# A Biologically-Inspired Power Control Algorithm for Energy-Efficient Cellular Networks
## 4 Proposed Bio-Inspired Transmit Power Control Algorithm  
Both the considered TPC algorithm and the flocking behavior described above allow the pursuit of the same objective of the _max-min_type in an interactive environment. Just as a flock of birds aims to maximize the minimum bird speed in an aerodynamic interactive environment, our proposed TPC algorithm is designed to maximize the minimum rate of the MSs in an inter-cell interference environment. Therefore, the proposed TPC algorithm controls the transmit power of each BS in such a way as to equalize the rates of all of the MSs (_i.e._, \(R_{i}=R_{j},\forall i,j\)). Because the rate of MS \(i\) (\(R_{i}\)) is related to the transmit powers of all of the other BSs (\(P_{j}\), \(\forall j\
eq i\)), as well as to the transmit power of its serving BS \(i\) (\(P_{i}\)), controlling the transmit power of one BS influences the rates of all of the other MSs; an iteration is therefore required to obtain the final equal rate value just as in the flocking algorithm. At each step, each MS recognizes the rate information of the other MSs from its neighboring BSs and sets its next target rate to the average of the the recognized rate values, just as each bird in a flock adjusts its velocity to the average velocity of its neighbors. Following the feedback of this target rate from the MS to its serving BS, the BS determines its transmit power to achieve the target rate individually. This distributed local rate-average operation is repeated until the target rate does not change any more (_i.e._, until all of the MS rates converge to the same value). Figure 2 shows the flow chart of the proposed TPC algorithm. Its operational procedure follows these steps:  
1. The serving BS \(i\) sets the transmit power to the maximum value \(P_{max}\) at the initial time. 2. BS \(i\) sends the data packet to its MS \(i\) using the transmit power \(P_{i}(t)\) determined for time \(t\). 3. On receiving the packet, MS \(i\) measures its SINR \(\gamma_{i}\). 4. MS \(i\) calculates its current rate as \(R_{i}(t)=\log_{2}(1+\gamma_{i}(t))\). 5. MS \(i\) overhears the rate information \(R_{j}(t)\) of the adjacent MS \(j\) from its neighboring BSs \(j\
eq i\) (generally, in cellular systems, the rate value is mapped to one of the modulation and coding sets (MCS), and the MCS value corresponding to the data channel is broadcast through a common control channel [31]; because this broadcast common control channel is modulated by the most robust MCS level, the MS can overhear it after just synchronization to the adjacent cell and then discover the rate information of the corresponding data channel [32]; moreover, it is worth noting that the direct wired communication among BSs is also possible for sharing the rate information, instead of the overhearing technique). 6. The MS \(i\) calculates the next target rate \(R_{i}(t+1)\) as: \[R_{i}(t+1)-R_{i}(t)=\frac{\lambda}{N}\sum_{j=1}^{N}\psi(|x_{j}-x_{i}|)\left(R _{j}(t)-R_{i}(t)\right)\] (8) which follows the same form as Equation (5) (note that Equations (5) and (8) have a similar form to one of the consensus protocols, so they can also be interpreted as the decentralized consensus protocol [33]). The only difference is that the velocity of bird \(v\) is replaced by the rate of MS \(R\). Similarly, \(\psi(|x_{j}-x_{i}|)\) is the communication range function where \(x_{j}\) and \(x_{i}\) are the positions of BS \(j\) and MS \(i\), respectively. Here, we assume that \(\psi(|x_{j}-x_{i}|)=1\) if the physical distance between two stations is less than the overhearing range \(r\), _i.e._, \(|x_{j}-x_{i}|\leq r\). Otherwise, \(\psi(|x_{k}-x_{i}|)=0\). If we choose \(\lambda=1\), then Equation (8) is re-expressed as: \[R_{i}(t+1)=\frac{1}{|N_{i}|}\sum_{j\in N_{i}}R_{j}(t)\] (9) where \(N_{i}\) is the set of neighboring BSs overheard by MS \(i\) and \(|\cdot|\) is the cardinality of a set. Clearly, this is a distributed local averaging algorithm for the rates of the MSs. 7.