Analysis of the probability distribution of the baseline wander effect for baseband PAM transmission with application to gigabit Ethernet

Communication systems that employ baseband transmission (i.e. signal spectrum centered around 0 Hz) may suffer from the baseline wander (BLW) phenomenon. This phenomenon occurs when the signal has to pass through a highpass filter element in the transmission path (e.g. a transformer in the line interface). A long sequence of symbols with constant value should generate a signal with constant level, but the signal will decay towards zero due to the highpass element. An example of a communication standard where baseband transmission is used with a DC-coupled channel is Ethernet. It can be shown that for baseband pulse amplitude modulation (PAM), the baseline wander phenomenon increases the dynamic range of the signal by a factor of 2, in worst case. This increases the cost of the receiver (for example, another bit may be needed in the analog to digital converter). However, the signal will reach its extreme values with very low probability, so it seems wasteful to design for worst case. It may be more economical to design for a smaller dynamic range, but then there must be a way to understand the probability that the signal will exceed this range. This can be done by using the probability distribution of the signal in the presence of BLW, which is calculated approximately in this paper.