## 3 State-of-the-Art MIMO-SDR Systems
### MIMO-OFDM Block Enhancements
#### 3.3.1 Channel Estimation
In [132], it is another semi-blind SAGE-based algorithm that contributes to a periodic update of the pilot-related MMSE estimate. Conventional estimators request the insertion of more pilots and more knowledge about large-scale fading coefficients to attain the desired performance, while this algorithm deploys the data symbols to estimate the missing information. The framework exposed in [133] is a special case for channels with faster time-varying characteristics. It is an optimized semi-blind sparse estimator with a cost function estimated by an enhanced differential evolution algorithm. The semi-blind estimation was performed by LMMSE and LS. Afterwards, the enhanced differential evolution algorithm was adopted to diminish the cost function and further optimize the estimator. * Decision-directed channel estimation algorithms  
For these techniques, the detected symbols are deployed in addition to relatively few pilots for estimating the channel. This kind of scheme gives more reliable results than the pilot-assisted techniques because there are no transmission errors. The decision-directed techniques first necessitate an initial estimation of the channel transfer function, calculated starting from the current received and detected data. This estimation is used afterwards as an a priori channel estimate during the treatment of the next symbols of the incoming time slot. Those techniques are in two groups: soft and hard decision-directed methods. In [134], a joint pilot-aided and hard blind decision-directed channel estimation (PADDCE) scheme is explained. The authors gather the initial channel estimate using the conventional LS algorithm. Then, this estimate is deployed to detect the next data symbol situated between any two adjacent pilot sub-carriers. Subsequently, those symbols become like additional pilot symbols that are used to complete the estimation of the missing channel coefficients on the frequency band. However, [PERSON], [PERSON], [PERSON] and [PERSON] [135], [PERSON], [PERSON] and [PERSON] [136] have a soft decision-directed strategy, drawing an interesting performance, which uses an iterative detector and decoder to optimize the estimation process. The algorithm (partially demonstrated in Figure 19) utilizes virtual pilots as well as pilots for the channel re-estimation. In the beginning, posteriori LLRs are built by an addition of the extrinsic LLRs resulting from the MIMO detector and the prior LLRs resulting from the decoder. Thus, those posteriori LLRs are translated to soft symbols. Afterwards, virtual pilots are selected from the data available in the current window. In fact, the virtual pilot signals need to meet two principal conditions:  
First, the magnitude of the posteriori LLRs needs to be high. Second, the channels for the virtual pilots and the pilots need to be highly correlated. However, after gathering those virtual pilots, the channel is re-estimated within the original pilots. The new estimate is given to the MIMO detection block in the next iteration. In [137], a Kalman-like estimator based on a specific pipelined turbo equalizer logic was verified (please refer to [137] for further details about the architecture). Before forwarding the data to the Kalman estimator block, a specific algorithm was used to diminish the decision error correlation between the different pipeline stages. Nonetheless, in [138], there is a deep neural network-based approach for the channel estimation of an STBC MIMO system. Two networks are trained to estimate the real and the imaginary part of the matrix of the fast-varying fading channel. Finally, in [139], the performances of the LS, MMSE, and SAGE algorithms for a decision-directed estimator are assessed. The performance is improved by substituting some of the pilots with data symbols; then, the SAGE technique is used to downslide the loss induced.