Merit Factor of Chu Sequences and Best Merit Factor of Polyphase Sequences

Chu sequences are a family of polyphase sequences that have perfect periodic autocorrelations and good aperiodic autocorrelations. It has previously been proved that the maximum offpeak (aperiodic) autocorrelation (in absolute value) of the Chu sequence of length n is asymptotically equal to 0.480261√n. It has also been empirically observed that the merit factor of Chu sequences appears to grow like a constant times √n. In this note, we provide an analytic proof that the merit factor of the Chu sequence of length n is bounded below by a constant multiple of √n for all n. To the author's knowledge, this is the first time a family of polyphase sequences of all lengths has been proved to have merit factor growing at least like order √n.