# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 5 Comparison of Research Literature and Analysis  
This section present some of the results obtained from the research literature, and their analysis was based on achievable sum rates (bits/s/Hertz) of the SU systems and SNR (dB). The first sets of results shown in Table 4 are for the achievable sum rates of the first paradigm. The sum rates for the leakage LIF algorithms are actually average values obtained from refs. [80; 81; 82; 83; 84; 85; 86; 87]. These results are strikingly similar despite the fact that the work in refs. [80; 81; 82; 83] assume perfect CSI while refs. [82; 83] take CSI estimation errors into consideration. This is an indication that LIF, is still very much a mitigating factor to achievable sum rates in the first paradigm, and as will be shown later, in the second paradigm as well. Even though not reflected in Table 4, the values for sum rates when symbol extensions [93; 97] are used are much higher than the other techniques. It should be noted that for ease of simplicity and analysis, this work only considered results with the minimal number of antennas at the PU and SU as well as the minimum DoF. Obviously, the higher the number of antennas, the higher the DoF and therefore the higher the achievable sum rates. Thus from the comparison of results in Table 4 and Figure 6, the enhanced algorithms associated with the LIF technique perform better than the others enhancements, despite its effects on achievable sum rates. Table 5 considers the IA sum rate values for the second paradigm with SWF for the single SU scenario. Even though the sum rate results from the work in ref. [24] are quite low, they do provide the basis for this paradigm and shows just how critical it is to not only identify TOs, but useable TOs for the system model to work. Thus, a lot depends on the methods adopted for optimizing the SU transmission rates. Of all the results obtained, the work in ref. [115] that makes use of an intermediate relay was shown in Figure 7, to achieve maximum sum rates, thus corroborating the benefit of incorporating relays in wireless systems [74]. The work done on symbol extensions was a stark contrast to the first paradigm because of the sum rates achieved. The use of symbol extensions did not produce greater performance as it did with the first paradigm even though it had slightly marginal performance than ref. [24]. This could be attributed to the fact that the power allocation method used for optimizing the SUs transmission is similar to ref. [24], which has been established to be sub-optimal. Whilst the LIF technique was shown to have greater performance to other IA techniques in the first paradigm, it did not have quite the same effect in the second paradigm as seen in Figure 8. This is due to the fact that the PU transmission is completely orthogonal to that of the SU, making the effects of LIF very minimal. It could be argued that the results comparison for LIF was similar across both paradigms, implying that however minimal, interference plays a significant role in wireless communications. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Average Sum Rates of the SU Network Based on the IA Techniques (bits/s/Hertz)**} \\ \hline
**SNR \(\lambda\) (dB)** & **Leakage of Interference**[80; 81; 82; 83; 84; 85; 86; 87] & **OFDM**[99; 100; 101] & **Other Endeavours**[103; 104; 105] \\ \hline
5 & 5.5 & 9.0 & 1.0 \\
10 & 11.0 & 10.0 & 5.0 \\
15 & 15.0 & 11.0 & 9.5 \\
20 & 20.0 & 12.0 & 16.0 \\
25 & 28.0 & 13.0 & 24.0 \\
30 & 32.5 & 23.0 & 33.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average sum rates against typical signal-to-noise ratio (SNR) values for the first paradigm [80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101; 103; 104; 105]. Figure 6: Average sum rates against typical SNR values for the first paradigm [80; 81; 82; 83; 84; 85; 86; 87; 89; 99; 100; 101; 103; 104; 105]. Table 6 considers sum rate values for the second paradigm with SWF, for the multiple SU MIMO link.