Unknown Channels

Abstract

The statistical characterization of a channel is often not given. Rather, it must measured. In many cases, the measurement process results in an accurate model of the channel for all time. The results of the previous two chapters are useful for these cases. But if the channel’s statistical characterization varies with time in an unknown way, then a measurement at a given point in time may not describe the channel at other times. As an example of a channel that varies with time in an unknown way, suppose that one has a wireless link from portable computer to a network node fixed in the ceiling. One might send a message from the computer to the node, move the computer, send another message, move it again, etc. Because each position of the computer results in a new set of physical paths over which the signal travels, the channel varies with time. Because each message is only affected by one position of the computer, each message is effectively transmitted over a different channel. The transmitter has to send data reliably over a number of possible channels. We say in this case that the channel is unknown, because it is one of a set of possible channels. The channel that actually prevails is called the realized channel.