The L1-norm of out-of-phase peaks of the aperiodic auto-correlation function of binary sequences

For the mean-square errors of the maximum-likelihood channel estimate, the noise enhancement factor of an aperiodic invertible sequence is an optimality criterion. Massey posed a question as to whether there exist binary sequences that achieve the absolute optimum for the sequence length N to infinity since then they would be preeminently eligible for channel estimation. However, the noise enhancement factor is extremely difficult to examine both analytically and numerically often making extensive investigations of sequences impossible. For this reason, it is convenient to consider the l1-norm of out-of-phase peaks of the aperiodic auto-correlation magnitude. In this paper, it is shown that the l1-norm can never have the required behaviour for solving Massey's problem in the case of binary sequences and that the best possible binary sequences in this connection are skew-symmetric Barker sequences. The paper is of interest in mobile radio channels' study.