Autocorrelation Peak Sidelobe Levels

The autocorrelation function serves as a critical tool in signal processing for measuring similarity between a signal and its time-shifted version. In radar, sonar, and similar applications, the autocorrelation properties directly impact detection performance. An ideal signal should exhibit a sharp main lobe and minimal sidelobe levels to reduce false detections.

Calculating Peak Autocorrelation Sidelobe Level (PASLR) typically involves these computational steps: First, compute the cross-correlation between the signal and its delayed copy. Then identify the main lobe peak (correlation value at zero delay) and the highest sidelobe magnitude. Finally, express the ratio of the highest sidelobe to the main lobe peak in decibels (dB) as the sidelobe level metric. In MATLAB implementation, this can be achieved using the xcorr function for correlation computation followed by peak detection algorithms to locate main and sidelobe peaks.

Different sequence designs exhibit distinct autocorrelation and cross-correlation characteristics: CE Sequences: Commonly used in communication systems, these sequences demonstrate balanced autocorrelation sidelobe performance with efficient FPGA implementation due to their periodic structure. Frank Sequences: As polyphase coded signals, they feature low sidelobe levels in autocorrelation functions, making them suitable for high-resolution radar systems. Their implementation involves phase rotation operations that can be optimized using lookup tables. P4 Sequences: An enhanced version similar to Frank sequences, P4 sequences achieve further sidelobe reduction through optimized phase coding, improving detection reliability. The phase optimization typically follows quadratic phase progression formulas that can be programmed using recursive algorithms.

Additionally, cross-correlation analysis studies interference between different signals. Sequences with low cross-correlation properties are particularly valuable in multi-user or multi-target scenarios. Through careful sequence selection and coding optimization, systems can significantly enhance anti-interference capability and detection accuracy. Code implementation often involves comparing multiple sequences using matrix-based correlation computations and evaluating performance metrics through statistical analysis.