# A Biologically-Inspired Power Control Algorithm for Energy-Efficient Cellular Networks
## 6 Results and Discussion  
Table 1 summarizes the simulation parameters used in our study. We consider a hexagonal multi-cell layout where the distance between adjacent BSs is 500 m and an MS is positioned randomly in each cell. Considering a multi-tier cell structure, the number of BSs varies up to 20. The maximum transmit power, the path loss and fading models and the noise figure are all based on the 3 GPPevaluation methodology [36]. We also set the required SINR to 0 dB, which is generally used as the threshold to decode the received signal in cellular networks. We assume that there is no error or delay in overhearing the rate information from the neighbor BSs. We perform a Monte Carlo simulation 10,000 times using MATLAB. For comparison, we also consider a scheme using maximum equal power without TPC and the SINR-based TPC algorithm with several target SINR values, in which each BS controls its transmission power in order that the received SINR satisfies a given target SINR [12; 13; 14]. Figure 3 shows the received signal strength (RSS) in a two-dimensional plane when the maximum equal power allocation and the proposed TPC algorithm are used in a seven-cell topology. Here, the black points in cells indicate the position of the MSs using the same channel. The transmit power of each BS and the rate of each MS are displayed in each cell. The maximum equal power allocation scheme shows a uniform RSS distribution and a variety of different rates, but the proposed TPC algorithm shows a dynamic RSS distribution (_i.e._, different transmit powers) and the same rate across all of the cells. It is notable that in this example, the proposed TPC algorithm increases the minimum \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Cell layout & Hexagonal, one sector per cell \\ Number of BSs & 3\(\sim\)20 \\ Inter-BS distance & 500 m \\ MS layout & Uniform in hexagonal cell \\ Maximum BS transmit power & 46 dBm \\ Distance-dependent path loss & 128.1 + 37.6 log\({}_{10}\)\(R\) (dB), \(R\) in km \\ Shadowing model & Log-normal with standard deviation of 8 dB \\ Fast fading model & Rayleigh \\ Noise figure & 9 dB \\ Channel bandwidth allocated to an MS & 100 kHz \\ Required SINR (\(\gamma_{req}\)) & 0 dB \\ Coupling strength (\(\lambda\)) & 1 \\ Overhearing range (\(r\)) & 500\(\sim\)900 m \\ Threshold for convergence check (\(\epsilon\)) & 10\({}^{-4}\) \\ Simulation trials & 10,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setup. MS, mobile station. MS rate from 1.58 to 3.47 \(\mathrm{b/s/Hz}\), while using 5.29 dB less transmit power compared to the maximum equal power allocation. Figure 4 shows the rate of each MS and the transmit power of each BS according to the iteration of the proposed algorithm in the same seven-cell topology as in Figure 3. As the iteration proceeds, all of the MS rates converge to the same value, and the maximum difference of transmit powers of the BSs is uniformly bounded. These results can be expressed as \(\lim_{t\rightarrow\infty}|R_{i}(t)-R_{j}(t)|=0\) for \(\forall i\
eq j\) and \(\sup_{0\leq t<\infty}|P_{i}(t)-P_{j}(t)|<P_{max}\) for \(\forall i\
eq j\), which correspond to the convergence properties of the flocking algorithm shown in Equations (6) and (7), respectively. Upon convergence, the MS that had the best rate initially (_i.e._, MS 2) makes its serving BS 2 use the lowest transmit power, but the MS that had the worst rate initially (_i.e._, MS 6) lets its serving BS 6 maintain the maximum transmit power. In other words, MSs with a good link quality reduce the transmit power of their serving BSs, while MSs with a poor link quality maintain or slightly reduce the transmit power of their serving BSs in order to equalize the rates of all of the MSs. Thanks to the altruistic nature of this arrangement, the final transmit power is inversely proportional to the initial rate of the MS.  
Figure 3: Distribution of received signal strength in two dimensions: (**a**) maximum equal power allocation; and (**b**) proposed TPC algorithm.