## 3 Chimera Algorithm  
One of the most significant shortcomings of PLC is the frequency response of the transmission channel, as it has an irregular gain diagram, with deep notches, and an irregular phase diagram. OFDM technology allows mitigation of such shortcomings [22]. As the charging stations served by one feeder share the same physical channel that connects them to the control node, each frequency band has to be assigned exclusively to one charging station. The optimization of the OFDM modulation should take into account the different frequency responses of all the channels. In this paper, an algorithm, called _Chimera_, has been proposed to optimize the allocation of sub-carriers to the nodes served by the same feeder. The output of the algorithm is a single frequency response (Chimera), obtained by combining the entire set of frequency responses of the charging stations. At the same time, the set of transmissions of all nodes is merged into a single bit stream, which is assumed to travel through the Chimera channel. The bit stream is first subdivided into frames of assigned numbers of bits, which have to be modulated. The frame, in turn, is subdivided into as many strings of bits (words) as the number of sub-carriers, and the length of each word is assigned according to the capacity of the sub-carrier where it will be loaded. Depending on the single capacity, a constellation, defined in the complex plane, is associated with each sub-carrier. Each point of the constellation is associated to a string of bits, so that each possible word can be transmitted by sending the coordinates of the corresponding point. Therefore, the length of each word, i.e., the number of bits, is equal to the base-2 logarithm of the number of points in the constellation. Having a constellation with many points favors the bit rate, but, at the same time, this reduces the margin among near points, which affects the \(BER\) of receiving data. In this paper, only a limited number of design parameters are considered, such as the transmission band and its subdivision into sub-carriers, the allocation of bits to each sub-carrier (bit loading) and the maximum power of transmission. Further design parameters, such as zero-padding, cyclic prefix, time guard, and so on [22; 23], have been considered here by assuming a proper margin for the duration of the single OFDM symbol. Let \(N\) be the number of nodes of the feeder that share the same transmission band, and \(K\) the number of sub-carriers in which the transmission band is subdivided. Each node is associated with a specific frequency response (see Figure 3). It is assumed that each node supplies \(V_{n}\) plugs, whose number can be different for different nodes. Moreover, it is assumed that the nodes communicate only with the central node, therefore, a number of frequency responses equal to the number of nodes have to be taken into account. The same subdivision in sub-bands is applied to all those frequency responses. The capacity \(C_{nk}\) of the \(k\)-\(th\) sub-carrier of the channel \(n\) is given by the formula of Shannon-Hartley [24], which depends on the bandwidth \(B\) and the signal-to-noise ratio (\(SNR\)):  
\[C_{nk}=B\cdot\log_{2}(1+SNR_{nk})\ [bit/s] \tag{1}\]  
The value in Equation (1) is the theoretical upper bound of \(BR\) in the sub-carrier, but a lower value of \(BR\) is assumed in order to maintain the \(BER\) within an acceptable threshold. The bandwidth is common to all the sub-carriers of all the frequency responses, therefore from here on we consider a normalized value of \(B\). The total capacity of \(n\)th channel, corresponding to a specific node, is given by the sum of the capacities of all sub-carriers:  
\[C_{n}=\sum\
olimits_{k=1}^{K}C_{nk} \tag{2}\]  
This expression can be calculated for each frequency response, and it assumes that all the sub-carriers are assigned to each node. An incidence matrix \(M_{NxK}\) is used to represent the assignment of sub-carriers to the single nodes.