# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 2 Related Works  
UWA communication has also been put forward for higher requirements with the continuous exploitation of global marine resources. The literature [38] pointed out that the two critical factors affecting UWA communication are the multipath effect and noise interference. The literature [39] introduced the diversity technique from base station communication into the underwater array to suppress the multipath effect. The BER is reduced to \(10^{-3}\) by increasing the receiver unit and using the maximal ratio combining (MRC) strategy to obtain the optimal diversity gain during the combining [40]. Due to the simple structure, the MRC method cannot work well in an environment with severe multipath effects. A differential channel method (DCM) using array communication was mentioned in the literature [41], where the estimation of the main path signal is obtained through beamforming. Then, the differential structure of the channels between multiple array elements is used to enhance the communication capability. However, it is difficult to improve the communication performance of the DCM when the number of array elements exceeds a threshold. With the continuous development of diversity technology, STD structures that combine spatial domain receiving and time-domain equalization processing have been applied to underwater communications [42]. STD can cooperate with the adaptive filter to complete the noise-reduction process and maintain the advantage of communication gain enhancement after the diversity combining. However, the complex operation seriously affects its operational efficiency. In the literature [43], a DS-CDMA signal based on the code filtering method was proposed to optimize the transmitting structure. The most significant advantage of this method is simplifying the equalization operation. The literature [44] used the 2D-RAKE technique to perform diversity combining. It pointed out that although the RAKE technique can define the energy of each branch by weight assignment, the multi-access interference due to CDMA signals cannot be avoided and can seriously affect the quality of the communication. In the earlier days, adaptive filtering was often applied in image noise-reduction. With the continuous development of adaptive filtering technology, UWA communication has started to apply this technology. The literature [45] proposed an RLS algorithm for linear noise-reduction processing of images. The literature [46] applied this algorithm to underwater communication and showed excellent results for simple noise. In [47], this literature considered VURN as the main reason affecting the UWA array communication, which can be viewed as a superposition of multiple linear spectra and continuous spectra in the frequency-domain. VURN generally exhibits convolutional properties, a nonlinear noise structure. The linear denoising methods, such as RLS, are not suitable. In [48], an array method was proposed for noise cancellation of sound signals, and adaptive filtering techniques were applied to nonlinear denoising structures. In the following years, ACN technology has developed rapidly, and the nonlinear algorithm represented by the KBM has shown excellent denoising performance in array communication. Typical KBM algorithms include RKHS [49] and KAPA [50]. The RKHS method accomplishes the estimation of errors in the Hilbert space by creating a nonlinear mapping of a high-dimensional space. KAPA transforms the affine projection algorithm into a kernel function to accomplish the filtering of noisy signals. RKHS was applied in the literature [51] to denoise hydroacoustic signals for hydroacoustic signal detection. However, unlike the STD processing of underwater array signals, the signal detection does not require phase solving, and the algorithm does not focus on the complex characteristics of the channel. A complex kernel least mean-squared (CKLMS) algorithm with a complex kernel function structure was mentioned in the literature [52].