Complementary sequences for ISI channel estimation

A merit factor based on the sequence autocorrelation function, whose minimization leads to the reduction in the Cramer-Rao lower bound (CRLB) for the variance of “two-sided” intersymbol interference (ISI) channel estimation is introduced. Pairs of binary pilot symbol sequences (a preamble and a postamble) for channel estimation are jointly designed to minimize this merit factor. Given that the number of channel taps is L and the length of a pilot symbol sequence is (N+L-1), where N⩾L, we distinguish between the case when N is even and the case when it is odd. For even N, we show that complementary sequences not only minimize the merit factor, but also the CRLB. For a subset of odd N we construct almost-complementary periodic sequence pairs that minimize the merit factor. The optimal pilot symbol block signaling requires alternating between two (in most cases) different binary sequences that form the merit-minimizing pair