As a memory channel, power-line communication (PLC) channel can be modeled by the finite states Morkov model. The memory order in an finite states Morkov model is a key parameter, which is not solved in PLC systems yet. In the paper, the mutual information is used as a measure of the dependence between the different symbols, treated as the received scalar network analyzer, or amplitude of the current channel symbol or that of previous symbols. The joint distribution probabilities of the envelopes in PLC systems are computed based on the multi-path channel model, which is commonly used in PLC. With the first-order Markovian assumption, we confirm that given the information of the symbol immediately preceding the current one, any other previous symbol is independent of the current one in PLC systems. The field test is also performed to model the received OFDM signals with the help of autoregressive model. The results show that the firstorder autoregressive model is enough to model the fading channel in PLC systems, which means the amount of uncertainty remaining in the current symbol should be negligible, given the information corresponding to the immediately preceding one. POWERLINCE COMMUNICATIONS FIRST-ORDER MARKOV CHANNELS 1069 noisy communications channel, which isn't favorable for the high-frequency communications signal transmission with frequency ranging 0 -30 MHz [7].Because of its ubiquity of already existing electrical power delivery networks, PLC is susceptible to numerous appliances and power networks [8]. Several studies have shown that the PLC channel is impaired by different types of noise, which are mostly produced by the electrical appliances in the networks [9]. The isolator switching or breaker in the grids can cause impulse noise [10]: The broadcast transmitters operating at frequencies higher than a few hundred kilohertz, can ingress the narrow band noise, mostly amplitude modulated sinusoidal signals [11,12]; The switching actions of silicon-controlled rectifier diodes found in many electrical appliances, brush motors, dimmer switches, and industrial sources directly connected to the supply network can cause periodic impulsive noise synchronous to the mains frequency [13]; The switched-mode power supplies can result periodic impulsive noise asynchronous to the mains frequency, with a short duration, random occurrence, and a high-power spectral density [14]; Switching transients in the power network can cause asynchronous impulsive noise.Because the impulsive noise is actually produced by appliances in the power network, the powerline noise can also be regarded as a combined sum of the background noise and the impulsive noises from all nearby appliances [15]. In addition to the behaviors of appliances, channel characteristics between the noise sources and a receiver may vary synchronously to the mains voltage [16]. This channel fluctuation also causes the periodic features of the noise [17]. As a result, PLC channels can be seen as typical noisy channels.Like other noisy channels, the PLC chan...