# Uplink Transmit Power Control for Single-Carrier Grouped FDMA with Iterative Multiuser Detection
## 4 Simulation Results and Discussion
### Spectral Efficiency Enhancement  
The previously proposed power control method for SC-GFDMA [7] achieves 7% higher spectral efficiency than that achieved by the conventional SC-GFDMA without power control (Figure 7) at \(\sigma_{N}^{2}=-10\) dBm. However, it is still considerably lower than the spectral efficiency achieved with the optimal transmit powers of the users determined based on an exhaustive method; this exhaustive method is only possible in simulations and is infeasible to implement in practical systems. In contrast, the proposed power control method provides near-optimal spectral efficiency. In simulations for Figure 7, the number of total users is fixed to 5 and pathloss is not applied to compare the proposed algorithm with the method proposed in [7]. The spectral efficiencies achieved by the proposed power control scheme are close to those achieved using exhaustively chosen optimal power allocations (Figures 8 and 9), regardless of the MCS. The spectral efficiencies of the proposed scheme are considerably higher than that of the conventional scheme without power control (\(P_{u,m}=1\)). The maximum spectral efficiency with QPSK-3/4 is 12; the proposed scheme achieves the maximum at \(\sigma_{N}^{2}<-50\) dBm (Figure 8). The spectral efficiencies of the proposed scheme with 16 QAM-1/2 become saturated at 15.87 when \(\sigma_{N}^{2}<-100\) dBm (99.2% of the maximum spectral efficiency of 16 is achieved) (Figure 9). That is, the proposed algorithm can exploit  
Figure 6: RMSE of \(\mu_{u_{1},m}\) at \(i=1\), caused by the approximation (25). Figure 7: Spectral efficiencies for QPSK-1/2 versus noise power; \(U=5\) and \(L_{u}=1,\forall u\). the benefits of high-order MCS efficiently; furthermore, it consumes less power than the conventional method without power control. In Figures 10 and 11, the spectral efficiencies obtained using the proposed power control algorithm are simulated with multiple values of \(\gamma\) including \(\gamma=\gamma_{sol}\). When \(\gamma\leq\gamma_{sol}\), the criterion (47) is not satisfied (see Figures 4 and 5); hence, the spectral efficiency is relatively low and becomes saturated when the noise power is relatively low. That is, the remaining interference from \(u_{k}\) can affect the signal detection of other users at \(i\geq k+2\), for some \(k\), and can thus degrade the spectral efficiency. When \(\gamma\geq\gamma_{sol}\), the maximum spectral efficiency is achieved, because (47) is still satisfied (Figures 4 and 5), but it is slightly lower at some noise power level, compared with the case using \(\gamma=\gamma_{sol}\); moreover, the use of \(\gamma\) larger than \(\gamma_{sol}\) results in the consumption of more transmit power. In both figures, the proposed power control algorithm increases the spectral efficiency regardless of the specific value of \(\gamma\). These results demonstrate the robustness of the proposed power control criterion analyzed in the previous section and also the importance of using an appropriate power control algorithm in the SC-GFDMA structure. Figure 8: Spectral efficiency for QPSK-3/4 versus noise power. Figure 9: Spectral efficiency for 16 QAM-1/2 versus noise power. Figure 12 depicts the spectral efficiency obtained using 64 QAM with 2/3 code rate, which demonstrates that the proposed power control also provides significant gain for high-order modulations. As seen in Figures 10 and 11, spectral efficiency increases as \(\gamma\) increases, and the amount of increase saturates as \(\gamma\) approaches the optimal value. Because the maximum spectral efficiency available by using MCS 64 QAM-2/3 with 8 users is \(32=4\times 8\), the proposed method achieves 68.7% of the maximum value, where the maximum is achieved only when all 8 users perfectly share each chunk, with the BER being less than the threshold. That is, the proposed method can schedule approximately 5.5 users on average in each chunk. This implies that the average number of users that can share each chunk while satisfying the QoS constraint decreases as the MCS level increases.