## 1 Introduction
Clearly, to cope with these challenges, several types of advanced algorithms have been developed and are increasingly embedded in many wireless MIMO communication systems, including spatial selectivity capability and breakthrough techniques (e.g., high-resolution beam-forming techniques [37; 38], hybrid beam-forming [39; 40], classical digital SIC [10], and non-conventional beam-forming based on Machine Learning (ML) digital SIC [41; 42], Non-Orthogonal Multiple Access (NOMA) algorithms [43; 44], and several algorithms for massive MIMO systems [30; 45; 46]). In recent years, these advanced techniques have combined several linear and non-linear detection algorithms that try to achieve optimal performance in aspects of low computational complexity, fast rate of convergence, the minimization of the BER, and maximizing the channel's capacity. Examples of using traditional linear and non-linear detector algorithms include Linear Minimum Mean-Square-Error Interference Cancellation (LMMSE-IC) [7] detector, Zero Forcing Interference Cancellation (ZF-IC) [7], Minimum Mean-Square-Error Interference Rejection Combined (MMSE-IRC) [2; 47; 48; 49], Message Passing Detection (MPD) [1] method, Low Complexity Message Passing Detection (LCMPD) algorithms [29], Log-Likelihood Ratio (LLR) algorithms [5; 50], Monte Carlo sampling techniques (e.g., Markov Chain Monte Carlo (MCMC) algorithms [51]), and the MGSTC algorithm [7; 52]. The common denominator of all these spatial SIC decoding algorithms is to focus on the ability to decode very quickly and with a high reliability and ultra-fast information rate based on the high order of QAM constellations while maintaining the complexity and low computational cost, all under the assumptions of MIMO Rayleigh fading channels. On one hand, all these algorithms achieve near-optimal performance and a high order of diversity gain with high BER performance. On the other hand, these techniques assume several fundamental assumptions, the non-existence of which in the real-physical environment of the MIMO wireless may cause significant performance degradation and even collapse (i.e., non-convergence or high BER levels) of the algorithms. Examples of basic assumptions in constructing the MPD and LCMPD are that the wireless matrix of the MIMO channels is under the hardening channel model and that its component values do not change throughout the channel estimation and the decoding process [1; 29]. In algorithms of a serial nature [1; 7; 29; 42; 52; 53; 54], these basic assumptions are critical since for any significant disturbance or distortion that was not taken into account in the assumed model, the serial process will lead to the amplification of computational errors and even to the collapse of the technique. Moreover, in the fast-scale medium, the assumption of the hardening channel model is not realistic [10; 45]. Advanced spatial SIC decoding algorithms must address the identity and nature of interference in space in wireless communication reality [3]. Rayleigh deep-fading is a prime example of a challenging interference phenomenon [4; 55]. Rayleigh deep-fading is one of the most complex and destructive phenomena in the MIMO wireless communication topics [4; 55]. This phenomenon occurs when objects with a reflective and dispersive nature, such as scatters, are located in close proximity to the antenna arrays on the transmitter/receiver side, causing self-interference between the antenna array. Rayleigh deep-fading also causes a high spatial correlation between the antennas in the array. The high-correlation effect destroys the orthogonality between the columns of the wireless MIMO channel matrix and hits on the spatial-multiplexing capabilities between the transmitting-receiving signals [4; 7; 55]. The likelihood of experiencing deep-fade in wireless channels is significantly higher in the lower region of the Probability Density Function (PDF) of the Rayleigh distribution, on average.