On Aperiodic-Correlation Bounds

Abstract

We present a new derivation of a lower bound for an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">aperiodic</i> correlation metric: the integrated sidelobe level (ISL) of a set of sequences under the energy constraint. Sequences (or sequence sets) with low aperiodic correlations are widely demanded in many applications, including radar/sonar range compression, medical imaging, channel estimation and multi-user spread-spectrum communications. While the lower bound has been implicitly discussed in the literature before, here we adopt a different framework to derive the bound. In particular, we make use in the derivation of our recently proposed cyclic algorithm framework, which can also be used to efficiently synthesize unimodular sequences with low correlations. We also show that by relaxing the unimodular constraint, the ISL lower bound can be approached closely.