## 1 Introduction  
With the rapid development of information technology, speech transmission technology brings more and more convenience to people's life. As the main form of human communication, speech information is widely used for its real-time and easy identification [1, 2, 3]. Whether it is indoor communication or outdoor transmission, the process of sending and receiving speech information will inevitably be affected by the effect of multipath transmission [4]. After the speech is sent out, it needs to reach the receiving end through multiple transmission paths, and the length and attenuation of each path are different, so the received signal presents the superposition of various speech signals affected by phase, delay and multipath [5]. In addition, an increasing number of fields and departments need safe and efficient speech transmission technology, and information security [6] is facing unprecedented development opportunities. Therefore, in the multi-path channel, studying the safe transmission and effective extraction of speech information in indoor and outdoor environments is one of the scientific issues that many scholars are interested in. In recent years, the chaotic phenomena of nonlinear systems have been studied throughout and more intensively [7, 8, 9]. Chaos is a nonperiodic bounded dynamic behavior caused by a deterministic nonlinear dynamic system. It has initial sensitivity, internal randomness and unpredictability [10], which make it play an important role in secure communication. Considering the secure transmission of speech information in wireless transmission environment, the speech signal can be chaotic encrypted or masked at the originating end. For indoor environments, a classic problem of speech communication is the \"cocktail party\". In a noisy indoor environment, the sound received by the information-collecting microphone is diverse. The sound received includes the speech, music and other sound sources of multiple people talking at the same time, and there is also the reflected sound generated by the reflection of these sounds by the walls and indoor objects. In fact, whether in indoor or outdoor environments, speech transmission under multipath channels can be abstracted as a convolutional mixed model of signals. At the same time, there is bound to be a lack of source information and channel information during the transmission process. Therefore, separating the desired speech signal from the unknown information is known as classic multichannel convolutional blind source separation (CBSS) [11; 12; 13]. There are two main types of methods to solve the CBSS problem in multipath channels: time domain and frequency domain. The idea behind time-domain approach [14; 15] is the need to compute a separation filter in the time domain of equal or greater order than the impulse response filter. The method is often computationally complex, making the complexity of the algorithm high and convergence slow. The frequency-domain approach [16; 17] is to transform the observed signal into the frequency domain using the short-time Fourier transform (STFT) [18]. The instantaneous BSS is performed separately for each frequency point in the frequency domain using the standard independent component analysis (ICA) method [19; 20], which is the key to blind source separation in the frequency domain. Although this method avoids tedious convolution operations and reduces computational effort, the ICA algorithm causes amplitude and permutation ambiguity to be blurred at each frequency point, which reduces the accuracy of the separated signals. The amplitude ambiguity can be handled by normalizing the separation matrix, while the permutation ambiguity is relatively difficult to solve. For this reason, numerous scholars have proposed different methods to solve the permutation ambiguity problem in frequency-domain convolutional blind source separation (FD-CBSS) [13; 21; 22; 23].