## 2 Proposed Scheme and RF Transmission Algorithm
### Signal Decryption  
Algorithm 4 is implemented during the final stage of the signal decryption process. The parameters of the master system are established, and the profits of the observer are initialized. The proposed algorithm then iterates over the synchronization signal (\(x1\)) duration, using the Euler method to approximate the state variables continuously. These variables estimate the chaotic components of the signal. The decrypted ECG signal (\(ECG_{dec}\)) is obtained by subtracting the approximated chaotic signal (\(x3s\)) from the encrypted signal (\(ECG_{encrypt}\)) that was received. The synchronization of the original and estimated signals emphasizes the observer's accuracy. In summary, the algorithm is defined by the subsequent stages:  
```
1:Encrypted signal \(ECG_{encrypt}\), synchronization signal
2:Decrypted ECG signal \(ECG_{dec}\)
3:procedureObserver Synchronization Process
4: Initialize parameters
5: Initialize observer gains
6:\(N\leftarrow\) Length of \(dS\)
7: Initialize states
8:\(dt\leftarrow\) Defined time step
9:for\(i\gets 1\) to \(N-1\)do
10:\(x1s[i+1]\leftarrow x1s[i]+h\cdot(x2s[i]+11\cdot(x1[i]-x1s[i]))\)
11:\(x2s[i+1]\leftarrow x2s[i]+h\cdot(x3s[i]+12\cdot(x1[i]-x1s[i]))\)
12:\(x3s[i+1]\leftarrow x3s[i]+h\cdot(-a1\cdot x1s[i]-a2\cdot x2s[i]-a3\cdot x3s[i ]+x4s[i]+13\cdot(x1[i]-x1s[i]))\)
13:\(x4s[i+1]\leftarrow x4s[i]+h\cdot 4\cdot(x1[i]-x1s[i])\)
14:endfor
15:\(ECG_{dec}\gets ECG_{encrypt}-x3s\)
16:return \(ECG_{dec}\)
17:endprocedure
```  
**Algorithm 4** Decryption of ECG Signal  
### Signal Decryption  
Algorithm 4 is implemented during the final stage of the signal decryption process. The parameters of the master system are established, and the profits of the observer are initialized. The proposed algorithm then iterates over the synchronization signal (\(x1\)) duration, using the Euler method to approximate the state variables continuously. These variables estimate the chaotic components of the signal. The decrypted ECG signal (\(ECG_{dec}\)) is obtained by subtracting the approximated chaotic signal (\(x3s\)) from the encrypted signal (\(ECG_{encrypt}\)) that was received. The synchronization of the original and estimated signals emphasizes the observer's accuracy. In summary, the algorithm is defined by the subsequent stages:  
```
1:procedureObserver Synchronization Process
2:Initialize parameters
3:Initialize observer gains
4:\(N\leftarrow\) Length of \(dS\)
5:Initialize states
6:\(dt\leftarrow\) Defined time step
7:for\(i\gets 1\) to \(N-1\)do
8:\(x1s[i+1]\leftarrow x1s[i]+h\cdot(x2s[i]+11\cdot(x1[i]-x1s[i]))\)
9:\(x2s[i+1]\leftarrow x2s[i]+h\cdot(x3s[i]+12\cdot(x1[i]-x1s[i]))\)
10:\(x3s[i+1]\leftarrow x3s[i]+h\cdot(-a1\cdot x1s[i]-a2\cdot x2 Subtract the observer's estimated signal from the encrypted signal to decrypt the ECG signal. An n-QAM algorithm was developed as an essential part of the transmission algorithm for the processing of ECG data. The system is adaptive for variable n-QAM resolution with the input stream consisting of \(x=[x_{1},...,x_{N}]\) for the I-Channel, \(y=[y_{1},...,y_{N}]\) for the Q-Channel, and a 2.45 GHz local oscillator that integrates the in-phase and quadrature components. The resulting signal vector \(s(b)=[(x_{1},y_{1}),...(x_{N},y_{N})]\) is composed of \(K\) bits of binary symbols. Figure 3 depicts the developed architecture of n-QAM:

The AD9361 transceiver sends the time-domain structure of the symbol packaging stage, which is based on K symbols modulated in the final waveform \(s(t)=[s_{1}(t),...,s_{N}(t)]\), to the transmission chain outside the transceiver. This chain comprises a bandpass filtering stage, the power amplifier under test, and the return signal obtained through the directional coupler and spectral analysis [23]. The following equation can be used to express the general QAM equation.