## 7 Results and Discussions  
DS-PIM conventional SIM-OFDM exhibits good spectral efficiency for lower-order modulation of B2. However, for higher-order modulation, the bits which were transmitted through the subcarrier indices are not enough to compensate for the loss of subcarriers. Table 6 shows how the contribution of carrier bits increases vs. index bits. \begin{table}
\begin{tabular}{c c c} \hline \hline
1 & Modulation Technique for B1 & DS-PIM \\ \hline
2 & Modulation Technique for B2 & 4-QAM \\ \hline
3 & Active subcarriers per subgroup & 2 \\ \hline
4 & Channel & AWGN \\ \hline
5 & Sub-block sizes for conventional & 4.8 and 16 subcarriers \\ \hline
6 & Maximum Sub-block sizes for DS-PIM SIM-OFDM & 5.9 and 17 subcarriers \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters used for Matlab simulation. Figure 7: Simulation setup used to obtain SNR vs CNR curve. Figure 8 shows the comparison between conventional and DS-PIM-SIM OFDM for different sub-block sizes versus modulation level M of the modulation bit stream. In this case, the number of active subcarriers are 2 (K = 2). The results show that the proposed scheme gives a much superior bandwidth efficiency when compared with conventional SIM OFDM, for a given sub-block size. Smaller sub-blocks have been shown to have a much larger bandwidth efficiency. Figure 9 shows the effect of increasing the number of ON subcarriers on spectral efficiency for both conventional and DS-PIM. It can be shown from Figure 9 that the bandwidth efficiency improves when the number of ON subcarriers is higher. However, the difference between spectral efficiencies of DS-PIM and conventional SIM OFDM is much smaller, although the proposed scheme still has a noticeable edge over conventional approaches, for larger sub-block sizes. The performance of the proposed approach suffers when smaller sub-blocks are used in combination with a larger value of K. Using larger values of K for a small sub-block however, is not practical since it takes away from the basic advantage of SIM OFDM, which is to save power. Figures 8 and 9 are plotted using Equations (10) and (11). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**n = 4**} \\ \hline \multirow{2}{*}{**M**} & **Bits/s per** & **Number of** & **Number of** & **Potential Capacity** \\  & **Sub-Block** & **Index Bits (B1)** & **Modulation** & **Lost Due to off** \\  & **(B1+B2)** & **Index Bits (B2)** & **Subcarriers (bits/s)** \\ \hline
4 & 6 & 2 & 4 & 4 \\ \hline
8 & 8 & 2 & 6 & 6 \\ \hline
16 & 10 & 2 & 8 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Distribution of bits between B1 and B2. Figure 8: Spectral Efficiency versus modulation order, for conventional and DS-PIM-based SIM OFDM (index word lengths of 2-bits, 3-bits and 4-bits) where K = 2. The bandwidth efficiency drops with the increasing sub-block size, as the number of unused subcarriers becomes larger. However, even in case of large sub-blocks, the proposed scheme has a superior bandwidth efficiency due to its variable block size. Figure 10 shows a theoretical vs. simulated results for spectral efficiency of conventional and DS-PIM-SIM OFDM at k = 2 and n = 4. The results show good agreement between theoretical and simulated values. Figure 11 presents a comparison between conventional SIM OFDM and the proposed variant. For a small sub-block size of 4 subcarriers (5 for Proposed approach), the SER performance is quite similar for the two approaches. However, as the sub-block size increases, the conventional approach shows a slight improvement over the proposed approach. This is due to the fact that in DPIM, error is not restricted to one symbol. The effects of error spill over into the next symbol as well (wrong slot error). However, at higher values of CNR, the difference between conventional and proposed approaches again starts to decrease. As discussed in Section 5, this is due to the fact that wrong slot error becomes less likely at higher values of CNR.