# A Biologically-Inspired Power Control Algorithm for Energy-Efficient Cellular Networks
## 6 Results and Discussion
Figure 5 shows the number of iterations needed for convergence as functions of the number of BSs and the overhearing range (\(r\)). As the number of BSs increases, the number of iterations increases, because the amount of rate information to be considered in the algorithm increases. The MS can overhear the rate information only from those BSs located within the overhearing range. Therefore, the number of iterations increases as the overhearing range decreases, because less rate information is offered to the algorithm for averaging. Here, we assume that the algorithm has converged if the rate differences in time \(|R_{i}(t+1)-R_{i}(t)|\) are less than \(10^{-4}\) for \(\forall i\). However, this convergence condition is a tight one because in practical systems, the rate does not have a real value, but a discrete one, as one of the predetermined MCS levels. Thus, this convergence time can be decreased according to the granularity of the rate information. Figure 6 shows the performance of the minimum rate of the MSs _versus_ the number of BSs. As the number of BSs increases, the minimum rate in all of the schemes decreases exponentially because the increased number of BSs causes more inter-cell interferences. The proposed TPC algorithm outperforms the scheme using the maximum equal power without TPC and an SINR-based TPC algorithm with a target SINR (\(\theta\)) of 0, 3 or 10 dB. This is because the proposed TPC algorithm dynamically achieves an SINR value that maximizes the minimum rate regardless of the interference level, while the SINR-based TPC algorithm always tries to achieve a static target SINR. The SINR-based TPC algorithm shows that there exists a suitable target SINR according to the number of BSs (_i.e._, interference level). Figure 4: (**a**) Rate of MS; and (**b**) transmit power of BS _vs._ number of iterations. The maximum equal power scheme has the lowest minimum rate, because it does not adjust the transmit power in consideration of the inter-cell interference situation. Figure 7 shows the average transmission power at the BSs _versus_ the number of BSs. As the number of BSs increases, the inter-cell interference increases, and so, the proposed TPC algorithm reduces the transmission power more in order to reduce the interference to the MSs that receive the strong interference. In particular, the proposed TPC reduces the transmit power adaptively depending on the interference level; therefore, it exhibits a lower power consumption than the other schemes as the interference level increases. On the other hand, the SINR-based TPC algorithm consumes a higher transmission power at a high interference level and also shows that an appropriate target SINR value varies with the interference level. Figure 8 shows the outage probability _versus_ the number of BSs when the required SINR threshold \(\gamma_{req}\) is 0 dB. The SINR-based TPC with \(\theta\)= 0 dB has the lowest outage probability, because its target SINR is set equal to the required SINR threshold. Apart from this, the proposed TPC shows the lowest outage probability. This implies that the proposed TPC algorithm almost satisfies the target SINR in a  
Figure 5: Number of iterations _vs_. number of BSs and overhearing range (\(r\)). Figure 6: Minimum rate _vs_. number of BSs. way adaptive to the change in interference level, even though it uses significantly lower transmission power than the other schemes. On the other hand, the SINR-based TPC with a high target SINR and the maximum equal power scheme show a much higher outage probability, because they cause more severe interferences to MSs with low SINR. Figure 9 shows the energy efficiency _versus_ the number of BSs. The energy efficiency indicates the number of data bits transmitted without error per unit bandwidth and per unit energy; thus, it reflects the transmission rate, transmission power and outage probability.