## 1 Introduction
Furthermore, the statistical dependencies between general interference (or jamming signal) and the user signals, as well as the AWGN and the user signals, further enhance the system's effectiveness (see Lemma F.1 in [56]). This represents a pivotal advancement in addressing interference and Rayleigh deep-fading effects. The remaining sections of the paper are as follows: Section 2 presents the proposed communication MIMO model under Rayleigh deep-fading scenarios. Section 3 introduces the changes in the new version of the AP-HSIC algorithm. Section 4 provides a description of the LM-HSIC algorithm, and Section 5 details the real-time simulations and numerical results based on SIMULINK and MATLAB platforms, offering a comparison of the performances of three methods: the MGSTC, the AP-HSIC, and the LM-HSIC. In Section 6, we draw conclusions and present a vision for further research on efficient solutions to communication system bottleneck problems under interference scenarios. Proposed Communication MIMO Model under Rayleigh Deep-Fading MIMO Channels with a High Order of QAM-Constellation Decoding Capability  
This section describes a proposed communication MIMO model for two methods under various Rayleigh deep-fading scenarios. Deep-fading correlation significantly impacts the performance of multiple-antenna systems, especially in the adaptive digital signal process and the decoding process [4; 55]. The double-correlated Rayleigh deep-fading channels are present on both sides of the system, on the transmitter and receiver sides, as was studied in [4]. Estimating Rayleigh deep-fading and improving the system's performance is one of the most significant challenges in wireless communication systems [4; 10; 55]. In this section, we describe and analyze two methods of wireless communication MIMO systems. The MIMO model assumes Rayleigh deep-fading MIMO channels, and in Section 5, we compare the BER performance aspects of these two architecture methods. The first method uses a transmitter based on the MGSTC scheme [7; 52]. It incorporates the diversity-transmitting technique known as OSTBC. The receiver employs the MGSTC-SIC decoding algorithm, as detailed in [7; 52]. The MGSTC scheme is capable of interference cancellation and decoding, allowing it to extract a single symbol information block from a group of transmitted blocks and merge them using an error-reducing mechanism. This technique operates by iteratively decoding the data at the receiver. It involves the parallel transmission of a sequence of blocks in space and, at the receiver, a serial decoding process (i.e., multi-stage decoding), which separates the different transmitted blocks. The MGSTC decoding algorithm decodes and separates the individual data streams from a specific user from the other streams. Multiple-stage decoding creates a communication mode that can mitigate the impact of noise, such as the sum of AWGN with the other broadcast blocks. This is achieved by leveraging the accuracy of a single decoding stream in relation to the previous decoding iteration. The primary advantage of the MGSTC decoding algorithm is that at the end of each iteration when we move to the next group order, it provides a diversity gain for every matrix of OSTBC transmission modulation symbols, \(S_{c_{i}}\) (MGSTC includes \(I\) component-blocks \(S_{c_{i}}\), for group \(c_{i}\), \(i=1,...,I\)). The diversity gain is increased by \(n_{i}\times(n_{1}+...+n_{i}+N_{r}-N_{t})\) when \(i\) is the iteration number and \(n_{i}\) is the number of transmission antennas in the \(i\)'th group, while \(N_{r}\), and \(N_{t}\) are the number of total receiver antennas and the number of total transmission antennas, respectively. The challenge with MGSTC and multi-stage decoding lies in the fact that the benefits in certain communication scenarios, such as when spatial interference occurs, can become drawbacks. The drawbacks are evident in the SIC process of the MGSTC, as it operates in a serial decoding mode for data blocks.