## 2 Proposed Scheme and RF Transmission Algorithm
### Signal Decryption
Figure 14 shows the relationship and trend of values throughout the transmission; the distribution of data by voltage range is shown in a relative equivalent compared to the transmitted signal concerning the 4.5% of the received data in the negative region. From 0 to 0.1, there is a distribution of 33.5% of the data; in the voltage ranges of 0.1-0.3, a distribution of 37% is observed, and in the higher-voltage peaks, it corresponds to 25% of the total data. This is the result of the 1402 samples that were utilized in the ECG. \[s(t)=\frac{1}{2}I(t)+\frac{1}{2}\big{(}I(t)\cos(4\pi f_{c}t)-Q(t)\sin(4\pi f_{ c}t)\big{)}, \tag{19}\]7 128-QAM constellation of an encrypted ECG signal. \[s(t)=\frac{1}{2}I(t)+\frac{1}{2}\big{(}I(t)\cos(4\pi f_{c}t)-Q(t)\sin(4\pi f_{ c}t)\big{)}, \tag{19}\]8 Cross-correlation of ideal received signal and transmitted–received ECG signal. \[s(t)=\frac{1}{2}I(t)+\frac{1}{2}\big{(}I(t)\cos(4\pi f_{c}t)-Q(t)\sin(4\pi f_{ c}t)\big{)}, \tag{19}\]9 Discrete Fourier transform of transmitted and received ECG signal. The transmission channel of the AD9361 transceiver provides a wide attenuation range that helps the design optimize the signal-to-noise ratio (SNR). In the transmitter stage, a constant called the scale factor is established during programming, which indicates the power level used within the board with these internal power amplifiers. This scale factor operates from 0 to 1.0, where the higher value indicates that you have taken it to saturation; in this implementation, the preamplifier was operated in the linear region of 0.5 to eliminate unwanted effects at the input of the external power amplifier. For LTE applications with bandwidth less than 10 MHz, there is a Tx SNR of 128 dB/hZ; with this level of linearity, there is a bit error rate of \(10^{-4}\), which indicates an error of 0.01%. In this condition, the external power amplifier adds nonlinearities to the system. However, the PA is the primary device in a transmission chain. ## 4 Conclusions

This research demonstrates the effectiveness of chaotic encryption, leveraging inherent randomness and sensitivity to initial conditions to enhance data security. The encryption method relies on synchronizing a master-slave chaotic system, where an ECG signal is encrypted using a master system (multi-scroll chaotic system) and decrypted using a slave system (extended state observer). Lyapunov stability analysis establishes sufficient conditions to ensure error state responses remain uniformly bounded around zero. The proposed system offers a viable alternative for processing and transmitting ECG signals in telemedicine. It is primarily based on four algorithms: the modulation and encryption of ECG signals, the generation and transmission of LTE signals, the post-processing of received signals, and the decryption of ECG signals. An FPGA development board was employed to design and integrate an RF transmission platform encompassing digital and power stages. A power amplifier, protected by a directional coupler and designed for base station and LTE applications, enhances power transmission. The experiments utilized the 128-QAM modulation scheme, demonstrating the system's adaptability to higher schemes up to 1024-QAM. \[QAM(t)=s(t)+n(t), \tag{20}\]0 Histogram of transmitted and received ECG signal. In this wireless transmission, data at the spectral level and data distribution analysis are compared to guarantee that the correlation of the received signal is ideal so that the health specialist can give an appropriate ECG diagnosis. The research confirmed the system's capability to prevent channel overlap during 2.5 GHz transmissions. The 2 GHz band, widely used in North America for RF signal transmission, was employed in the experiments. The precise recovery of signals, including frequencies induced in QRS complexes and QT waves, ensures accuracy for further analysis and classification, showcasing the system's potential for broader telemedicine applications.