## 1 Introduction
### Motivations and Contributions  
* New communication scenarios often require each user to send and receive private as well as public information, which is called heterogeneous signal transmission. Users transmit heterogeneous signals at the same time, which leads to a sharp increase in the complexity of signal processing at relay nodes, and also increases the difficulty of interference suppression for receiving users.
* The existing algorithms aim to emphasize how to construct the spatial alignment of interactive signals, however, there is less consideration given to the correlation between different alignment directions. If the alignment direction can be jointly optimized, the Euclidean distance between the received signals can be expanded and the decoding accuracy can be improved.
* At present, most of the PNC principles only consider the use of low-dimensional modulation such as Binary Phase Shift Keying (BPSK) or Quadrature Phase Shift Keying (QPSK) in the additive white Gaussian noise (AWGN) channel to verify the feasibility of the scheme. At this time, it is relatively easy for multiple access signals to obtain PNC symbols based on an XOR operation. However, in real environments, wireless channels are time-varying channels with fading, and actual communication systems often use higher order modulation to improve spectral efficiency. In these cases, PNC-based or simple XOR will have application limitations due to fuzzy mapping.  
The spatial degrees of freedom of a relay signal are optimized through machine learning to select the best precoding vector, and the selection of degrees of freedom can maximize the performance of the transmission. The design goal of effective utilization of wireless resources is to balance the performance of each user by using the degrees of freedom of antenna selection and transmission diversity gain. The main contributions of this paper are as follows:  
* According to the principle of minimum system antenna resource consumption and optimal interference suppression performance, public and private information are effectively separated by using signal subspace alignment and orthogonal subspace technology. In order to avoid mutual interference between the two types of information, it is necessary to ensure that the system can provide the optimal precoding vector selection mechanism no matter how the interference environment changes.
* If the alignment directions can be orthogonal to each other, each bit is determined by the projection signal of the orthogonal axis. According to the orthogonal projection Euclidean distance of two possible points, the decoding process is simplified. By optimizing the orthogonal directions of different user pairs to determine order and power allocation, the ML decoding complexity is further simplified, and the decoding reliability is improved.
* Aiming at the problem of constellation point ambiguity mapping in the high-order amplitude and phase modulation of PNC, a physical layer network coding denoising mapping algorithm is proposed. In this algorithm, relay nodes rearrange constellation points of received signals and merge constellation points according to certain rules. After processing, the signal constellation point is reduced by half. The Euclidean distance between the adjacent points of the constellation becomes larger, and the bit error rate (BER) performance of the system is improved.  
The remainder of this paper is organized as follows: Section 2 formulates the system model and MIMO-Y channel in detail. In Section 3, signal spatial alignment is used to model the co-channel interference suppression problem, and a spatial reconstruction method is proposed to improve performance. Section 4 presents the simulation and experimental results in comparison with other interference suppression-based relay cooperative methods. Section 5 provides a discussion. Finally, Section 6 concludes the research work.