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Nowadays, the demand for communication multi-carriers’ channels, where the sub-channels are made mutually independent by using orthogonal frequency division multiplexing (OFDM), is widespread both for wireless and wired communication systems. Even if OFDM is a spectrally efficient modulation scheme, due to the allowed number of subcarriers, high data rate, and good coverage, the transmitted signal can present high peak values in the time domain, due to inverse fast Fourier transform operations. This gives rise to high peak-to-average power ratio (PAPR) with respect to single carrier systems. These peaks can saturate the transmitting amplifiers, modifying the shape of the OFDM symbol and affecting its information content, and they give rise to electromagnetic compatibility issues for the surrounding electric devices. In this paper, a closed form PAPR reduction algorithm is proposed, which belongs to selected mapping (SLM) methods. These methods consist in shifting the phases of the components to minimize the amplitude of the peaks. The determination of the optimal set of phase shifts is a very complex problem; therefore, the SLM approaches proposed in literature all resort to iterative algorithms. Moreover, as this calculation must be performed online, both the computational cost and the effect on the bit rate (BR) cannot be established a priori. The proposed analytic algorithm finds the optimal phase shifts of an approximated formulation of the PAPR. Simulation results outperform unprocessed conventional OFDM transmission by several dBs. Moreover, the complementary cumulative distribution function (CCDF) shows that, in most of the packets, the proposed algorithm reduces the PAPR if compared with randomly selected phase shifts. For example, with a number of shifted phases U=8, the CCFD curves corresponding to the analytical and random methods intersect at a probability value equal to 10−2, which means that in 99% of cases the former method reduces the PAPR more than the latter one. This is also confirmed by the value of the gain, which, at the same number of shifted phases and at the probability value equal to 10−1, changes from 2.09 dB for the analytical to 1.68 dB for the random SLM.

In this paper, a procedure is proposed to design a power line communication (PLC) system to perform the digital transmission in a distributed energy storage system consisting of fleets of electric cars. PLC uses existing power cables or wires as data communication multicarrier channels. For each vehicle, the information to be transmitted can be, for example: the models of the batteries, the level of the charge state, and the schedule of charging/discharging. Orthogonal frequency division multiplexing modulation (OFDM) is used for the bit loading, whose parameters are optimized to find the best compromise between the communication conflicting objectives of minimizing the signal power, maximizing the bit rate, and minimizing the bit error rate. The off-line design is modeled as a multi-objective optimization problem, whose solution supplies a set of Pareto optimal solutions. At the same time, as many charging stations share part of the transmission line, the optimization problem includes also the assignment of the sub-carriers to the single charging stations. Each connection between the control node and a charging station has its own frequency response and is affected by a noise spectrum. In this paper, a procedure is presented, called Chimera, which allows one to solve the multi-objective optimization problem with respect to a unique frequency response, representing the whole set of lines connecting each charging station with the central node. Among the provided Pareto solutions, the designer will make the final decision based on the control system requirements and/or the hardware constraints.