Optimal placement of known symbols for slowly varying frequency-selective channels

The problem of placing known symbols in a data stream for a slowly varying frequency-selective channel is considered from an information-theoretic perspective. Given the amount of redundancy associated with known symbols, placement schemes that minimize the outage probability are derived by assuming that the transmitted codewords consist of packets that are constrained to have the same known symbol placement. Under the assumption that each known symbol cluster is at least as large as alpha >= 2L + 1 (where L is the channel order), we show that the optimal placement is obtained by arranging the known symbols into as many clusters as possible and placing them such that the unknown symbol blocks are as equal as possible. It is shown that the optimal placement of known symbol clusters does not depend on the probability density of the channel. Numerical examples are used to illustrate the ideas and potential gains of using optimal known symbol placement..