# Complex-Valued Phase Transmittance RBF Neural Networks for Massive MIMO-OFDM Receivers
## 6 Conclusions  
This work proposes a novel MIMO scheme for M-QAM systems that aims to achieve diversity gain for any number of antennas and at a lower computational cost when compared with traditional methods. The presented architecture is based on existing systems but with substantial improvements in the coding and decoding methods, based on conventional MIMO-OFDM systems with quasi-orthogonal coding but implemented with complex-valued Radial Basis Functions neural networks. The state-of-the-art algorithms and the proposed approach have been simulated in MATLAB to measure their relative performance under fading scenarios.  
Based on the synergistic combination of the coding and decoding algorithms presented in Section 2, the proposed MIMO-PTRBF system is discussed and analyzed in Section 3. The main functional features of the proposed architecture can be summarized as follows: (1) the proposed coding algorithm generalizes the generation of quasi-orthogonal coding matrices, (2) the MIMO-PTRBF algorithm decodes the signal with satisfactory performance and feasible computational cost, presenting low steady-state MSE with fast convergence, and (3) the proposed approach seems practically feasible, at least for 32 \(\times\) 32 MIMO systems, which are simulated in this work. We conjecture the practical feasibility of higher-order systems if faster hardware, such as FPGAs, is used.  
The MIMO-PTRBF algorithm has been proposed in this work to implement massive MIMO schemes as an alternative to the classic MIMO-OSTBC systems under maximum likelihood detection. Simulations have shown that the proposed technique has a great potential to improve the signal-to-noise ratio at the receiver, with competitive computational complexity. Although there are recent works in the literature proposing techniques for MIMO decoding, they are focused on reducing computational complexity at the cost of performance and are limited by the simulated ML decoding. In this work, results show that the proposed approach achieves better results than ML decoding for higher-order modulation schemes with nonlinearities from power amplifiers, keeping a competitive computational complexity. Moreover, the proposed system is easily scalable in terms of the number of antennas, meaning that a wide range of transmitting and receiving antennas can be used. This is especially important for the next generations of mobile communications, such as 5G, 6G, and probably beyond.  
The proposed architectures and algorithms find potential applications in some configurations of the next generations of wireless systems. For example, some specialized hardware improvements currently aim exclusively at real-time neural network algorithms. These are intended to be implemented in low-power graphical processing units (LPGPUs), favoring the speed and energy consumption of these algorithms. Therefore, the proposed  
Figure 25: Computational complexities as a function of \(M_{T}=M_{R}\).  
architecture will be able to work with low-power consumption devices, with the ability to handle the distortions of nonlinear power amplifiers while maintaining a fast convergence rate. It should be emphasized that a fast convergence characteristic is essential for wireless channels with dynamic fluctuations.  
This paper addresses some crucial aspects of MIMO-OFDM coding and decoding schemes for quasi-static channels. A complementary analysis of dynamic scenarios is also presented. We conjecture that the proposed work may be further improved using additional techniques, such as a mathematical approach for designing an optimum adaptive configuration.  
Furthermore, it would be interesting to study and validate the proposed architecture for dynamic scenarios. In addition, as challenging and promising future work, the proposed algorithm can be adapted and implemented in advanced optical communication systems with Spatial Division Multiplexing (SDM), which is similar to a MIMO wireless system.