# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 1 Introduction  
High-quality UWA communication is essential for underwater data transmission, ocean resource exploration, and underwater vehicle information acquisition [1]. However, multipath effects can seriously disrupt UWA communication. The multipath effects contain multipath fading and inter-symbol interference (ISI) [2]. These phenomenons are due to the fact that the acoustic signal can be reflected along multiple paths with different incidence angles and propagation time delays while superimposing with underwater noise on the receiver [3]. STD is widely used as a conventional method to suppress multipath effects in underwater communication [4, 5]. In the STD structure, \"S\" indicates space-domain receiving, and \"T\" indicates time-domain equalizing. The underwater acoustic array receives the space-domain of the signal and decides the main path direction using beamforming technology [6, 7, 8, 9]. Then, after equalization processing and diversity receiving in the time-domain, the multipath interference is suppressed and the BER of the communication is reduced [10]. However, the noise distributed in the underwater environment is a factor severely limiting high-speed and reliable underwater communication [11]. Noise can prevent the STD structure from accurately resolving the transmit signal and severely limit theprocessing performance of STD [12]. Generally, underwater noise can be divided into water body noise and artificial noise [13]. The former is natural sound sources mainly including marine and biological noise. The latter is mechanical, especially noise from navigation and underwater operations. Vessel's underwater radiated noise (VURN) is recognized as a significant source of artificial noise [14]. It has been challenging to maintain high STD processing quality in an environment heavily affected by VURN. To minimize the VURN effect, adaptive noise control (ANC) technology is commonly used as a noise-reduction method before the STD structure [15]. After ANC processing, the received signal will be diversity processed by the STD equalizer. Meanwhile, combined signals have higher communication gain [16]. A typical STD structure using ANC processing is shown in Figure 1.  
According to the object to be processed, ANC technology can be classified into linear and nonlinear methods. The linear method features simple computation and high real-time performance. However, it can only handle simple linear systems with limited applicability. The linear algorithms such as Wiener filtering [17], median filtering [18], and wavelet variation [19] may not work well for VURN, the nonlinear noise. In nonlinear signal processing, the kernel-based method (KBM) creates a nonlinear mapping in the input data and feature space to reduce noise, which can be considered a noise-reduction technique using a kernel learning model. KBM is widely used in image denoising and speech enhancement due to its excellent denoising performance [20]. In UWA array processing, KBM-based array noise cancellation is a typical application scenario, and its structure is shown in Figure 2.  
In the structure of Figure 2, assume that the transmit signal is \(\mathbf{s}(t)\), the receive signal is \(\mathbf{y}(t)=\mathbf{s}(t)+\mathbf{n}(t)\), and \(\mathbf{n}(t)\) is the noise. Define the reference noise as \(\tilde{\mathbf{n}}(t)\), which is the noise collected before communication, and \(\tilde{\mathbf{n}}(t)\) can be considered as an infinite approximation to \(\mathbf{n}(t)\). The KBM-ANC uses online iterations of \(\mathbf{y}(t)\) and \(\tilde{\mathbf{n}}(t)\) to obtain the estimated noise \(\hat{\mathbf{n}}(t)\), and then, the noise-reduction signal \(\hat{\mathbf{y}}(t)\) is obtained by the cancellation. \(\hat{\mathbf{y}}(t)\) can be considered as a constant approximation fit to \(\mathbf{s}(t)\). The key part of the KBM-ANC is an adaptive filter. The adaptive filter of the KBM-ANC can be classified as a single-core function type and a multi-core function type [21]. The representative  
Figure 1: A typical STD structure using ANC processing.