signal at the receiving end, \(\mu\) is the number of clusters of electromagnetic waves. \(p_{i}\), \(q_{i}\) are the mean values of the homogeneous and quadrature components of the \(i\)-th cluster of multipath waves, respectively, and \({p_{i}}^{2}\), \({q_{i}}^{2}\) are the real and imaginary parts of the \(i\)-th cluster of the deterministic component signal. \(x_{i}\), \(y_{i}\) are the real and imaginary parts of the scattered wave signal in the \(i\)-th cluster signal, respectively, which are the mutually independent Gaussian processes and satisfy the relationship of \(E[x_{i}]=E[y_{i}]=0\) and \(E[x_{i}^{2}]=E[y_{i}^{2}]=\sigma^{2}\). Therefore, the probability distribution function (PDF) of the \(k\)-\(\mu\) distribution can be expressed as [24]  
\[f(\alpha)=\frac{2\mu(1+k)^{(\mu+1)/2}\cdot\alpha^{\mu}}{k^{(\mu-1)/2}e^{(\mu k +\mu(1+k)\alpha^{2})}}I_{\mu-1}(2\mu\sqrt{k(1+k)}\alpha) \tag{3}\]  
where \(\alpha\) is the normalized envelope and satisfies the relationship of \(\alpha=r/\sqrt{E[r^{2}]}\).