Weak Linear Frequency Modulation Signal Detection Algorithm Based on Coprime Sampling

Weak linear frequency modulation (LFM) signal detection constitutes a critical challenge in radar and communication systems, where traditional detection methods exhibit significant performance degradation under extremely low signal-to-noise ratio (SNR) conditions. The coprime sampling-based detection algorithm provides a novel solution to this problem through advanced signal processing techniques.

The algorithm's core innovation lies in two key technologies: coprime sampling and segmented coherent accumulation with polynomial phase transform. In implementation, coprime sampling utilizes two sampling sequences with different rates (e.g., M and N where gcd(M,N)=1) to achieve an equivalent high sampling rate while avoiding spectral aliasing. Code implementation typically involves designing coprime sampling intervals and combining samples through mathematical operations like the Chinese Remainder Theorem.

The segmented coherent accumulation strategy divides the signal into multiple time segments, performing coherent processing within each segment to enhance SNR. Algorithmically, this involves windowing the signal and applying phase compensation before accumulation. The polynomial phase transform accurately estimates nonlinear phase characteristics through higher-order phase differentiation, which is crucial for LFM signal parameter extraction. This can be implemented using algorithms like the high-order ambiguity function (HAF) or cubic phase function (CPF).

The algorithm's advantages include: 1) Coprime sampling reduces hardware implementation complexity by allowing lower-rate analog-to-digital converters; 2) Segmented processing enhances weak signal detection capability through distributed SNR gain; 3) Polynomial phase transform ensures parameter estimation accuracy via higher-order moment calculations. These characteristics make it particularly suitable for weak signal detection scenarios in complex electromagnetic environments.

The algorithm's innovation combines coprime sampling theory with nonlinear signal processing techniques, providing an effective solution for signal detection under low-SNR conditions. Implementation typically involves MATLAB or Python coding with signal processing toolboxes for FFT operations, filter design, and parameter estimation routines. Its application prospects span multiple domains including radar target detection, communication signal reception, and electronic warfare systems.