# Channel Characterization and SC-FDM Modulation for PLC in High-Voltage Power Lines
## 1 Introduction  
A power-line carrier (PLC) designates the technique employed to send communication signals through power transmission lines [1]. Its use dates back to the 1920s and it was the principal communication method used by power-supplying companies all over the world until the 1970s. Those PLC systems were based on analog techniques. By the 1980s, these were considered expensive and of a low communication capacity. Newer communication systems, such as fiber optics and ultrahigh frequency (UHF) and superhigh frequency (SHF) radio, took precedence among power companies.  
The renewed interest in the PLC systems started in the 1990s with the advent of newer digital communication methods that allowed for a substantial capacity increase in PLC channels. Digital PLC communication is, at present, a very active area of research and development. Nevertheless, the vast majority of studies in this field are devoted to low-voltage (LV) and medium-voltage (MV) power systems, and very little attention has been given to the high-voltage (HV) systems (i.e., above 100 kV). HV-PLC systems are attractive at present due to two factors. One is that, with de-regulation, power companies are also becoming providers of communication services. The other one is the introduction of smart-grid technologies into power systems, which rely considerably on communication systems.  
To adequately characterize the PLC channel, corona is considered the dominant noise present in the PLC system, as it is generated by the operation of the HV lines [2]. This noise varies in intensity, depending on the operating power-voltage and weather conditions as reported in a previous work [2]. The effects of an impulsive noise of a random nature and of a short duration due to the faulty, switching and lightning discharge in lines [3; 4] will not be analyzed in this work as they are not indispensable to the channel characterization in the operating conditions of a PLC system. The study of the effects on the performance of the proposed system in the presence of this noise is left for further work.  
Conventional PLC systems use the analog single-side band (SSB) modulation technique in combination with frequency-shift keying (FSK), with operating bandwidths of 4 kHz or multiples of 4 kHz, up to 16 kHz by using frequency-division multiplexing (FDM) for simultaneous transmission channels [1], achieving transmission speeds up to 64 kbps. Current HV-PLC systems provide data rates between 28 kbit/s and 100 kbit/s. The main reason for operating in such narrow bands is that the single-carrier modulation schemes being used are unable to counteract the distortion caused by a selective PLC channel [5; 6].  
A PLC channel can be considered time-invariant for long periods of time compared with the symbol time-duration. The invariability of time for PLC channels on HV lines encourages the use of new modulation schemes of multiple carriers (MC) and channel estimation methods to mitigate the effects of distortion caused by the channel, as these have been analyzed in recent works for low-voltage PLC systems [7; 8; 9; 10; 11; 12] and for wireless standards such as the 3 GPP long-term evolution (LTE) and IEEE 802.16e (WiMax).  
In this paper, we use modal analysis and nodal two-port **AB** matrices [13; 14] to characterize the frequency response of the PLC channel. The effects of wave reflections and of the limited bandwidth caused by the coupling configurations and the coupling equipment being used, which were not considered in previous works [5; 6], are included here. In order to evaluate the performance of PLC systems in higher bandwidths, we propose as a solution the use of the MC scheme OFDM (Orthogonal Frequency-Division Multiplexing) used to transmit on highly frequency-selective channels [15; 16; 17] at high transmission rates. The use of OFDM simplifies the processes of channel estimation and equalization on the receptor [15; 16; 17], resulting in an increased spectral efficiency of the assigned bandwidth.