## 3 Communication Scheme Based on CMPS
### Communication Scheme for Wireless Body Area Network  
In wireless body area networks, sensors are used to measure the temperature, blood pressure, heart rate, and other physiological information of users, first transmitting the measurement results to smart mobile devices (e.g., smartphones) and, then, sending them to a telematics terminal. After mutual authentication between the smart mobile device and the telematics terminal, the smart mobile device encrypts the collected sensor information (clear text) and the shared chaotic signal (produced from time delay complex Chen system with the same parameters and initial values) of the telematics terminal after authentication and sends them to storage devices for remote services. After the remote service storage device successfully receives the data, it synchronously decrypts the data, according to the complex modified proportional projection, such that the plain-text is obtained in the data buffer of the remote service storage device. The communication block diagram is based on CMPS, as shown in Figure 6.  
We use \(L1\) and \(L2\) to represent smart devices (transmitting end) and the telematics terminal (receiving end), respectively. The plain-text signals to be transmitted are body temperature \(h_{1}^{r}\), high blood pressure value \(h_{1}^{i}\), low blood pressure value \(h_{2}^{r}\), heart rate \(h_{2}^{i}\), and blood sugar \(h_{3}\), which are all complex scale factors in CMPS; the duration of every sample was 1 min. Then, the ciphertext transmission signal  
Figure 6: Communication scheme based on complex modified projection synchronization (CMPS) for a wireless body area network. \[s(t) =Hg(y)+D\varepsilon(t)\] \[=diag\{h_{1}^{r}+jh_{1}^{i},h_{2}^{r}+jh_{2}^{i},h_{3}\}g(y) \tag{7}\] \[+diag\{D\varepsilon(t)+jD\varepsilon(t),D\varepsilon(t)+jD \varepsilon(t),D\varepsilon(t)\}\]  
is expanded into five channels; that is,  
\[ \begin{cases}s_{1}^{r}(t)=h_{1}^{r}g_{1}(y)^{r}-h_{1}^{i}g_{1}(y)^{i}+D \varepsilon(t),\\ s_{1}^{i}(t)=h_{1}^{r}g_{1}(y)^{i}+h_{1}^{i}g_{1}(y)^{r}+D\varepsilon(t),\\ s_{2}^{r}(t)=h_{2}^{r}g_{2}(y)^{r}-h_{2}^{i}g_{2}(y)^{i}+D\varepsilon(t),\\ s_{2}^{i}(t)=h_{2}^{i}g_{2}(y)^{r}+h_{2}^{r}g_{2}(y)^{i}+D\varepsilon(t),\\ s_{3}(t)=h_{3}g_{3}(y)+D\varepsilon(t),\end{cases}  \tag{8}\]  
where \(D\varepsilon(t)\) simulates the noise generated by the communication channel and noise source. The controller \(v\) at the receiving end was designed as (6), which contains the transmission signal \(s(t)\) and \(v=s(t)-f(x)+ke\). As CMPS occurs, \(\mathbf{x}(t)\) approaches \(\mathbf{H}(t)\mathbf{y}(t)\) (\(H(t)=diag\{h_{1}^{r}+jh_{1}^{i},h_{2}^{r}+jh_{2}^{i},h_{3}\}\)). The information signal recovered at the receiving end is \(H_{g}(t)=diag\{h_{g1},h_{g2},h_{g3}\}=diag\{x_{1}/y_{1},x_{2}/y_{2},x_{3}/y_{3}\}\). Compared with other examples of communication systems [26; 27; 28; 29; 30; 31; 32; 33], the CMPS-based communication scheme has the following advantages:  
(1) As shown in Equation (7), two layers masked by noise and chaotic signals are used here, where the chaotic signal is the derivative of the system state variable, not the state variable itself, which differs from traditional chaotic masking, thus increasing the difficulty of decoding. (2) The method of recovering plain-text signals is essentially different. In traditional chaos masking, a transmission signal is used to subtract a synchronized chaotic signal, in order to recover a plain-text signal. The effect of channel noise is theoretically ignored and the bit error rate (BER) cannot be guaranteed to be zero. In our communication scheme, we use a CMPS controller to ensure that the signal at the receiving end is equal to the product of the plain-text and chaotic signals. Therefore, BER = 0 for the recovered signal in theory. (3) Compared with CS, which is often used for chaotic communication, CMPS can be observed from partially or completely different dynamic systems.