## 1 Introduction  
Chaotic signals exhibit several special characteristics such as extraordinary sensitivity to initial conditions, aperiodicity, broad Fourier transform spectra and high security, which coincide with the requirements for signals used in secure communication systems [1; 2; 3; 4]. In secure communication, chaotic signals make the received signals seem like noises, thereby hiding the transmitted messages efficiently and securely. So far, a large number of chaotic secure communication schemes have been advanced in the last decades, including chaotic masking [1], chaotic shift keying [2], chaotic modulation [3], and chaotic direct sequence spread spectrum (CDS-SS) [4]. CDS-SS, where a binary message is multiplied by the chaotic carrier and encrypted into a CDS-SS signal, has been extensively studied as an approach of chaotic secure communication owing to its relatively good security [5; 6; 7]. [PERSON] [6] demonstrated that CDS-SS has the merit of physical-layer security, and [PERSON] [7] showed that CDS-SS has a low probability of interception. Therefore, the research on the blind demodulation of CDS-SS signals is considered to have great prospects for communication management and military reconnaissance, also it can guide the further improvement of CDS-SS schemes' security. Viewed from the principle of demodulation in the chaotic communication field, most demodulation methods are based on two major characteristics of chaotic secure communications. The first characteristic is that there are two chaotic attractors, where a binary message is encoded into two different chaotic attractors. The second one is that the relation of the message and the chaotic carrier is completely additive. However, CDS-SS has neither of the two characteristics [6; 7]. In CDS-SS, the relation between the message and the chaotic carrier is multiplicative and there is only one chaotic attractor, so existent demodulation methods are inapplicable to CDS-SS. So far, many works [8; 9; 10; 11; 12; 13; 14] break chaotic secure communications with the requirement that the structure of the chaotic map is given. [PERSON] _et al_. [8] develop a particle filter (PF) algorithm to solve the problem of chaotic state and unknown additive input estimation even if Gaussian or non-Gaussian noises that are known exist in the chaotic maps. Some approaches [9; 10] estimate simultaneously the state of the system and the unknown inputs using a generalized state space observer. [PERSON] _et al_. [11] developed a Maximun _A Posteriori_-particle filter (MAP-PF) to estimate not only the chaotic state, but also the secure message which is added directly to the chaotic carrier. [PERSON] _et al_. [12] proposed an adaptive bidirectionally coupled synchronization method to estimate the chaotic states with unknown parameters. Several researchers [13; 14] have developed adaptive control based approaches to estimate the states of chaotic systems with uncertain parameters and uncertain disturbances. However, when the structure of the chaotic map (_i.e._, the transmitter's structure) is unknown for the non-cooperative communication condition, the methods mentioned above will be disabled. [PERSON] and [PERSON] [15] proposed a modified unscented Kalman filter to blindly demodulate the CDS-SS signals relying on the white Gaussian approximation which is a very stringent assumption in practical communication systems. A nonlinear Resilient back PROpagation (RPROP) neural network was proposed to estimate the chaotic sequences without knowing the transmitter's structure under the additive white Gaussian noise (AWGN) condition [16], but the RPROP neural network method requires a training sequence that passes through the CDS-SS communication system to identify the unknown transmitter's system, which can be hardly implemented in practice.