The dependence of the thumbtack shape of the auto-ambiguity of frequency-hop waveforms on the number of hops and time-bandwidth product

In this work we consider the impact of the number of hops of a frequency hopped code on the autocorrelation surfaces it produces. First, we review two common choices for the number of hops, namely the `Minimal Sidelobe Region´ (MSR) choice, and the `Nyquist´ choice. The MSR method ensures that peaks in the sidelobe region are small, while the Nyquist method exhibits much cleaner center region behavior. We then propose two new methods for choosing the length of the frequency hopped code. The first, named `Minimize Maximal Sidelobe´ (MMS), attempts to minimize sibelobes in both regions, and the second, `Minimize Maximum Peak Sidelobe´ (MMPS), focuses on center region behavior. We then compare the results to the two existing methods.