# Uplink Transmit Power Control for Single-Carrier Grouped FDMA with Iterative Multiuser Detection
## 4 Simulation Results and Discussion
### Computational Complexity  
The SC-GFDMA uses iterative detection to decouple signals from multiple users sharing the same chunk. This iterative approach requires additional computations to achieve a higher spectral efficiency. Thus, as discussed in Section 1, a commercial network operator should consider a trade-off between the additional complexity and the increase in spectral efficiency. In this section, to support such a decision, we provide some quantitative results on the computation complexity.  
As a measure of the computational complexity, we use the number of performing SNR-variance density evolutions per chunk during iterative detection. The primary purpose of the proposed method is to secure as many users as possible by properly adjusting the transmit powers of users. In this aspect, the proposed method may require more computations to secure more users. On the other hand, as discussed in Section 2.3 (Figure 2), the proposed power control method functions as a pre-scheduler by excluding inappropriate users before the scheduling. Since the number of candidates for scheduling is (appropriately) decreased, we can say that the proposed method also has an aspect that corresponds to the reduction in computational complexity. In summary, the proposed method does not always require more computational complexity than the conventional method without power control, and it depends on the systems parameters such as the number of users, SNR, the number of iterations, and the channel coefficients.  
Figure 15 compares the computation complexity simulated with and without the proposed power control. The proposed method generally had lower complexity than the conventional method without power control, except when \(U=16\). For both cases, the computation complexity depends on the number of iterations for the IMD. As the number of iterations decreases, both the computational complexity and the available spectral efficiency decrease with high probability. Thus, a network operator should find an appropriate number of iterations for commercial services. However, it is extremely difficult to explicitly find an optimal number as it depends on various system parameters. Instead, one may consider an algorithm that adaptively terminates the IMD at a certain point if no significant improvement is expected, such that the proposed method can reduce the computational complexity without much loss in the available spectral efficiency. For example, at each iteration \(i\), we may check the following criterion:  
\[\left|\sum_{k}\Gamma_{u_{k},m}^{(i)}-\sum_{k}\Gamma_{u_{k},m}^{(i-1)}\right|<\kappa, \tag{57}\]  
with a threshold \(\kappa\). The difference \(\left|\sum_{k}\Gamma_{u_{k},m}^{(i)}-\sum_{k}\Gamma_{u_{k},m}^{(i-1)}\right|\) measures the amount of increase in SINR between consecutive iterations. Thus, if this difference is very small, we may consider that no significant improvement will be expected in remaining iterations. In this context, the proposed method  
Figure 14: Transmit power of 16 QAM-1/2 versus noise power.  
terminates the IMD if this inequality is satisfied. This type of adaptive algorithm, with an appropriate value of \(\kappa\), can further decrease the complexity of the proposed scheme as demonstrated in Figure 15 (the dashed line with circle marker is the complexity obtained by applying this adaptive algorithm, with \(\kappa=0.01\), to the proposed method).