## 3 State-of-the-Art MIMO-SDR Systems
### MIMO-OFDM Block Enhancements
#### 3.3.2 Equalization  
There are several logics to categorize the equalization algorithms. There are linear and non-linear equalizers. The linear algorithms are less complex than the non-linear ones, but they do not take into consideration the additive noise. Zero-forcing (ZF) [147], MMSE [148], and Least Mean Square (LMS) are all linear equalizers. The decision feedback equalizer (DFE) is a nonlinear equalizer that reduces ICI by an adopted filtering technique. We propose to categorize the existing algorithms as follows:  
Figure 19: Channel iterative estimation scheme.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **References** & **Year** & **Main Idea** & **Key Algorithms** \\ \hline Type 1 & [150] & 2019 & A symmetric successive over-relaxation (SSOR) method to reduce the complexity of the classical ZF precoding which uses the channel property of asymptotical orthogonality to compute the optimal relaxation parameters. & SSOR technique for ZF precoding \\  & & - & A supervised learning architecture to predict the constellation points based on pilot signals which constitute training data. & Deep neural network with gradient descent algorithm \\ Type 3 & [151] & 2019 & A new activation function was proposed to be able to use the famous stochastic gradient descent algorithm for optimization. & Turbo MMSE equalizer with MAP decoder \\  & & - & The Kalman channel estimation and turbo MMSE equalization are used. & Turbo MMSE equalizer with MAP decoder \\  & & - & The iterative algorithm repeats the channel estimation, equalization, and decoding operations until convergence. The feedback information received from the decoder is injected another time into the equalisation process. & Turbo MMSE equalizer with MAP decoder \\  & & - & Testing MMSE equalizer with a decision-directed channel estimator in a multipath fading channel Iterative receiver based on equal gain combining (EGC) and maximum ratio combining (MRC) & RMSE, MRC and LLR \\  & & - & An independent component analysis-based equalizer: First the received signal is whitened by principal component analysis, using JADE to gather uncorrelated signals. A phase shifting is performed as well as a reordering technique. & JADE batch algorithm \\  & & - & Exchanging the order of the processing block: interpolation and the ZF equalizer stage. This operation is performed at each pilot position, then the ZF equalizer is interpolated over the whole grid. & ZF equalization \\  & & - & The oblique projection (OB) with QR-based factorization is used to separate the noise from the data. Afterwards, the resulting matrix is forwarded to the DFE equalizer. & DFE equalizer, associated with the OB to the DFE equalizer. & A semi-blind time domain equalization, using second-order statistics and a one-tape equalizer. & ZF equalization \\  & & - & A DFE equalizer combined with Recursive Least Squares (RLS) to compute the coefficient of the adaptive filter. & RLS algorithm \\  & & - & An MMSE equalizer based on QR factorization implemented on FPGA to compute the inverse of the filter matrix. & MMSE and QR factorization \\ \hline \hline \end{tabular}
\end{table}
Table 7: MIMO-OFDM equalization algorithm classification.