# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 1 Introduction
Figure 2: Schematic diagram of the adaptive noise-reduction structure of the KBM. algorithms are kernel recursive least squares (KRLS) [22], reproducing kernel Hilbert space (RKHS) [23], and the kernel affine projection algorithm (KAPA) [24]. It is worth noting that the KBM-ANC performs very effectively in acoustic array noise cancellation, but is not very suitable for UWA channels with complex-type characteristics. The above KBM-ANC algorithm is mostly applied to noise-reduction of real-type signals. At the same time, it has the minimal capability to handle complex-type signals. \(\mathbf{s}(t)\) passes through the channel, resulting in \(\mathbf{y}(t)\). \(\mathbf{y}(t)\) is a complex structure containing amplitude information in its real part and phase information in its imaginary part. Phase information is an essential part when performing STD processing [25]. If the phase calculation is inaccurate, it will hinder the time delay alignment of the beam formation in STD, affect diversity combining, and degrade the communication performance. Structurally, the noise cancellation system of the KBM is already very close to the simplest form of the deep neural network (DNN), and both contain vital parts such as the kernel function filtering structure, learning mechanism, and online iteration [26]. Recently, the DNN has been widely used in image and speech noise-reduction and has made breakthroughs. DNN models have been the trend ofconventional noise-reduction algorithms. The DNN has a more flexible hyperparameter approach and feature-rich modules [27]. However, there is little research on noise-reduction of UWA signals with the DNN. Researchers mainly focus on weak signal identification and signal type classification [28; 29]. Using the direct sequence spread spectrum (DSSS) technique to optimize the transmission structure can significantly simplify the computational system of the equalizer in STD [30]. Code division multiple access (CDMA) is a specific DSSS technology application. CDMA signals have a delay extension in the UWA channel transmission, recognized as a signal re-transmission [31]. If the CDMA is used with theRAKE technique for transmitting and combining, the main path signal and the multipath signal can be summed according to a linear relationship. The above operation can simplify the structure of the equalizer and even omit the equalizer. However, the use of CDMA as the transmit signal introduces the problem of multi-access interference (MAI) [32]. CDMA applies different address codes to distinguish each transmit signal. It easily makes the received signal aliased in the time-domain and susceptible to co-channel interference (CCI) in the frequency-domain [33]. The STD structure using CDMA as the transmit signal does not effectively cope with MAI; although the computing efficiency is effectively improved, the communication effect is not improved. In the STD structure of Figure 1, the space-domain receiving uses the beamforming method. Beamforming performs time delay estimation on the filtered \(\mathbf{y}(t)\), aligns each path of the signal, and then, performs time-domain processing. The time-domain equalization algorithm generally uses the least-mean-squares (LMS) method and the recursive least-squares (RLS) method [34; 35]. The LMS method achieves the update of the adaptive filter weight parameters by the least mean squares, while the RLS method achieves the update of the adaptive filter weight parameters by the least squares and converges faster than the LMS method. Although both the LMS and RLS methods can effectively solve the multipath effect, an equalizer needs to be connected after each beamformer [36; 37]. The computational complexity increases dramatically as the number of received array elements increases. In summary, the KBM-based array noise cancellation technique can effectively cope with nonlinear noise environments in terms of noise-reduction. Still, it is less capable of handling underwater noise with complex-type characteristics.