## 3 State-of-the-Art MIMO-SDR Systems
### Mimo-Sdr Waveforms
#### 3.2.2 OFDM/Cyclic Prefix OFDM (CP-OFDM) Theory Aspects  
The OFDM transmitter scheme (please refer to Figure 7) is composed of several signal-processing blocks: inverse fast Fourier transform (IFFT) processing, cyclic prefix (CP) insertion, and spectrum enhancement. Serial to parallel block converts several consecutives bits to parallel streams with a low bit rate. The modulation (or symbol mapping) is conducted with QAM, QPSK, or Binary Phase Shift Keying (BPSK). In the receiver side, we have inverse operations to decapsulate the signal, including fast Fourier transform (FFT) processing and cyclic prefix removal. Additional processing is required to estimate the channel effect and to allow a synchronized communication between the transmitter and the receiver. The cyclic prefix insertion and the removal blocks are more appropriate to the cyclic prefix OFDM (CP-OFDM) scheme. Additionally, the filtering block in the transmitter and receiver parts exist in the filtered OFDM (F-OFDM) version. \begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{2}{c}{**Waveform**} & \multicolumn{1}{c}{**Reference**} & \multicolumn{1}{c}{**Advantages/Disadvantages/Summaries**} \\ \hline \multirow{6}{*}{Sparse code multiple access} & \multirow{2}{*}{SCMA} & \multirow{2}{*}{[82]} & - & For small number of end-users, SCMAs have a lower complexity. & \multirow{2}{*}{\begin{tabular}{c} Higher PAPR compared with SC-RSMA. \\ Offers a very low density spreading, requires \\ synchronous multiplexing and iterative \\ joint detection. \\ \end{tabular} } \\  & & & & SCMA does take advantage of the fully available diversity; it uses any portion of the \\  & & & & time/frequency slots. \\  & & & & For end users deploying different spreading factors, \\  & & & SMA is not a good candidate. \\ \cline{2-5} \multirow{3}{*}{**Non-Orthogonal**} & \multirow{3}{*}{Filter Bank Multi-Carrier} & \multirow{3}{*}{FBMC} & - & It is an OFDM evolution. \\  & & & & - & The existing research papers show that it is poorly \\  & & & & - & It is not an attractive candidate for 5G systems. \\ \hline \multirow{3}{*}{\begin{tabular}{c} Space Division Multiple Access \\ \end{tabular} } & \multirow{3}{*}{SDMA} & \multirow{3}{*}{[85]} & - & High overloading factor. \\  & & & & - & Robust blind detection. \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Multi-User Shared Access \\ \end{tabular} } & \multirow{3}{*}{MUSA} & \multirow{3}{*}{[86]} & - & Higher PAPR \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Nonorthogonal multiple access \\ \end{tabular} } & \multirow{3}{*}{NOMA} & \multirow{3}{*}{[87]} & - & Users are superimposed in the spectral domain, \\  & & & they could share the same frequency bin in the same \\ \cline{1-1}  & & & time instance. \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._Let us consider a symbol to transmit:  
\[s^{T}=[s_{0}\;s_{1}\dots\;s_{L-1}] \tag{7}\]  
\(L\) is the size of the symbol \(s\). Considering the CP, the symbol is presented by the next formula:  
\[s^{T}=\left[s_{L-L_{g}}\dots s_{L-1}\;s_{0}\;s_{1}\dots\;s_{L-1}\right] \tag{8}\]  
\(L_{g}\) is the number of CP samples. We assume that the channel is time invariant with N taps and an impulse response given by:  
\[c^{T}=[c_{0}\;c_{1}\dots\;c_{N-1}] \tag{9}\]  
For single-carrier systems, the received signal is obtained through a simple convolution of the channel impulse response with the initial symbol. Nevertheless, for CP-OFDM  
Figure 7: OFDM transceiver: firstly, the serial to parallel (S/P) converter splits the given data to several parallel streams which are converted to symbols through the mapping block. Secondly, the output of the IFFT block, after parallel to serial (P/S) conversion, is given to the next block for insertion of the CP. After the spectrum shaping process, the data are converted to analogue signals to be transmitted through the Tx antenna. In the receiver side, other filtering and S/P conversion processes are performed, and the signal is converted to digital data (symbols). Afterwards, the CP needs to be removed from the symbols, and an FFT is performed.