The peak sidelobe distribution for binary codes

Low aperiodic-autocorrelation peak sidelobe levels (PSLs) relate to enhanced range resolution for binary-phase-coded radar and communication waveforms. Typical methods to identify the minimum-attainable PSL for a given code length N require exhaustive calculations whose computational burden grows exponentially with N. In this project, exact PSL histograms were determined for computationally practical lengths. These histograms may lead to ways to estimate PSL distributions for computationally impractical lengths. Plots of the lower four moments for N between 1 and 45 showed that the moments can be approximated closely by aN^k. Histograms for N = 45 were compared to a binomially-distributed PSL PDF model based on statistically independent sidelobes. The independent-sidelobe model agreed closely with truth for middle-to high-PSL values, and only varied significantly from truth for PSLs one or two units away from the lowest achievable PSL. Future work will examine ways to develop the PDF from the moments accurately enough to estimate minimum PSL for a given N, and ways to account for sidelobe dependence in the probabilistic model.