# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 5 Comparison of Research Literature and Analysis
As was expected, the results from the feasibility condition technique of linear IA over constant MIMO channels were the most optimal sum rate values because of the feasibility condition defined in ref. [121], which states that by counting the number of equations and the number of variables in the IA condition, the DoF can be analysed. This flexible approach to determine the feasibility of a network makes it easy to define a system as proper or improper, and does so with an improved iterative algorithm that has a faster convergence rate [123]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**SNR \(\lambda\) (dB)**} & \multicolumn{2}{c}{**Symbol**} & \multicolumn{2}{c}{**Feasibility**} & \multicolumn{2}{c}{**LIF Perfect CSI**} & \multicolumn{2}{c}{**LIF CSI**} \\  & **Extensions [93; 97]** & **[119; 120; 121; 122; 123]** & **[80; 81; 82; 83]** & **Estimation [82; 83]** \\ \hline
5 & 5 & 16 & 4.5 & 7 \\
10 & 4 & 24 & 6.5 & 14 \\
15 & 4 & 30 & 8.5 & 20 \\
20 & 2 & 38 & 10.0 & 30 \\
25 & 1 & 46 & 11.5 & 38 \\
30 & 0.5 & 56 & 12.5 & 47 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average sum rates against typical SNR values for the second paradigm with SWF for the multiple SU MIMO link [80; 81; 82; 83; 93; 97; 119; 120; 121; 122; 123]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Average Sum Rates of the SU Network Based on the IA Techniques (bits/s/Hertz)**} \\ \hline
**SNR \(\lambda\) (dB)** & **OPA/UPA [24]** & **Relay [115]** & **Spectrum Sharing [68]** & **Fast Sensing [61]** \\ \hline
5 & 2.5 & 7.5 & 3.0 & 4.0 \\
10 & 2.0 & 13.5 & 6.0 & 7.0 \\
15 & 1.8 & 19.0 & 10.0 & 10.0 \\
20 & 1.5 & 25.5 & 14.0 & 13.0 \\
25 & 0.5 & 32.5 & 14.0 & 16.0 \\
30 & 0.1 & 38.0 & 13.5 & 20.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average sum rates against typical SNR values for the second paradigm with spatial water filling (SWF) for the single SU MIMO link [24; 61; 68; 115]. Figure 7: Average sum rates against typical SNR values for the second paradigm with SWF for the single SU MIMO link [24; 61; 68; 115]. Table 7 shows the sum rate values for the second paradigm with ST-WF and MEB. It can be seen from both Table 7 and Figure 9 that the scheme used in ref. [127] performs better than the other techniques despite the single SU scenario. The OIA schemes in refs. [69, 73] had similar performance in terms of sum rates largely because they both employed TBF to optimize the SU transmission, which is effective for saving the transmit energy in poor channel conditions and thus improving the spectrum efficiency of the SUs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Average Sum Rates of the SU Network Based on the IA Techniques (bits/s/Hertz)**} \\ \hline
**SNR \(\lambda\) (dB)** & **Blind [127]** & **DOIA-TBF with MEB [73]** & **OIA-FAP with MEB [69]** & **OFDM-VPDM [99]** \\ \hline
5 & 6.0 & 3.0 & 3.0 & 3.0 \\
10 & 8.0 & 4.0 & 4.0 & 5.0 \\
15 & 13.0 & 5.0 & 6.0 & 8.0 \\
20 & 17.0 & 7.0 & 8.0 & 12.0 \\
25 & 22.0 & 9.0 & 10.0 & 16.0 \\
30 & 26.0 & 12.0 & 14.0 & 20.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average sum rates against typical SNR values for the second paradigm with space-time water-filling (ST-WF) for the multiple SU MIMO link [69, 73, 99, 127]. Figure 8: Average sum rates against typical SNR values for the second paradigm with SWF for the multiple SU MIMO link [80, 81, 81, 81, 81, 82, 83, 93, 97, 119, 120, 121, 122, 123]. Figure 9: Average sum rates against typical SNR values for the second paradigm with ST-WF for the multiple SU MIMO link [69, 73, 99, 127]. The proposed OFDM-VFDM scheme seems to increase the sum rate performance especially within the intermediate SNR range. On a wider scope, this scheme can simultaneously transmit more symbols for each SU than TDMA, and with the potential of extending the SU system to more than two cells, the spectral efficiency can only be improved.