## 3 State-of-the-Art MIMO-SDR Systems
### Mimo-Sdr Waveforms
#### 3.2.3 MIMO-OFDM Variants  
There are five (principally four) OFDM variants tested within MIMO systems, as summarized in Table 4. The most important, drawing real improvement with MIMO technology, are CP-OFDM, UF-OFDM, GFDM, and F-OFDM. Nevertheless, CP-OFDM-WOLA is cited by several researchers as a good candidate to work with MIMO systems. Instead of using filters, as with the normal OFDM scheme, WOLA-OFDM uses extension and windowing techniques to reduce OOB emissions [88, 89]. In addition, the classic FBMC technique has been announced as being incompatible with MIMO systems [84] as it makes the implementation of traditional coding and channel estimation algorithms very difficult. However, the MIMO FBMC-OQAM scheme has attracted a lot of researchers [90]. Figure 7 explains very clearly the additional blocks needed to implement CP-OFDM and F-OFDM as well. Nonetheless, a brief introduction to UF-OFDM, GFDM, and FBMC-OQAM is given in the following. \(\bullet\)  
GFDM \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{4}{c}{**OFDM Variants**} \\ \hline CP-OFDM & Cyclic prefix OFDM & [91] \\ UF-OFDM or UFMC & Universal filtered OFDM or universal filtered multi-carrier & [83, 91, 92] \\ CP-OFDM-WOLA & Weighted overlap and add CP-OFDM & [88, 89]1 \\ GFDM & Generalized OFDM & [93, 94] \\ F-OFDM & Filtered OFDM & [95] \\ FBMC & Filter-bank multi-carrier & [83, 96] \\ \hline \hline \end{tabular} \({}^{1}\) WOLA-OFDM was analyzed by several researchers as being a good candidate that will perform very well with MIMO systems, but to the best of our knowledge, there is no experimental study which proves it.  
\end{table} 
Table 4: MIMO-OFDM variants. GFDM deploys a circular pulse shaping to diminish the inter-carrier interference (ICI) phenomena. In comparison with OFDM, GFDM is more flexible to carrier frequency offset and time synchronization-induced errors [97]. The baseband scheme of a MIMO-GFDM transceiver [94,97] is given in Figure 8.  
The mapped symbols (with QAM, QPSK, or BPSK) are converted to parallel sub-streams for padding K subcarriers with M sub-symbols. The parallel streams are up-sampled, with a sampling factor N, to correct the sub-symbol position in the block [97]. Afterwards, a circular convolution with a Tx filter is performed to exclude replicated samples; so, the subcarriers could be shifted to their center frequencies afterwards. Only one CP is inserted for all the concatenated M sub-symbols. In the receiver side, the CP is cut from the data, in addition to the other reversed operations performed to retrieve the final data. The equalization is for channel effect correction. The GFDM still suffers from a few drawbacks, especially a higher out-of-band (OOB) emission problem and high-complexity computation. Figure 8: GFDM transceiver: the GFDM modulator consists of two stages, pulse shaping and subcarrier up-conversion. In the demodulator, those operations are inversed: subcarrier down-conversion and filtering. UF-OFDM  
UF-OFDM is a promising waveform which uses linear filters and eliminates the cyclic prefix. The baseband structure of the transceiver [97] is presented in Figure 9. The mapped symbols are converted to parallel streams. After computing an M-point IFFT over each sub-band, a band filter is applied. In fact, the use of the Dolph-Chebyshev bandpass filter (BPF) helps to tackle the OOB emissions [97, 97]. Next, the filtered sub-bands are superposed and sent through the channel. A zero-padding process is performed from the receiver side. In fact, every symbol is padded with \(\mathrm{N-L}\) zeros, where L is the BPF filter (in the transmitter side) length. Afterwards, the signals are demodulated by 2M-point FFT. The demodulated signals, excluding the padded zeros, are given to the equalizer to eliminate the channel distortions. Finally, the symbols are de-mapped to bits. UF-OFDM outperforms OFDM in terms of ICI and ISI reduction, PAPR, and spectral efficiency. * FBMC-OQAM  
The original version of FBMC does not deploy any CP and uses a pulse-shaping filter.