## 3 State-of-the-Art MIMO-SDR Systems
### MIMO-OFDM Block Enhancements
#### 3.3.1 Channel Estimation
* Blind and semi-blind channel estimation algorithms  
The blind channel estimation algorithms rely on statistical proprieties, do not need prior knowledge about the transmitted signal, and do not require inserting pilots or training symbols at the transmitter level, thus allowing the sending of more data and the attainment of higher spectral efficiency. However, the semi-blind techniques use a part of the knowledge of the signal in addition to some statistical characteristics. Under this category, there are two sub-categories: statistical methods and deterministic techniques. For statistical techniques, the cyclic statistic properties of the signals are requested in the receiver side, although the deterministic techniques need both the coefficients and the received signal for estimating the channel matrix. The statistical techniques are second- [125, 126, 127] or higher-order statistics (HOS) [128, 129]. In [125], a blind scheme for a zero-padding MIMO-OFDM system, based on the covariance statistics, was presented. The channel matrix was obtained by resolving an equation series resulting from the covariance matrix of the received signal by exploiting the block Toeplitz structure. The linear equations were reformulated into a set of decoupled groups. Then, the channel matrix was calculated within an eigen-decomposition of the outer product matrix. In [126], a semi-blind scheme based on circular precoding was suggested, where the autocorrelation matrix of the received data engenders a set of mathematical equations in relation with the outer product of the channel matrix and the coefficients induced by the precoder. Some information about channel matrices was extracted from those equations, thus a Hermitian matrix was created within it. The corresponding positive eigenvalues and eigenvectors of this Hermitian matrix allow, finally, the gathering of the channel matrix. However, [PERSON], [PERSON] and [PERSON] [127] tested an idea to cancel the signal perturbation of the second-order statistics estimators. First, it was necessary to analyze the correlation matrix of the received data. Afterwards, a novel way to transmit the data, considering the perturbation that could be cancelled, was applied. Moreover, the authors proved that by using a few specific additional slots the performance of this technique could achieve an ideal case. In [128], a blind iterative hybrid independent component analysis (HICA) estimation schema is presented. Initially, the authors apply the pulse-shaping method with a square root-raised cosine filter to reduce the ISIs. Next, the signals in the receiver are identified by determining the separation matrix. The estimated signal order is different for every HICA iteration because the algorithm is randomly initialized. Hence, only the information that will appear repetitively in every iteration will be significant. The estimated desired signal is selected based on HOS from common signals resulting from different iterations of the HICA algorithm. Despite this, [PERSON], [PERSON] and [PERSON] [129] introduced another less complex adaptive independent component analysis-based scheme, applied to massive MIMO. The algorithm is an improvement of the work carried out in [145]. To resume, the performance of statistical algorithms is usually influenced by the finite data effect. The deterministic algorithms [130, 131, 132, 133, 134, 139] are the more complex ones, but they converge faster. In [130], a compressed sensing-based algorithm was suggested, where only a deterministic subset of the index is selected to place the pilots in the data to be transmitted. Hence, this leads to some new measurement matrices and a new reconstruction algorithm. However, in [131] a space-alternating generalized expectation-maximization (SAGE)-related scheme for STBC is divulged. The channel coefficients are estimated at pilot positions by a decomposition of the superimposed received signals, while the rest of the coefficients are calculated by Wiener interpolation.