## 2 Proposed Scheme and RF Transmission Algorithm
### Signal Decryption
\[s(t)=I(t)\sin(2\pi f_{c}t)+Q(t)\sin(2\pi f_{c}t-90^{\circ}), \tag{18}\]

where the carrier frequency is denoted by \(f_{c}\), and a coherent demodulator at the receiver multiplies the received signal with a cosine and sine signal to produce the received estimates of \(I(t)\) and \(Q(t)\). By employing conventional trigonometric identities, this can be expressed as Equation (19):

\[s(t)=\frac{1}{2}I(t)+\frac{1}{2}\big{(}I(t)\cos(4\pi f_{c}t)-Q(t)\sin(4\pi f_{ c}t)\big{)}, \tag{19}\]

The representation of digital transmission denoted by the n-QAM constellation is represented as follows

A signal which is represented in an n-QAM constellation can be expressed as follows:

\[QAM(t)=s(t)+n(t), \tag{20}\]

where \(n(t)\) represents the additive white Gaussian noise (AWGN), while \(s(t)\) denotes the signal modulated under an n-QAM scheme mainly determined by the n scheme under the transmission, which can be defined as

\[s_{k}(t)=a_{j\delta}(t-nT_{B})\sin(2\pi f_{c}t)+b_{j\delta}(t-nT_{B})\sin(2\pi f _{c}t+90^{\circ}), \tag{21}\]

where \(a_{j}\) and \(b_{j}\) represent the in-phase and quadrature, respectively. The function \(g(\cdot)\) is the base-band tone, and \(T_{B}\) represents the symbol time duration. Figure 3: Architecture of n-QAM scheme. ### Summarize

In summary, the design procedure for chaotic encryption and transmission can be summarized as follows:

1. Construct the master-slave system stated in Equations (1) and (3). 2. Apply any pole assignment technique to compute the values of observer gains \(l_{i},\ (i=1,2,3,4)\) to ensure that all eigenvalues of matrix \(A_{e}\) have a negative real part, i.e., \(\Re(\lambda_{i}\{A_{e}\})<0\). 3. Combine the ECG signal with the chaotic signal to generate the encrypted ECG signal. Subsequently, the signal is pre-processed for modulation using n-QAM. 4. Set the configuration parameters and generate the RMC waveform for LTE transmission. Subsequently, transmit the encrypted ECG signal. 5. The encrypted ECG signal is post-processed through an n-QAM demodulation process and filtering stage. 6. Set the configuration parameters for decryption. Subsequently, the decryption of the ECG signal is carried out; i.e., the ECG signal is reconstructed by subtracting the chaotic encryption signal from the encrypted signal. An overall diagram of the proposed chaotic encryption and transmission scheme is presented in Figure 4.

## 3 Experimental Results

A block diagram of the experimental RF system is depicted in Figure 5. Part A proposes using a PC/Host that runs MATLAB version R2024a and is connected to a Cyclone V FPGA SoC development kit manufactured by Intel Corporation (Altera), (Santa Clara, CA, USA) via Ethernet. For the transmission process of the encrypted \(ECG_{TX}\) signal, one of the channels of the dual-band transceiver is used that contains the biological ECG information of interest added to the chaotic information. In this work, the synchronization channel \(x_{1s}\) is carried out in the Host. In the simulation, the decryption key is not sent through the same wireless medium operating in the same 2.45 GHz RF band. If the transmitted synchronization signal is intercepted, the purpose of guaranteeing the privacy of the information would be lost. It is essential to send by an alternative path or, even better, an embedded system located in the specialist doctor to contain the encryption key as a further implementation stage. Finally, the PC/Host regulates and configures the transmission and reception of signals by utilizing MATLAB to store the data in the FPGA's DDR memories. Part B of the diagram corresponds to the analog proposal in which the signal transmitted by the AD9361 transceiver

Figure 4: Overall diagram scheme. is subjected to the ZFBP-2400-S+ bandpass filter amplified by a ZV60-V63+ power amplifier. Lastly, a ZV60-63-S+ directional coupler is employed to divide the amplified signal, enabling the spectrum analyzer to analyze a portion of it while the remaining portion continues its transmission path.