## 3 System Model
### Clustering and Selection of Cluster Heads
\[P_{\text{C}}=N_{\text{T}}(P_{\text{mix}}\,+P_{\text{DAC}}+P_{\text{BH}}\,)+2P_ {\text{synth}}\,+N_{\text{R}}(P_{\text{mix}}\,+P_{\text{LNA}}+P_{\text{IFA}} \,+P_{\text{ADC}}) \tag{16}\]

where \(P_{\text{DAC}}\) and \(P_{\text{ADC}}\) are the power consumed by digital-to-analogue and analogue-to-digital converters, respectively; \(P_{\text{fit}}\) and \(P_{\text{filr}}\) indicate transmitter and receiver end filters; \(P_{\text{mix}}\) refers to the power consumed by the mixer; \(P_{\text{synth}}\) is the power consumed by the frequency synthesizer; \(P_{\text{LNA}}\) denotes the power consumed by the low noise amplifier; and \(P_{\text{IFA}}\) is the power consumed intermediate frequency of SN. Then, the overall energy consumption per bit becomes

\[E_{\text{pb}}=\frac{P_{\text{PA}}+P_{\text{c}}}{R_{\text{b}}} \tag{17}\]

\(R_{b}\) can be altered by setting \(R_{\text{b}}^{\text{eff}}=R_{\text{b}}\frac{(F\,-\,pN_{T})}{F}\), where \(pN_{T}\) training models are inserted in each block. Specifically, TC refers to the fading coherence time, and RS is the symbol rate. For the greatest Doppler shift, \(T_{\text{C}}=3/4f_{m}\sqrt{\pi}\) is coherence time \(T\) (\(FM\)) = \(v\)/\(\lambda\), where \(v\) signifies the velocity. When \(pN_{T}\) training symbols are presented in each block, the overall energy usage per bit is as given by Equation (18):

\[E_{\text{pbt}}=\frac{F}{(F-pN_{T})}\bigg{[}\frac{P_{\text{PA}}+P_{\text{c}}}{ R_{\text{b}}}\bigg{]} \tag{18}\]

The letter \(p\) denotes the overhead training factor. A 2 \(\times\) two virtual MIMO link connects all CGs to the next master CG. As a result, the per-bit energy usage is given by Equation (19):

\[E_{\text{pbt}}^{\text{DSC-MIMO}}(d)=\frac{F}{(F-pN_{\text{T}})}\bigg{[}E_{ \text{pb}}(d)\Big{|}_{N_{\text{T}}=2,N_{\text{R}}=2}\bigg{]}R_{\text{X1}} \tag{19}\]

Particles in a swarm-based algorithm update their position about a group's position and velocity. The i-th particle \(P_{i}\) of \(n\) D-dimensional population is represented as

\[P_{i}=[X_{i,1},X_{i,2},X_{i,3},\ldots,X_{i,D}] \tag{20}\]

The position of each particle is assessed by utilizing a fitness function that assesses the quality of the answer it provides in that iteration. For each particle's velocity and location, the \(V_{i}\) and \(X_{i}\) can be updated by Equation (21):

\[V_{\text{new}\,i}=w*V_{i}+c_{1}*r_{1}*(\,\text{Xpbest}\,_{i}-X_{i})+c_{2}*r_{2 }*\Big{(}X_{gbest}-X_{i}\Big{)} \tag{21}\]where w stands for the inertia weight; \(c_{1}\) and \(c_{2}\) are acceleration factors; and \(r_{1}\) and \(r_{2}\) are random values in the range [0, 1]. \[w=w_{\text{initial}}\ -\ \frac{\text{Max. Iteration}\ -\ \text{Current Iteration}}{\text{Total Number of Iterations}} \tag{22}\]

\[\text{New}i,j=X_{\text{old},i}+V_{\text{new},i}\]

To produce the optimal number of CHs, a swarm-based approach is used. The value of the inertia weight is evaluated in the proposed PSO method, utilizing Equation (22), which is a time-varying operation that yields distinct values for every iteration. Furthermore, if an SN is within its communication range, it can be used as a CH. The core knowledge concept is similar to traditional algorithms, such as LEACH. Every node delivers data to the CH at the start of each new iteration. Facts are aggregated, redundant data are deleted, and remaining data are passed onto the next hop, CH or BS, as shown in Algorithm 3. Refl b and \(R\)b are related by Equations (23) and (24):

\[ \begin{array}{c}E_{\text{ppt}}=\frac{F}{(F-pN_{\text{T}})}\left[\frac{p_{ \text{PA}}+P_{\text{c}}}{R_{\text{b}}}\right]E_{\text{ppt}}=\frac{3\lambda R_{ \text{S}}}{(3\lambda R_{\text{S}}-4\
u pN_{\text{T}}\sqrt{\pi})}\left[\frac{p_ {\text{PA}}+P_{\text{c}}}{R_{\text{b}}}\right]\\ R_{\text{b}}^{\text{eff}}=\frac{F-pN_{\text{T}}}{F}R_{\text{b}}=\frac{T_{ \text{c}}R_{\text{b}}-pN_{\text{T}}}{T_{\text{c}}R_{\text{s}}}=\frac{\frac{3} {4\
u\sqrt{\pi}R_{\text{s}}-pN_{\text{T}}}}{4\
u\sqrt{\pi}R_{\text{s}}}R_{ \text{b}}\frac{3\lambda}{4\
u\sqrt{\pi}R_{\text{s}}}R_{\text{s}}-pN_{\text{T}} \end{array}  \tag{23}\]

\[