Recently, significant improvements in hardware technology and wireless communications have enabled the use of wireless sensor networks (WSNs) in a wide range of real-world applications. The extensive application of WSNs has also attracted the attention of criminals; therefore, the security of data transmissions in WSNs is becoming increasingly crucial. A WSN is composed of at least one sink node and many sensor nodes with a number of limitations, including battery lifetime, processing power, and memory capacity. The network topology diagram of a WSN is presented in Figure 1. Because of the low cost and high security provided by the chaotic signals, the implementation of chaos communication can significantly improve the security of WSNs. [PERSON] et al. investigated the chaotic modulation approach for secured wireless medical sensor network (WMSN) in e-healthcare applications [32]. [PERSON] et al. proposed a novel asymmetric cryptographic algorithm based on matrix decomposition in wireless body area networks (WBANs) [33]. However, insufficient information is available on communication in WSNs based on CMPDFS of CVCSs in noisy conditions, and the relevant theoretical developments based on CMPDFS have seldom been studied in the literature. In order to make up for the blind spot, the relevant simulation experiments and result analysis are carried out. The main contributions of this paper are summarized as follows:  
(1) We describe CMPDFS, which is a new synchronization scheme for CVCSs. The modified projective matrix is able to change the amplitude of complex chaotic signals, and effectively overcome the amplitude limitation of chaos communication. This helps diversify the available synchronization schemes and increases the security of the transmitted messages. (2) We design control laws with guaranteed performance to construct the slave system. These laws take the bounded disturbances into consideration and ensure that the reconstructed slave system is chaotic. The controller has good robustness to the bounded noise. (3) We propose a novel communication scheme for WSNs based on CMPDFS, which outperforms traditional chaotic masking. The communication scheme is able to theoretically achieve a bit error rate (BER) of zero. The results from simulation and security analysis demonstrate that the CMPDFS communication scheme provides a large key space, high sensitivity to encryption keys, high security, and an acceptable encryption speed. The arrangements of our paper are as follows: we give the definition of CMPDFS in Section 2. In Section 3, we design control schemes to construct a slave system, propose the communication scheme for a WSN and discuss its special advantages. The process of WSN communication by simulation experiments are shown in Section 4. Finally, we give the conclusions of the whole paper. The descriptions of all notations in the paper are shown in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**The Symbol** & **Meanings** \\ \hline \(n\) & The dimension of system \\ \(q\) & The dimension of uncoupled variables \\ \(L1\) & The drive system \\ \(L2\) & The response system \\ \(\mathbf{y},\mathbf{z}\) & The complex state vector of the drive system \\ \(\mathbf{x}\) & The complex state vector of the response system \\ \(r\) & The real part of a complex variable \\ \(i\) & The imaginary part of a complex variable \\ \(\mathbf{f},\mathbf{p},\mathbf{g}\) & Nonlinear function of complex variables \\ \(\mathbf{v}\) & The designed controller \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The descriptions of all notations. Figure 1: The topology diagram of wireless sensor networks.