Ambiguity Function of Pseudo-Random Codes and Their Related Characteristics

Pseudo-random codes have wide applications in communication and radar systems, where their ambiguity function serves as a critical tool for evaluating signal performance. The ambiguity function simultaneously reflects a signal's time-delay and frequency-shift characteristics, making it an effective means for analyzing signal resolution capability and anti-jamming performance.

The ambiguity function of pseudo-random codes is primarily obtained by calculating their autocorrelation properties. Ideally, the autocorrelation function of pseudo-random codes should exhibit a sharp main lobe and uniformly low sidelobes. This characteristic provides the signal with excellent range resolution capability and resistance to multipath interference.

Implementing pseudo-random code ambiguity function simulations in MATLAB typically involves the following steps: First, generating pseudo-random sequences using common types such as m-sequences and Gold sequences. Then calculating the sequence's autocorrelation function, which can be achieved through circular shift correlation methods. Finally, obtaining the ambiguity function plot through two-dimensional Fourier transform to fully display the signal's joint time-frequency characteristics.

Feature analysis of the ambiguity function plot is crucial for simulations. The main lobe width reflects the signal's resolution capability, while the sidelobe level determines the system's anti-interference performance. By adjusting the generation parameters of pseudo-random codes, these characteristic indicators can be optimized.