## 3 State-of-the-Art MIMO-SDR Systems
### MIMO-OFDM Block Enhancements
#### 3.3.1 Channel Estimation  
The MIMO-OFDM channel estimation schemes in the literature could fall under three main classes: pilot-aided (or training-based), blind techniques and semi-blind ones, and decision-directed channel estimation. Quite a few innovative works have been found in the literature with regard to pilot-aided techniques, due to the induced processing overload of the pilots' data. Table 6 gives a vision about the general classification of channel estimation for MIMO-OFDM wireless communication systems, in addition to the corresponding study references for every algorithm type. In the following, those studies will be more detailed in the proper context. \(\bullet\) Pilot-aided channel estimation algorithms  
The pilot-assisted channel estimation or training-based technique inserts training pilots, which are well known by the receiver, to the transmitted sequence of symbols. Therefore, the receiver could extract CSI information, which is gathered by an interpolation between the different CSI values already extracted from the pilot sequences. In fact, the pilots' arrangement could be in three types: comb type [113], block type [113, 114], or 2D-grid type [118]. Figure 17 gives a better vision of the three situations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Classification**} & \multirow{3}{*}{
\begin{tabular}{c} **Pilot-Aided (or** \\ **Training-Based)** \\ \end{tabular} } & \multicolumn{2}{c}{**Blind [112] and Semi-Blind**} & \multicolumn{2}{c}{**Decision-Directed**} \\ \cline{3-6}  & & **Statistical Methods** & & **Deterministic** & **Hard** & **Soft** \\ \cline{3-6}  & & **2 nd Order** & **High Order** & **Methods** & & \\ \hline
**References** & [113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124] & [125, 126, 127] & [128, 129] & [130, 131, 132, 133] & [134] & [135, 136, 137, 138, 139] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MIMO-OFDM channel estimation algorithms classification. Figure 16: TIBWB-OFDM transceiver. The shaded circles represent pilot symbols, whereas the unshaded ones represent the symbols to be transmitted. The horizontal axis is the time direction, and the vertical one is the frequency direction that represents the OFDM subcarriers. The general scheme of a pilot-aided channel estimator (please refer to Figure 18) is composed of an LS/LMMSE estimator block, a frequency, and a time interpolator block, respectively, and a denoising and truncation block. The LS/LMMSE block calculates the channel frequency response using the received pilot symbols. The next step is to convert this response to the time domain. Afterwards, a denoising and truncation process is performed. Some of the used frequency interpolators in the literature are: linear, second order, cubic spline, time domain-based, low-pass [140]; and DFT-based interpolators [117, 118]. The block-type estimation is performed in the time domain, while for the comb type it is performed in the frequency domain. The most adopted algorithms for channel estimation using the block-type pilot are: least squares [113, 121, 122] and Linearity Minimum Mean Squared Error (LMMSE) [139]. In [113], an LS channel estimator was investigated based on the block-type pilot structure and the comb-type pilot structure, with average MSE lower bounds. In [114], a reduced-based LS estimator was designed, accepting the assumption that the channel was quasi-static over every two OFDM symbols, and their neighboring pilots were consecutively grouped as an equispaced cluster. The pilot is inserted into a designated block at each Tx antenna, i.e., it is sent periodically in the time domain. The channel response matrices are decoupled for every Tx antenna. Therefore, the MIMO channel estimation problem is formulated as a simple Single Input Output (SISO) corresponding channel estimator. In [115], a channel estimator based on MMSE, which requires the calculation of the inverse of the channel autocorrelation matrix, was proposed. Hence, a singular value decomposition was used to reduce the induced complexity.